# Why would a tidally-locked rocky planet have a first-order spherical harmonic surface temperature distribution?

The new Letter to Nature Absence of a thick atmosphere on the terrestrial exoplanet LHS 3844b (also ArXiv) analyzes the thermal infrared light curve from the system (about 4.5 to 5.5 um). The planet is assumed to be tidally locked, so lack of asymmetry in the curve is cited as evidence that there is not thermal inertia due to a thick atmosphere, which is what one would expect for this planet.

In the beginning of the paper the authors say:

We fit the extracted light curve with a simultaneous model of the astrophysical signal and the instrument behavior. The astrophysical signal consisted of a transit model and a first-degree spherical harmonics temperature map to represent the planet's thermal phase variation.

and later:

In addition to the spherical harmonics model, we also tested a sinusoid model, which has been commonly used to fit other phase curve data.

I am thinking that the incident flux at a given point on the tidally-locked planet would be

$$I sim max (0, cos( heta))$$

where $$heta$$ is the static zenith angle at a given point, and so the temperature would be something like

$$T sim I^{1/4} sim max (0, cos( heta))^{1/4}.$$

Why do they use a first-order spherical harmonic model instead? Is it related to the thermal conductivity of rock?

It probably wouldn't. But when studying these things, you don't want to go in assuming you know more than you do or you might bias the analysis.

I am thinking that the incident flux at a given point on the tidally-locked planet would be

$$I∼max(0,cos( heta))$$

where θ is the static zenith angle at a given point, and so the temperature would be something like

$$T∼I^{1/4}∼max(0,cos( heta))^{1/4}.$$

Unfortunately this assumes that the planet is a blackbody with zero heat redistribution over the surface, e.g. by winds or currents in a magma ocean, and no sources of heat on the nightside such as tidally-driven hyperactive volcanism which is something you certainly do not know starting out.

Spherical harmonics are a generic set of basis functions over a sphere, so it does make sense as a fit which does not assume any physical processes operating or their relative importance. In fact, this is noted in Louden & Kreidberg (2018) "SPIDERMAN: an open-source code to model phase curves and secondary eclipses" (reference 15), which is referenced when they talk about using a spherical harmonic model. Conveniently, the paper shares the lead author with the LHS 3844 b paper, so presumably this does reflect some of the thought that went into the LHS 3844 analysis. A relevant quote from that paper:

A useful and physics-independent model is a sum of spherical harmonics. This method was used for the case of the phase curve of HD 189733b by Majeau et al. (2012). An example map generated by SPIDERMAN is displayed in Figure 4. The main observational features of a phase curve, including the offset hotspot, can typically be recovered with a only the first spherical harmonic, with the centre offset from the substellar point. (Cowan et al. 2017) explore the effects of odd harmonics in phase curve data, and find that these can correspond to weather features in the planet atmosphere.

(emphasis mine)

Kreidberg et al. (2019) do note that a simple sinusoidal fit produces unphysical negative temperatures on the nightside which can be corrected using odd harmonics, hence their choice of the first-order model.

Physics-based models probably would start to introduce a whole bunch of poorly-constrained parameters, probably overkill for the first analysis: this is mapping the terrain, figuring out how the terrain ended up like that is another stage entirely. This is a Nature paper, so brevity is par for the course.

## Gliese 581c

Gliese 581c / ˈ ɡ l iː z ə / (Gl 581c or GJ 581c) is a planet orbiting within the Gliese 581 system. It is the second planet discovered in the system and the third in order from the star. With a mass at least 5.5 times that of the Earth, it is classified as a super-Earth (a category of planets with masses greater than Earth's up to 10 Earth masses).

Gliese 581c gained interest from astronomers because it was reported to be the first potentially Earth-like planet in the habitable zone of its star, with a temperature right for liquid water on its surface, and by extension, potentially capable of supporting extremophile forms of Earth-like life. However, further research casts doubt upon the planet's habitability. It is tidally locked (always presents the same face to the object it is orbiting) so if life had a chance to emerge, the best hope of survival would be in the "terminator zone".

In astronomical terms, the Gliese 581 system is relatively close to Earth, at 20.37 light-years (192 trillion km or 119 trillion miles) in the direction of the constellation of Libra. This distance, along with the declination and right ascension coordinates, give its exact location in the Milky Way.

## Tidally locked planet - is Goldilocks zone wider?

Okay, so planets in the habitable zone are pretty far from the star to get tidally locked any time soon. But assuming such a thing would exist - wouldn't the habitable zone be slightly wider for a locked planet?

E.g., imagine it's pretty far from the star, far enough that only an Antarctica-sized area under the hot spot contains liquid water the planet is frozen solid everywhere else. This seems like it's outside of the habitable zone for a rapid-spinning planet (which might be too cold everywhere on its surface).

Or, similarly, if it's too close to the star so that the entire surface is a hot steamy inferno - except for the cold spot which may contain a decent area of livable temperatures. A rapid-spinning planet like the Earth, on the same orbit, would be too hot everywhere.

### #3 llanitedave

My intuition, which also may be wrong, is that having a hot side and a cold side would act as a filter for volatiles, including water and atmosphere. Water evaporating off the hot side would make its way to the cold side of the planet, where it would freeze out onto the surface. You'd have a big low pressure system under the hot spot, which would send air and moisture rising and then spreading out toward the other hemisphere. On the dark, cold side you'd have high pressure as the cooling air sinks back to the surface, wringing out whatever moisture it was carrying. That air would flow back over the surface, sending cold, dry winds back towards the lit side. In that scenario, any volatiles would rapidly be depleted from the hot side, and you'd end up with no area that's truly habitable. Even zones with the right temperature would have no remaining moisture.

Whether the same process would act progressively on CO2, Methane, and then the atmospheric gases themselves, I don't know.

### #4 Jason H.

Hi,
Here's a link that might be of interest

Also, there's been work on atmospheric transport in tidally locked systems. Distance, eccentricity and the presence of other system bodies of course are major factors, but the mix of greenhouse and inert gases is also of great import (look at Venus, rotates like it's virtually tidally locked, and it's far side without atmosphere would be incredibly cold, but obviously the CO2 hasn't frozen out on the far side i.e. greenhouse gases are big fudge factors.)

On a different note, last year I attended the SETIcon conf. in California, and the "habitable zone" subject came up in several sessions, but the one that stuck in my head was by Frank Drake (of Drake Equation fame.) He said of habitable zones, that he finds them very speculative, because life is very adaptive (and I wrote down the following quote at the time)

“I always have my doubts as to how seriously we should take these things.”

Indeed, when one considers extremophiles on Earth, the range of temperatures and pressures that can be endured by some is amazing, the one that I think is way up there on the macro side is Tardigrade

It may be interesting to note an imminent space mission that will be transporting Earth's toughest extremophiles to Phobos (and there is some controversy around it.) I put the link to it here

though just to show what some people have selected as being our toughest most-spaceworthy extremophiles.

If ice moons like Enceladus can have liquid oceans existing way out beyond the "Goldilocks zone" spraying water ice into space, aside from being a possible ecosystem environment down below, I could see a potential launch/transport mechanism for spores or organisms that employ cryptobiosis (or cryostasis if you like), organisms like Tardigrades, first born from deep within, but transported all the way to other moons (why not, Enceladus ice makes it all the way to Saturn's rings).

If Enceladus-like moons are throughout the cosmos, spewing their (hypothetical and speculative on my part) life payloads into space, including spraying their inner-stuff onto those billions of moon and planet-sized objects that undoubtedly have been tossed from their original star systems (but generate their own internal heat, causing subduction that could eventually bring those spores/cryptobionts down to a liquid environment again), would there even be such a thing as a "Goldilocks zone"?

### #5 FlorinAndrei

any volatiles would rapidly be depleted from the hot side, and you'd end up with no area that's truly habitable. Even zones with the right temperature would have no remaining moisture.

I thought a lot about that, it's an idea that readily presents itself when you start thinking about tidal locking.

However, the atmosphere (and hydrosphere, if any) would act like a gigantic thermodynamic machine, powered by the star and the cold spot. There would be permanent winds exchanging stuff between hot and cold poles. Keep in mind, even ice has some vapor pressure. Also, some (possibly lots of) heat would be transported by the perma-toroidal wind system towards the cold pole. Moving along these lines, you end up with what Jason said:

look at Venus, rotates like it's virtually tidally locked, and it's far side without atmosphere would be incredibly cold, but obviously the CO2 hasn't frozen out on the far side i.e. greenhouse gases are big fudge factors

But I admit, it's hard to decide between the alternatives, just based on intuition. I suspect a lot of number crunching might help.

The wikipedia link on red dwarf systems is very interesting.

If Enceladus-like moons are throughout the cosmos, spewing their (hypothetical and speculative on my part) life payloads into space, including spraying their inner-stuff onto those billions of moon and planet-sized objects that undoubtedly have been tossed from their original star systems (but generate their own internal heat, causing subduction that could eventually bring those spores/cryptobionts down to a liquid environment again), would there even be such a thing as a "Goldilocks zone"?

### #6 llanitedave

any volatiles would rapidly be depleted from the hot side, and you'd end up with no area that's truly habitable. Even zones with the right temperature would have no remaining moisture.

I thought a lot about that, it's an idea that readily presents itself when you start thinking about tidal locking.

However, the atmosphere (and hydrosphere, if any) would act like a gigantic thermodynamic machine, powered by the star and the cold spot. There would be permanent winds exchanging stuff between hot and cold poles. Keep in mind, even ice has some vapor pressure. Also, some (possibly lots of) heat would be transported by the perma-toroidal wind system towards the cold pole. Moving along these lines, you end up with what Jason said:

look at Venus, rotates like it's virtually tidally locked, and it's far side without atmosphere would be incredibly cold, but obviously the CO2 hasn't frozen out on the far side i.e. greenhouse gases are big fudge factors

Yes, intuition is probably a pretty poor guide when trying to figure out what's going on in planetary atmospheres. But I wouldn't call Venus anywhere near "virtually tidally locked". Even a slow rotation rate, especially with an atmosphere that dense, can help keep the heat distributed. But I can think of a lot of ways a system of volatiles can work around the boiling/freezing dichotomy, through tectonics, internal heating, orbital ellipticity, atmospheric density, and probably a few things I haven't thought of.

The wikipedia link on red dwarf systems is very interesting.

If Enceladus-like moons are throughout the cosmos, spewing their (hypothetical and speculative on my part) life payloads into space, including spraying their inner-stuff onto those billions of moon and planet-sized objects that undoubtedly have been tossed from their original star systems (but generate their own internal heat, causing subduction that could eventually bring those spores/cryptobionts down to a liquid environment again), would there even be such a thing as a "Goldilocks zone"?

Well, Goldilocks was a humanoid, after all.

### #7 FlorinAndrei

Well, I guess we'll know for sure when we get out of the "cradle" and start exploring.

Note to my descendants: if you're reading this and are in possession of the time machine, please let me know what the results are. Also, I'm so jealous of you.

### #8 dickbill

Depends on how the moon was formed. If it was formed by a Mars-sized impactor, then even if the earth was tidally locked before impact, it wouldn't have been after impact.

And once you have the moon, its tidal influence greatly outweighs the sun's, so if earth is going to be tidally locked to anything, it will be to the moon, not the sun.

So, in generaly, I think the answer that if a planet has a single large moon, it is unlikely to become tidally locked to its star. If it has multiple moons, it's unlikely to become tidally locked to any single one of them (too many different tidal influences for any single one to dominate stably). In order to become tidally locked to the star, I think a planet would have to have either no moons, or ones that were very small compared to the planet so their tidal influence is negligible compared to the star's.

### #11 llanitedave

I wonder, though, that if a planet is close enough to its star to become tidally locked (at least in a time frame that's significant for life's development), could it even retain hold on a moon? A collision similar to the one that created the Moon, if the Earth was three times closer to the Sun than it is now, may not have allowed a moon to form from the debris at all, or may have eventually pulled the Moon out of orbit entirely.

There may be a reason why Venus and Mercury don't have moons of their own.

### #15 llanitedave

One possibility is that a planet without a large moon might be rotating faster -- the Moon has acted as a brake on Earth's rotation over time -- and the tides, even if lower, would have been more frequent. It might have evened out.

Anyway, you don't really need regular tides as long as you have occasional storms to whip things up and mix them about.

### #16 FlorinAndrei

Anyway, you don't really need regular tides as long as you have occasional storms to whip things up and mix them about.

### #17 dickbill

I think the hypothesis about the tides is that when the moon was first formed, it was orbiting much closer (and faster). This created very large tides - as in high tides that were hundreds of feet higher than low tide, causing massive, violent water movement across the rocks. The idea is that this broke up rocks by erosion, and dissolved salts into the water, producing the salty sea water where life evolved.

The hypothesis is that without that harsh tidal action, the water would have stayed relatively pure, and not contained the salts that were necessary for life to evolve.

### #19 llanitedave

While I understand the logic of the argument, I'm not convinced of it's exclusive necessity. Salts are by definition water soluble and it doesn't require tsunamis to liberate them. In addition, a moonless Earth, spinning faster, would have had an enhanced coriolis effect, which I gather would have led to some incredibly intense storms. Plenty of sloshing. Also, more internal heating would have meant more volcanism, more rapid emplacement of volatiles into the water by eruption, as well as more frequent earthquakes, and probably actual tsunamis. More carbon dioxide and methane in the air would have meant a larger greenhouse effect -- I don't actually know if this would have enhanced violent weather or suppressed it.

Either way, though, I don't think there is any problem in obtaining and mixing the ingredients that we know are required for life on a rocky, watery planet, with or without a moon. The Moon is an aesthetic bonus, and maybe one could accept Ward and Brownlee's argument that the stabilizing influence of the Moon is necessary for advanced life (I don't), but I see no necessity for it as requirement for life to begin.

ETA: Except for the extent to which it may prevent tidal locking, which I've already mentioned my doubts about.

### #20 Pess

On a different note, last year I attended the SETIcon conf. in California, and the "habitable zone" subject came up in several sessions, but the one that stuck in my head was by Frank Drake (of Drake Equation fame.) He said of habitable zones, that he finds them very speculative, because life is very adaptive (and I wrote down the following quote at the time)

“I always have my doubts as to how seriously we should take these things.”

Indeed, when one considers extremophiles on Earth, the range of temperatures and pressures that can be endured by some is amazing, the one that I think is way up there on the macro side is Tardigrade

I agree, and I've posted as much many times. If you are a proponent of current evolutionary theory then you must embrace the concept that life evolves along the path before it..not along a predetermined path.

What that means is given energy, basic chemical building blocks and a stable niche--life should find a way to evolve. It may not be anything we even recognize as life based on our experiences --but life nonetheless.

I think it is silly to think that evolution has only one path to follow.

Pesse (I may be right or I may be wrong but I remain convinced) Mist

What that means is given energy, basic chemical building blocks and a stable niche--life should find a way to evolve. It may not be anything we even recognize as life based on our experiences --but life nonetheless.

I think that's the concept behind the "goldilocks" zone. In addition to the presence of basic building blocks, you need a solvent that they can dissolve in, move around and interact, and the energy level has to be high enough that thermal energy provides enough energy to make and break some chemical bonds, but not so much energy that all chemicals become unstable.

So, once you get below freezing, water won't work as a solvent. There are some other things that might (like methane), but most aren't as polar or as good at catalyzing reactions, so you would need more thermal energy to support chemical reactions (but since it's colder, you have less). So that seems unlikely. Perhaps something like ammonia (which is fairly reactive) could work, and extend the range a bit on the colder side.

When you start getting into high temperatures, water vaporizes (so again, it's out as a solvent). You could hypothesize life evolving in liquid magma, but the energy levels are so high that very few chemical bonds are strong enough to hold stable. No chemical stability, no way for life to become structured. Again, the range may be a bit higher than here on earth if you consider a planet with lots of deep water, since water stays liquid under high pressure, but at some point even enormous pressure stops helping when the temperature gets high enough to break hydrogen-oxygen bonds (one of the most stable bonds around). At that point, almost no chemicals will be stable.

So, while I think there is room for debate on exactly how wide the goldilocks zone is, I do think there is probably some temperature range below which life is impossible, and above which life is impossible, due to the requirements for energy, chemical building blocks and a stable niche.

### New planet classification

Recently HarbingerDawn and I have been working on a new planet classification system for SE. Our goal is to have a classification system which meets several criteria:

- Being physically based. Class name must reveal the most important properties of a planet: it's size, bulk composition, surface conditions.
- Must describe all known planet types and theoretical ones, like carbon and chthonic planets.
- Being descriptive. No abstract Star Trek-style classes M, F, G etc. Class name must immediately give the user information about the basic nature of a planet. I mean that it must be a set of words, like in the current SE classification: "temperate terra with life".
- But the description also cannot be too long.
- Class names must be single-word. One can use "very hot" instead of "scorched", but we must try to avoid this, to reduce confusion and makes description more compact.
- Class names must have a scientific style. I.e. using Latin/Greek prefixes "hypo-", "meso-", "cryo-" is a good choice. Also, "terra", "selena" etc.

There are several alternate classification schemes which we have developed, and I started to implement some of them in the code. I hope your suggestions in this thread will help us to select the best one. It is very important to make this classification readable and nice-sounding in other languages. So if you are not an English speaker, try to translate the classnames in your mind, and write here if you find some issues. We shall try to change words/scheme to satisfy all languages. At least to avoid ridiculous combinations

So the planet description is made by combining several class names:
- temperature class
- atmosphere class (atmosphere pressure + breathability)
- surface volatiles class (volatiles composition, amount and physical state)
- surface bedrock composition class
- size class
- bulk composition class
- additional info (tidal locked, life etc)

Some classes could be skipped entirely, to make the description more compact. Example layouts:

"temp_class atmo_class [additional] volatiles_class surface_class size_class bulk_class".
Earth: "temperate mesobaric inhabited marine rocky terra"
Mars: "cool hypobaric hypoglacial rocky subterra"
Titan: "frigid mesobaric cryolaky icy subaquaria"

"temp_class volatiles_class surface_class size_class bulk_class [additional]".
Earth: "temperate marine rocky terra with life"
Mars: "cool hypoglacial rocky subterra"
Titan: "frigid mesobaric cryolaky icy subaquaria"

"temp_class surface_class size_class bulk_class [with volatiles_class] [with/and additional]".
Earth: "temperate rocky terra with water seas and life"
Mars: "cool rocky subterra with CO2 glaciers"
Titan: "frigid icy subaquaria with hydrocarbon lakes"

First, I'll describe the bulk and size classes, because they are the most important.

Bulk class
Describes the bulk composition of a planet, i.e. the major substance forming the planet.
terra - rocky planet (combined old terra, desert and selena classes)
aquaria - water/ice planet (combined old oceania, ice world and titan classes)
carbonia - carbon/carbid/diamond planet (new class, hypothetical carbon-dominated planet)
ferria - iron/metal planet (new class, hypothetical)
neptune - ice giant planet
jupiter - gas giant planet
chthonia - core of an evaporated ice/gas giant, or a helium-rich giant (not sure about this class)
asteroid - for asteroids, comets and dwarf moons (irregularly-shaped small bodies)

The terra class could use the alternate class name earth. The reason for this is making classification closer to modern astronomy. In SE you sometimes visit a large terrestrial planets, which will be called "superearth" - matching the astronomical term (see below).

The aquaria class could use the alternate class name: oceania or glacia/cryogenia, depending on temperature. Because frozen oceania (= ice world) will sound strange, as will warm glacia (molten, = oceania). But this is not a very good solution, because it adds messiness to the classification, and also some uncertainty exists: imagine a tidally locked planet, which have a global water ocean on a day side and a global ice glacier on a night side (TRAPPIST-1 f). What would you call it, oceania or glacia? Also, "glacia" does not have a good translation to Russian.

The ferria class could use alternate names: ironia, metallica, but they sound funny Also, ferrum in Latin means "iron" - I think it is suitable class name, to continue the pattern (terra - ground, aqua - water, carbo - coal).

The neptune and jupiter classes alternatively could be named "ice giant" and "gas giant". But it has two drawbacks: first, it makes a double-word class name, which I want to avoid (like getting rid of old "ice world" class). This also makes some trouble with adding a size class prefix (see below). Second, using the word "neptune" removes annoying questions like "how can an ice giant be hot". Also, "neptune" and "jupiter" are commonly used class names in modern astronomy.

By the way, I made an option to switch between these alternate class names for developing and debug usage. I simply can leave it in the release as a config file parameter or even a switch in the settings menu. So you could switch "jupiter" back to "gas giant" if you like.

Size class
It is proposed as a simple prefix to the bulk class:
mega - huge
super - big
(no prefix) - normal
sub - small
mini - little
micro - tiny

Examples: superterra, subaquaria, minineptune.

More specifically, this is a mass class, not size. Because mass is more important, it defines how match matter forms the planet size (radius) depends not only on mass, but also on chemical (bulk) composition.

Possible subdivision between classes for solid planets, in Earth masses:
<2*10 -6 (micro), 2*10 -6 -0.0002 (mini), 0.0002-0.02 (sub), 0.02-2 (no prefix), 2-20 (super), >20 (mega)
<2*10 -6 (micro), 2*10 -6 -0.0002 (mini), 0.0002-0.02 (sub), 0.02-2 (no prefix), 2- 10 (super), >10 (mega) - more corresponds to a scientific definition of superearth (2-20 Earth masses)

Alternate, "natural" (logarithmic). Earth in this system will be "superterra", not very nice. Shifting it by a factor of 2 is better.
<0.0001 (micro), 0.0001-0.001 (mini), 0.001-0.01 (sub), 0.01-0.1 (no prefix), 0.1-1 (super), >1 (mega)

Examples:
Kepler-10b - superterra (superearth)
Kepler-10c - megaterra? (17 Earth masses)
Earth, Venus - terra
Mars - terra (because it is > 0.02 Earth masses)
Mercury - ferria (it has an iron core 60% by mass, the whole planet is also > 0.02 Earth masses)
Moon, Io - subterra (they are < 0.02 Earth masses)
Ceres - miniterra (Ceres is rocky, it has ice as a relatively thin mantle, 25% by mass)
Europa - subterra (it is also a rocky world, the ice and subsurface water ocean is just 10% of its mass)
Ganymede, Titan - aquaria (they are by 50% composed of water, and also fall into the "no prefix" class due to mass > 0.02 Earth masses)
Callisto - subaquaria (it is < 0.02 Earth masses)

Gas giants (jupiters) must use a different scale. Possible subdivision in Earth masses:
<6 (mini), 6-60 (sub), 60-600 (no prefix), >600 (super)
The same in Jupiter masses:
<0.02 (mini), 0.02-0.2 (sub), 0.2-2 (no prefix), >2 (super)

For ice giants (neptunes), I'm not sure about the subdivision. One possible way (in Earth masses):
6-10 (sub), 10-40 (no prefix), >40 (super)
The same in Jupiter masses:
0.02-0.03 (sub), 0.03-0.13 (no prefix), >0.13 (super)

6 Earth masses is the theoretical subdivision limit between rocky planets and planets with a large gaseous atmosphere (so-called mini-neptunes), so is a good choice for the classification. But in our classification they must be called sub-neptunes, to save the "sub - (no prefix) - super" scheme. Super-neptunes are very rare transitional planets with a mass of

60 Earth masses, similar to those of a very lightweight gas giants, but still not having the metallic hydrogen layer. Presence of metallic hydrogen is a natural physical criteria to distinguish "true" gas giants from other planets.

An example of a mini-neptune (or subneptune in our scheme) is Kepler-11f: 2.3 Mearth and 2.6 Rearth. It could be classified as a superearth or superaquaria with a large atmosphere though, so subneptune class could be omitted. Subdivision line between aquaria (icy/water planet) and neptune (icy planet with a H/He atmosphere) is not very sharp. Considering this, one could exclude the ice giants class at all - they are the same as "mega-aquaria" (>10 or >20 Mearth). But "ice giant/neptune" is the commonly used term in astronomy.

Alternatively, ice and gas giants could be merged into a single "giant" class. Then we could use this scheme (in Earth masses):
<6 (mini), 6-60 (sub), 60-600 (no prefix), >600 (super)
or the same in Jupiter masses:
<0.02 (mini), 0.02-0.2 (sub), 0.2-2 (no prefix), >2 (super)
This scaleis beautifully monotonic, but not physically-based. We omitted the criterion of the presence of metallic hydrogen. Use this for "true" gas giants only, and merge neptunes with aquaria?

Asteroids should use either different size scheme, or even omit it (call them just "asteroid", not depending on size/mass). HarbingerDawn proposed to use the same class names as for terrestrial planets for a large asteroids with differentiated interiors (thus Vesta will be microterra), and call other asteroids "asteroid" (without size class). In my system, asteroids are bodies with irregular shape smaller than 300 km (rocky) or 200 km (icy).

Temperature class
Describes temperature on a planet's surface, or equilibrium temperature for gas giants. Could be changed to equilibrium temperature for all planets, but this will make Venus and Earth in the cool class.
scorched - hot - warm - temperate - cool - cold - frozen (like in SE now)
scorched - hot - warm - temperate - cool - cold - cryogenic (like in the SE translation to Russian now)
torrid - hot - warm - temperate - cool - cold - frigid (HarbingerDawn's proposal, but the word "frigid" has a ridiculous translation to Russian)
very hot - hot - warm - temperate - cool - cold - very cold (satisfies Russian language, and removes the word "cryogenic", which could conflict with other class names but I want to avoid double words in the class name)
The temperature ranges which are used in SE now are:
>800K (scorched), 800-400K (hot), 400-300K (warm), 300-250K (temperate), 250-200K (cool), 200-100K (cold), 100K-0K (frozen)

Atmosphere pressure class
Describes the pressure range of the atmosphere. This class name is not used for gas giants, because they all will be ultrabaric/megabaric.
airless - infrabaric - hypobaric - mesobaric - hyperbaric - ultrabaric
Proposed pressure range (in atmospheres/bars):
0-10 -6 (airless) - 10 -6 -10 -3 (infrabaric) - 10 -3 -10 -1 (hypobaric) - 10 -1 -10 1 (mesobaric) - 10 1 -10 3 (hyperbaric) - >10 3 (ultrabaric)
Thus Venus would be hyperbaric, Earth - mesobaric, Mars - hypobaric, Pluto - infrabaric.

Another interesting option is using the metric system prefixes to describe the atmospheric pressure: milli-, kilo- etc:
airless - nanobaric - microbaric - millibaric - centibaric - decibaric - unibaric - decabaric - hectobaric - kilobaric - megabaric
10 -9 -10 -6 (nanobaric) - 10 -6 -0.001 (microbaric) - 0.001-0.01 (millibaric) - 0.01-0.1 (centibaric) - 0.1-1 (decibaric) - 1-10 (unibaric) - 10-100 (decabaric) - 100-1000 (hectobaric) - 1000-10 6 (kilobaric) - >10 6 (megabaric)
But this system has some problems. First is using exact "1.0" borders makes Earth with 1.0 atm pressure - unibaric, but a planet with 0.999 atm pressure - decibaric (because its atmospheric pressure is 9.99 decibars). Second is it produces too many classes. One can skip centi-, deci-, deca- and hecto-, but then the first problem became even worse: if Earth is unibaric, then planet with 0.999 atm will be millibaric (999 millibars).

We decided to remove the atmo pressure class from the description, to make it more compact (see below).

Atmosphere breathability class
We did not consider this much. If we were going to remove the atmo pressure class, this would be useless anyway.
toxic - unbreathable - breathable - bio-hazardous

tidally-locked - volcanic - cryovolcanic - cometary - inhabited
Some planets could have these subclasses, some could not, depending on a planet properties. They also could be combined, for example "tidally-locked cometary jupiter" (evaporating planet). But this is not a good way, because it generates double-wording again. The class "inhabited" could be used here instead of a suffix "with life" in the end of description, like in SE 0.9.8.0.

Volatiles class
This is a double/triple-word class, describing volatiles (liquids) composition, their amount and state, which could be combined into a single word. Volatiles are substances which are in liquid form on a planetary surface - forming lakes, seas and oceans, or in a partially frozen form - forming glaciers, which still could evaporate (like water glaciers on Earth, carbon dioxide on Mars and nitrogen on Pluto). This class name is not used for gas giants.

Volatiles composition
lava/magma - water - carbon dioxide/CO2 - ammonia - methane/hydrocarbons - nitrogen (countless of them. some planets could have multiple volatiles, which makes this system too difficult)
pyro - thermo - (none) - hypo - cryo (more simple option, describing only the temperature range of a liquid see examples below)

Volatiles amount
desertic/arid - laky - marine - oceanic
desertic/arid - laky - marine - oceanic - superoceanic (for a planets with a global 100 km deep ocean)
desertic/arid - laky - marine - oceanic - superoceanic - glacial (for a planets with glaciers, for example Pluto has nitrogen glaciers)
If we are decided to omit the atmosphere class, we could add the "airless" here as a volatiles amount class. Airless bodies couldn't have liquids on their surfaces, so always will be "desertic". They could have glaciers though.

Examples:
Venus - desertic terra (so simple )
Earth - water-marine terra / (none-) marine terra
Moon - airless subterra
Mars - CO2-glacial + water-glacial terra / hypoglacial terra (as you can see, the first option is too messy)
Io - magma-laky subterra / pyrolaky subterra (Io has lava lakes)
Titan - hydrocarbons-laky aquaria / cryolaky aquaria (first option is not very precise, because Titan's lakes are composed of hydrocarbons and liquid nitrogen)
Pluto - nitrogen-glacial + CO-glacial subaquaria / cryoglacial subaquaria
Kepler-10b - magma-oceanic superterra / pyrooceanic superterra (example of a molten planet)

Alternate scheme (HarbingerDawn): add a description "with xxx" to the end of a planet class.
Volatiles composition:
lava/magma - water - carbon dioxide - ammonia - methane/hydrocarbons - nitrogen
Volatiles amount:
lakes - seas - oceans
lakes - seas - oceans - glaciers (combined with volatiles state)
Volatiles state:
liquid - glacial

Examples:
Earth - terra with water seas / terra with liquid water
Mars - terra with CO2 glaciers and water glaciers / terra with glacial CO2 and glacial water (oh. we probably must left only CO2 description - as the most prominent volatile on Martian surface)
Io - subterra with magma lakes / subterra with liquid magma
Titan - aquaria with hydrocarbons lakes / aquaria with liquid hydrocarbons
Pluto - subaquaria with nitrogen glaciers / subaquaria with glacial nitrogen
Kepler-10b - superterra with magma oceans / superterra with liquid magma

Surface class
Describes the main bedrock substance. Is not used for gas giants.
metallic - rocky - carbid - icy - watery

Examples:
Earth - rocky terra
snowball Earth - rocky terra
Europa - icy subterra
Hypothetical ocean planet - watery aquaria / watery terra (depending on its bulk composition)
Hypothetical carbon planet - carbid carbonia (carbon planet are theorized to have rocks made of carid instead of silicates)
Hypothetical metal planet - metallic ferria

## Abstract

Satellite and recent Earth-based observations of Io's surface reveal a specific spatial pattern of persisting hotspots and sudden high-intensity events. Io's major heat producing mechanism is tidal dissipation, which is thought to be non-uniformly distributed within Io's mantle and asthenosphere. The question arises to what extent Io's non-homogeneous heat production can cause long-wavelength variations in the interior and volcanic activity at the surface. We investigate dissipation patterns resulting from two different initially spherical symmetric visco-elastic rheological structures, which are consistent with geodetic observations. The spatial distributions of the time-averaged tidal heat production are computed by a finite element model. Whereas for the first rheological structure heat is produced only in the upper viscous layer (asthenosphere-heating model), the second rheological structure results in a more evenly distributed dissipation pattern (mixed-heating model) with tidal heating occurring in the deep mantle and the asthenosphere. To relate the heat production to the interior temperature and melt distribution, we use steady-state scaling laws of mantle convection and a simple melt migration model. The resulting long-wavelength thermal heterogeneities strongly depend on the initial tidal dissipation pattern, the thickness of the convective layer, the mantle viscosity, and the ratio between magmatic and convective heat transport. While for the asthenosphere-heating model a strong lateral temperature signal with up to 190 K peak-to-peak difference can remain, convection within a thick convective layer, as for the mixed-heating model, can reduce the lateral temperature variation to <1 K, if the mantle viscosity is sufficiently low. Models with a dominating magma heat transport preserve the long-wavelength pattern of tidal dissipation much better and are favoured, because they are better to explain Io's thick crust. The approach presented here can also be applied to investigate the effect of an arbitrary interior heating pattern on Io's volcanic activity pattern.

## Free bodily vibrations of the terrestrial planets

A comparison is made of the work in geophysics, astronomy, and atomic physics on free oscillations of spherical models. The mathematical formulation of the eigenvibrations of an elastic sphere is outlined and the geometry of the vibrations and the effects of rotation and ellipticity discussed. Conditions for the generation of planetary free oscillations and their measurement on seismometers, gravimeters, and magnetometers are presented along with a discussion of observations made already on the Earth. For the Earth, Moon, Venus, and Mars, models of velocity and density as functions of depth are defined which satisfy available data on mass, radius, and other physical parameters. The position is taken that Venus probably has a liquid core, while the Moon and Mars probably do not.

The future will see seismometers on the Moon, and probably on Mars and Venus as well, which will yield information on structure, pressure, density, temperature, viscoelastic parameters, and composition. Lunar seismometers have already been constructed and attempts made to land them on the Moon instruments capable of recording eigenvibrations on Mars or Venus present some problems. The likelihood of volcanic, tectonic, and meteoritic sources of seismic energy on the Moon, Mars, and Venus is discussed.

Three experiments are considered. (1) Observations of free oscillations of a planet, 0S2 and 0T2 in particular, would provide crucial evidence on the existence of a large concentration of mass towards the center and of a liquid core. (2) Crustal structure could be determined by observations of high order oscillations (surface waves). (3) Even in the absence of recordable seismicity, the measurement of bodily tides would give information on internal mechanical properties.

## Planetary magnetic fields: Observations and models

The state of knowledge and understanding of planetary magnetic fields is reviewed. All of the planets, with the possible exception of Venus, have had active dynamos at some time in their evolution. The properties and characteristics of the dynamos are as diverse as the planets themselves. Even within the subclasses of terrestrial and giant planets, the contrasting compositions, sizes, and internal pressures and temperatures of the planets result in strikingly different dynamos. As an example, the dynamos in Mercury and Ganymede are likely driven by compositional buoyancy distributions different from that in the Earth’s core. Dynamo models operate far from the parameter regimes appropriate to the real planets, yet provide insight into the dynamics of their interiors. While Boussinesq models are generally adequate for simulating terrestrial planet dynamos, anelastic models that also account for large density and electrical conductivity variations are needed to simulate the dynamos in giant planets. Future spacecraft missions to planets with active dynamos are needed to learn about the character and temporal variability of the planetary magnetic fields.

### Highlights

► The properties and characteristics of planetary magnetic fields are reviewed. ► With the possible exception of Venus, all planets have or have had active dynamos. ► Planetary dynamos in diverse settings are driven by different sources of buoyancy. ► Magnetic fields of Mercury, Jupiter, and Saturn will be obtained in detail.

## 3.3. What determines if a planet can have life?

Do you know the story of Goldilocks and the Three Bears? Goldilocks thought the Papa Bear’s porridge was too hot and Mama Bear’s porridge was too cold and Baby Bear’s porridge was just right. That’s a great story but it’s also a good way to think of our home. Sometimes we can feel cold or hot but really most the time, it’s just right. When we think about our planet, the warmth that comes from the Sun keeps our world from being too cold. Earth is far enough from the Sun that it is not too hot for us to live. It’s just right.

#### Disciplinary Core Ideas

LS1.C: Organization for Matter and Energy Flow in Organisms: All animals need food in order to live and grow. They obtain their food from plants or from other animals. Plants need water and light to live and grow. (K-LS1-1)

LS4.D: Biodiversity and Humans: There are many different kinds of living things in any area, and they exist in different places on land and in water. (2-LS4-1)

PS3.B: Conservation of Energy and Energy Transfer: sunlight warms Earth’s surface. (K-PS3-1, K-PS3-2)

LS2.A: Interdependent Relationships in Ecosystems: Plants depend on water and light to grow. (2-LS2-1)

ESS3.A: Natural Resources: Living things need water, air, and resources from the land, and they live in places that have the things they need. Humans use natural resources for everything they do. (K-ESS3-1)

#### Crosscutting Concepts

Patterns: Patterns in the natural world can be observed, used to describe phenomena,and used as evidence. (K-ESS2-1)

Big Ideas: The Earth is just right for life – it is not too hot or too cold.

Boundaries: Temperature is limited to relative measures such as warmer/cooler. (K-PS3-1)

K-5 The Science of the Sun: The Source of Energy Lab. Understanding the relationship between Earth and the Sun is a fundamental concept in elementary level science. In this 30-minute lab, students focus on the Sun as the source for all energy on Earth. Students gain a perspective of how powerful the Sun is and the small fraction of its energy we receive. Students also gain an understanding of how Earth relates to the other planets in the solar system. NASA . Goddard Space Flight Center. https://sdo.gsfc.nasa.gov/assets/docs/UnitPlanElementary.pdf#page=49

K-8 Searching for the Sun. In this activity (two to four 45 minute lessons) about sunlight as an energy source, learners create a plant box and observe that a plant grows toward the Sun, its primary source of energy. This lesson also includes a hands-on activity about habitability connected to the book, The Day Joshua Jumped Too Much. NASA Goddard Space Flight Center.. https://sdo.gsfc.nasa.gov/assets/docs/Book1_resources.pdf#page=3

Do you know the story of Goldilocks and the Three Bears? Goldilocks thought the Papa Bear’s porridge was too hot and Mama Bear’s porridge was too cold and Baby Bear’s porridge was just right. That’s a great story, and it’s also a good way to think of our Earth. Even though there are really hot places on Earth, like the Sahara Desert, they still have living things there. Other places are very cold, like in Antarctica, but some living things survive there, too. Everywhere on Earth living things can survive. Our whole planet is really “just right” for life.

Do you think that there are other places beyond Earth that are too cold or too hot for anything to survive? The Earth is heated by the Sun and it happens to be not too close (too hot) and not too far away (too cold) from the Sun. Scientists sometimes call this the Goldilocks Zone. There are some planets that are too close and some that are too far away to get the right amount of heat for living things. It turns out that there are planets around other stars that are also in the Goldilocks Zone! If we want to try to find life somewhere besides Earth, then these places might be some of the best places to explore.

#### Disciplinary Core Ideas

PS3.D: Energy in Chemical Processes and Everyday Life: The energy released [from] food was once energy from the Sun that was captured by plants in the chemical process that forms plant matter (from air and water). (5-PS3-1)

LS1.C: Organization for Matter and Energy Flow in Organisms: Food provides animals with the materials they need for body repair and growth and the energy they need to maintain body warmth and for motion.

LS4.D: Biodiversity and Humans: Populations live in a variety of habitats, and change in those habitats affects the organisms living there. (3-LS4-4)

LS4.C: Adaptation: For any particular environment, some kinds of organisms survive well, some survive less well, and some cannot survive at all. (3-LS4-3)

ESS1.A: The Universe and its Stars: The Sun is a star that appears larger and brighter than other stars because it is closer. Stars range greatly in their distance from Earth. (5-ESS1-1)

ESS2.A: Earth Materials and Systems: Rainfall helps to shape the land and affects the types of living things found in a region. Water, ice, wind, living organisms, and gravity break rocks, soils, and sediments into smaller particles and move them around. (4-ESS2-1)

#### Crosscutting Concepts

Cause and Effect: Cause and effect relationships are routinely identified, tested, and used to explain change. (4-ESS2-1, 4-ESS3-2)

Big Ideas: The Goldilocks Zone is the area around a star where a planet can maintain the right temperature for life. The Earth is in the Sun’s Goldilocks Zone and is just right for life – it is not too hot or too cold. Examples of being “just right” could include moving their hands closer and further from a heat source such as a light bulb. Feeling a comfortable distance where the heat is just right. Living things can survive everywhere on Earth. Learning about life on Earth helps with the search for life beyond Earth.

Boundaries: Students in this grade band begin exploring renewable and nonrenewable energy resources. Examples of renewable energy resources could include wind energy, water behind dams, and sunlight examples of non-renewable energy resources are fossil fuels and fissile materials. (4-ESS3-1)

K-5 The Science of the Sun: The Source of Energy Lab. Understanding the relationship between Earth and the Sun is a fundamental concept in elementary level science. In this 30-minute lab, students focus on the Sun as the source for all energy on Earth. Students gain a perspective of how powerful the Sun is and the small fraction of its energy we receive. Students also gain an understanding of how Earth relates to the other planets in the solar system. NASA . Goddard Space Flight Center. https://sdo.gsfc.nasa.gov/assets/docs/UnitPlanElementary.pdf#page=49

K-8 Searching for the Sun. In this activity (two to four 45 minute lessons) about sunlight as an energy source, learners create a plant box and observe that a plant grows toward the Sun, its primary source of energy. This lesson also includes a hands-on activity about habitability connected to the book, The Day Joshua Jumped Too Much. NASA Goddard Space Flight Center.. https://sdo.gsfc.nasa.gov/assets/docs/Book1_resources.pdf#page=3

5-9 Project Spectra: Planet Designer: Martian Makeover. This is an activity (two 50-minute lessons) about the atmospheric conditions (greenhouse strength, atmospheric thickness) Mars needs to maintain surface water. Learners use a computer interactive to learn about Mars past and present before exploring the pressure and greenhouse strength needed for Mars to have a watery surface as it had in the past. This lesson is part of Project Spectra, a science and engineering education program focusing on how light is used to explore the Solar System. University of Colorado, Boulder/NASA. http://lasp.colorado.edu/home/wp-content/uploads/2013/06/martian_makeover_teacher_20130617.pdf

The Sun is really important for life as we know it, since the Sun is the source of nearly all Earth’s warmth. At our distance from the Sun, it’s not so cold that the oceans freeze solid and it’s not so hot that the oceans evaporate into the atmosphere. It’s just the right temperature to have liquid water on the surface of our planet. This is such an important thing to have happen that we gave it a name. We call the area around a star where a planet can be at just the right temperature for liquid water to exist the Goldilocks Zone. This comes from the old story of Goldilocks and the Three Bears, where the main character finds that something can be too hot, too cold, or just right. Since having a planet that’s just right for liquid water is important for living things, one important place for us to look for possible alien life is on planets that are also in the Goldilocks Zone around their stars.

There are probably several hundred billion planets in our galaxy. As we keep finding more planets around other stars, a lot of astrobiologists are really interested in looking at those planets that are in the Goldilocks Zone around their stars. Also, since stars get hotter as they get older, the Goldilocks Zone around a star can actually move out over time. So, it’s also important to look at the planets that stay in the Goldilocks Zone as their stars get older. This area is called the Continuous Goldilocks Zone. Our planet Earth is in this zone around our star!

Are all stars the same as the Sun? No. Some stars are smaller, dimmer, and redder while others are larger, brighter, and white or blue. This tells us that there is a different size for the Goldilocks Zone for each type of star depending on its brightness. Larger stars have wider Goldilocks Zones, which may include more planets. However, large stars burn their fuel faster and do not exist as main sequence stars for a really long time and there aren’t a lot of them in the universe. Stars that are smaller than the Sun last a very long time and there are a lot of them, but many have smaller Goldilocks Zones with less planets or even no planets in them.

Stars that are similar to our Sun, kind of average in size, may be good planetary system candidates because their Goldilocks Zones can be big enough to have at least a few planets and they exist much longer than the really big blue and white stars. The only example of life we are aware of is around this kind of star. Categorizing stars and planets by their potential for liquid water allows researchers to more efficiently search for life. With so many planets out there to search, narrowing it down is helpful.

It also turns out that the distance from a star isn’t the only thing that matters when it comes to how hot a planet will be. The atmosphere of a planet also affects its surface temperature. On Earth, greenhouse gases like water vapor, carbon dioxide, and methane keep warmth at the surface, much like a blanket. Earth is much warmer than it would be without these greenhouse gases. But too much of an atmosphere can make a planet too hot. Venus isn’t the closest planet to the Sun (that’s Mercury), but Venus has the hottest surface because it has a really thick atmosphere.

Considering if planets have atmospheres and how close to their stars they are helps us to narrow the search for life beyond Earth. However, there are worlds in our solar system that are not in the Goldilocks Zone and yet may have had life in the past or may even have life on them right now. These are places like Mars, Titan, Europa, and Enceladus. As astrobiologists search for life out there they consider all of the possible places where life is most likely to survive and flourish.

#### Disciplinary Core Ideas

PS3.A: Definitions of Energy: Motion energy is properly called kinetic energy it is proportional to the mass of the moving object and grows with the square of its speed. (MS-PS3-1) ▪A system of objects may also contain stored (potential) energy, depending on their relative positions. (MS-PS3-2) Temperature is a measure of the average kinetic energy of particles of matter. The relationship between the temperature and the total energy of a system depends on the types, states, and amounts of matter present. (MS-PS3-3, MS-PS3-4)

PS3.D: Energy in Chemical Processes and Everyday Life: The chemical reaction by which plants produce complex food molecules (sugars) requires an energy input (i.e., from sunlight) to occur. In this reaction, carbon dioxide and water combine to form carbon-based organic molecules and release oxygen. (MS-LS1-6)

LS2.C: Ecosystem Dynamics, Functioning, and Resilience: Biodiversity describes the variety of species found in Earth’s terrestrial and oceanic ecosystems. The completeness or integrity of an ecosystem’s biodiversity is often used as a measure of its health. (MS-LS2-5)

ESS1.A: The Universe and Its Stars: Patterns of the apparent motion of the Sun, the Moon, and stars in the sky can be observed, described, predicted, and explained with models. (MS-ESS1-1) ▪ Earth and its solar system are part of the Milky Way galaxy, which is one of many galaxies in the universe. (MS-ESS1-2)

ESS1.B: Earth and the Solar System: The solar system consists of the Sun and a collection of objects, including planets, their Moons, and asteroids that are held in orbit around the Sun by its gravitational pull on them. (MS-ESS1-2, MS-ESS1-3)

ESS2.A: Earth’s Materials and Systems: All Earth processes are the result of energy flowing and matter cycling within and among the planet’s systems. This energy is derived from the Sun and Earth’s hot interior. The energy that flows and matter that cycles produce chemical and physical changes in Earth’s materials and living organisms. (MS-ESS2-1)

ESS2.C: The Roles of Water in Earth’s Surface Processes: Water continually cycles among land, ocean, and atmosphere via transpiration, evaporation, condensation and crystallization, and precipitation, as well as downhill flows on land. (MS-ESS2-4) ▪ Global movements of water and its changes in form are propelled by sunlight and gravity. (MS-ESS2-4)

ESS3.A: Natural Resources: Humans depend on Earth’s land, ocean, atmosphere, and biosphere for many different resources. Minerals, fresh water, and biosphere resources are limited, and many are not renewable or replaceable over human lifetimes. These resources are distributed unevenly around the planet as a result of past geologic processes. (MS-ESS3-1)

ESS2.D: Weather and Climate: Weather and climate are influenced by interactions involving sunlight, the ocean, the atmosphere, ice, landforms, and living things. These interactions vary with latitude, altitude, and local and regional geography, all of which can affect oceanic and atmospheric flow patterns. (MS-ESS2-6) *The ocean exerts a major influence on weather and climate by absorbing energy from the Sun, releasing it over time, and globally redistributing it through ocean currents. (MS-ESS2-6)

#### Crosscutting Concepts

Cause and Effect: Cause and effect relationships may be used to predict phenomena in natural or designed systems. (MS-ESS2-5) Systems and System Models ▪ Models can be used to represent systems and their interactions — such as inputs, processes and outputs — and energy, matter, and information flows within systems. (MS-ESS2-6)

Big Ideas: The Goldilocks Zone is the area around a star where a planet can maintain the temperature necessary for liquid water to exist. Because Earth is in the Goldilocks Zone of the Sun, it is the right temperature to have the liquid water necessary for life. While there are billions of planets in the galaxy, planets that are in the Goldilocks Zone around their stars are of particular interest in the search for life beyond Earth. A planet’s atmosphere also helps maintain surface temperature and is critical for life.

Boundaries: Students in this grade band develop models to show gravity as the force that holds together the solar system and Milky Way galaxy and controls orbital motions within them. Examples of models can be physical (such as the analogy of distance along a football field or computer visualizations of elliptical orbits) or conceptual (such as mathematical proportions relative to the size of familiar objects such as students’ school or state). MS-ESS1-2

K-8 Searching for the Sun. In this activity (two to four 45 minute lessons) about sunlight as an energy source, learners create a plant box and observe that a plant grows toward the Sun, its primary source of energy. This lesson also includes a hands-on activity about habitability connected to the book, The Day Joshua Jumped Too Much. NASA Goddard Space Flight Center.. https://sdo.gsfc.nasa.gov/assets/docs/Book1_resources.pdf#page=3

5-9 Project Spectra: Planet Designer: Martian Makeover. This is an activity (two 50-minute lessons) about the atmospheric conditions (greenhouse strength, atmospheric thickness) Mars needs to maintain surface water. Learners use a computer interactive to learn about Mars past and present before exploring the pressure and greenhouse strength needed for Mars to have a watery surface as it had in the past. This lesson is part of Project Spectra, a science and engineering education program focusing on how light is used to explore the Solar System. University of Colorado, Boulder/NASA. http://lasp.colorado.edu/home/wp-content/uploads/2013/06/martian_makeover_teacher_20130617.pdf

6-8 SpaceMath Problem 545: Measuring Atmospheric Trace Gases Using Parts Per Million. Students convert from percentage units to parts per million and compare trace gases in the atmospheres of various planets. [Topics: percentages unit conversions] https://spacemath.gsfc.nasa.gov/Grade67/10Page8.pdf

6-8 SpaceMath Problem 544: The Composition of Planetary Atmospheres. Students study the composition of planetary atmospheres and compare the amounts of certain compounds in them [Topics: pie graphs percentages scientific notation] https://spacemath.gsfc.nasa.gov/Grade67/10Page7.pdf

6-8 SpaceMath Problem 335: Methane Lakes on Titan. Students use a recent Cassini radar image of the surface of Titan to estimate how much methane is present in the lakes that fill the image, and compare the volume to that of the freshwater lake, Lake Tahoe. [Topics: estimating irregular areas calculating volume from area x height scaled images] https://spacemath.gsfc.nasa.gov/Grade67/6Page148.pdf

6-8 SpaceMath Problem 403: The Goldilocks Planets – Not too hot or cold. Students use a table of the planets discovered by the Kepler satellite, and estimate the number of planets in our Milky Way galaxy that are about the same size as Earth and located in their Habitable Zones. They estimate the average temperature of the planets, and study their tabulated properties using histograms. [Topics: averaging histogramming] https://spacemath.gsfc.nasa.gov/astrob/7Page66.pdf

6-8 or 9-12 Mars Image Analysis. In this one-three hour lesson, students analyze and interpret the accompanying large-format images of Mars taken by NASA’s Mars Thermal Emission Imaging System ( THEMIS ) camera. The analysis involves identifying geologic features, calibrating the size of those features, and determining surface history. The lesson culminates in students conducting in-depth research on questions generated during their analyses. Can be used independently or part of the Mars Science Imaging Project through Arizona State University. NASA /Arizona State University. http://marsed.asu.edu/mars-image-analysis

6-9 Planet Hunters Education Guide. Lesson 3: Finding the habitable zone (page 41). This activity explores four types of stars and their characteristics, such as color, temperature, size, and lifespan. These characteristics are then used to determine the conditions for planets around each of them. Next, students compare and contrast their results to develop ideas about where it is reasonable to expect that life could be found outside our own solar system. This lesson is part of a nine lesson unit that takes learners through engaging activities that feature habitability, identifying and characterizing exoplanets, and citizen science. NASA . https://s3.amazonaws.com/zooniverse-resources/zoo-teach/production/uploads/resource/attachment/122/Planet_Hunters_Educator_Guide.pdf

6-9 Rising Stargirls Teaching and Activity Handbook: A public service announcement ( PSA ) for Life (page 57). Students work cooperatively in teams to solidify the concept of what life needs to survive. Each team pursues an in-depth study of a particular planetary environment and its prospects for life, then presents this information as a PSA to the larger class. Rising Stargirls is a 10-day workshop dedicated to encouraging girls of all backgrounds to learn, explore, and discover the universe through interactive astronomy using theater, writing, and visual art. This provides an avenue for individual self-expression and personal exploration that is interwoven with scientific engagement and discovery. Rising Stargirls. https://static1.squarespace.com/static/54d01d6be4b07f8719d7f29e/t/5748c58ec2ea517f705c7cc6/1464386959806/Rising_Stargirls_Teaching_Handbook.compressed.pdf

6-12 Astrobiology Math. This collection of math problems provides an authentic glimpse of modern astrobiology science and engineering issues, often involving actual research data. Students explore concepts in astrobiology through calculations. Relevant topics include Habitability Zones and Stellar Luminosity (page 57) and The Greenhouse Effect and Planetary Temperature (page 41). NASA . https://www.nasa.gov/pdf/637832main_Astrobiology_Math.pdf

6-12 Extreme Planet Makeover. This online interactive allows students to change the settings of a planet’s size, distance to star, age, and type of star it orbits in order to understand the habitability zone. The habitability zone is a very important concept in astrobiology and is tied to CLQ1.2 in terms of the creation of Earth as a habitable environment. NASA . https://exoplanets.nasa.gov/interactable/1/index.html

6-12 (3-5 adaptable) Project Spectra! – Goldilocks and the Three Planets. In this lesson (two class periods), students determine what some of Earth, Venus, and Mars’ atmosphere is composed of and then mathematically compare the amount of greenhouse gas and CO2 on the planets of Venus, Earth, and Mars, in order to determine which has the most. Students brainstorm to figure out what things, along with greenhouse gases, can affect a planet’s temperature which can determine its habitability. University of Colorado, Boulder/NASA. http://lasp.colorado.edu/home/wp-content/uploads/2011/08/Goldilocks.pdf

6-12 Ocean Worlds. In this web interactive, students learn about water on Earth, in the cosmos and on other planetary bodies. It tells the story of water from its creation and its delivery to the Earth, as well as up-to-date information about water on planetary bodies within the Solar System such as Mars, Europa and others and far away in a variety of places such as planet formation nebulae and exoplanets. The learner comes away with a true sense of how common water is in the universe. NASA . https://www.nasa.gov/specials/ocean-worlds/

7-8 Life Underground. This game is an interactive outreach experience for 7th and 8th grade classrooms. Life Underground is presented in a video game experience that is highly motivating for students. The goal is for students to visualize microscopic life at a range of terrestrial and extraterrestrial subsurface conditions. Students take the role of a young scientist investigating extreme subsurface environments for microbial life. They navigate through extreme conditions, including those of temperature, pressure, acidity, and energy limitations, and they begin to recognize what characterizes life in this context. NASA Astrobiology Institute. https://gameinnovationlab.itch.io/life-underground

8-10 SpaceMath Problem 124: The Moon’s Atmosphere! Students learn about the moon’s very thin atmosphere by calculating its total mass in kilograms using the volume of a spherical shell and the measured density. [Topics: volume of sphere, shell density-mass-volume unit conversions] https://spacemath.gsfc.nasa.gov/moon/4Page26.pdf

8-10 SpaceMath Problem 292: How Hot is That Planet? Students use a simple function to estimate the temperature of a recently discovered planet called CoRot-7b. [Topics: algebra II evaluating power functions] https://spacemath.gsfc.nasa.gov/astrob/6Page61.pdf

8-10 SpaceMath Problem 264: Water on Planetary Surfaces. Students work with watts and Joules to study melting ice. [Topics: unit conversion, rates] https://spacemath.gsfc.nasa.gov/astrob/Astro3.pdf

8-10 SpaceMath Problem 263: Ice or Water? Whether a planetary surface contains ice or liquid water depends on how much heat is available. Students explore the concepts of specific heat and latent heat of fusion to better understand and quantify the energy required for liquid water to exist under various conditions. [Topics: unit conversion, scientific notation] https://spacemath.gsfc.nasa.gov/astrob/Astro1.pdf

We use the word habitable to define a planet or an environment on a planet where we think life might be able to thrive. For instance, our planet is habitable since we know that we have a biosphere of living things at the surface. But what other kinds of planets or places on planets might be habitable? An important first step in answering that question is to think about liquid water. All of life as we know it needs liquid water to survive. So, one important characteristic that might make a planet habitable is if it has liquid water at its surface like we do here on Earth. The Earth is 93 million miles from the Sun. At this distance, it’s not so cold that the oceans freeze solid and it’s not so hot that the oceans evaporate into the atmosphere. It’s just the right temperature to have liquid water on the surface of our planet. We call this region around our Sun the Goldilocks Zone, because the conditions are “just right” for liquid water at the surface of our world.

There are probably several hundred billion planets in our galaxy. As we keep finding more planets around other stars, a lot of astrobiologists are really interested in looking at those planets that are in the Goldilocks Zone around their stars. Also, since stars get hotter as they get older, the Goldilocks Zone around a star can actually move out over time. So, it’s also important to look at the planets that stay in the Goldilocks Zone as their stars get older. This area is called the Continuous Goldilocks Zone. Our planet Earth is in this zone around our star!

Are all stars the same as the Sun? No. Some stars are smaller, dimmer, and redder while others are larger, brighter, and white or blue. This tells us that there is a different size for the Goldilocks Zone for each type of star depending on its brightness. Larger stars have wider Goldilocks Zones, which may include more planets. However, large stars burn their fuel faster and do not exist as main sequence stars for a really long time and there also aren’t a lot of them in the universe. Stars that are smaller than the Sun last a very long time and there are a lot of them, but many have smaller Goldilocks Zones with fewer planets or even no planets in them. Some of our research tells us that these smaller stars may have more solar flares that could be harmful to life.

Stars that are similar to our Sun, kind of average in size, may be good planetary system candidates because their Goldilocks Zones can be big enough to have at least a few planets and they exist much longer than the really big blue and white stars. The only example of life we are aware of is around this kind of star. Categorizing stars and planets by their potential for liquid water allows researchers to more efficiently search for life. There are just so many planets out there to search that narrowing it down is helpful. It also turns out that the distance from a star isn’t the only thing that matters when it comes to how hot a planet will be. The atmosphere of a planet also effects its surface temperature. On Earth, we have greenhouse gases like water vapor, carbon dioxide, and methane. These greenhouse gases allow radiation from the Sun to enter the atmosphere and warm the surface of our planet, but then they stop the heat that is released from the surface from leaving. This keeps the surface warmer the atmosphere works like a greenhouse or a blanket for the planet. Earth is much warmer than it would be without our greenhouse gases. But too much of an atmosphere or too much of greenhouse gases can make a planet become too hot. For instance, Venus isn’t the closest planet to the Sun (that’s Mercury), but Venus has the hottest surface because it has a really thick atmosphere with a lot of greenhouse gas. This keeps the surface of Venus around 850°F.

There are also other things to consider in the search for potentially habitable planetary systems, such as type of planetary orbit (nearly circular vs very elliptical), multiple star systems, tidal locking, and the effects of moons on a planet’s tilt and rotation. It is not thorough enough to simply say that if a planet is a certain distance from its central star (i.e., if it’s in the Goldilocks Zone), then it is habitable. What if the orbit is highly elliptical (not very circular)? It may only have an average distance that is in the Goldilocks Zone but then spends most of its time beyond the inner and/or outer range. Our solar system has planets with low eccentricity (i.e., they’re really circular) but that is not the case for all planetary systems. Our solar system also only has a single star, but it turns out that this isn’t really common. Most stars are in binary or multiple star systems. The Goldilocks Zones for liquid water for these systems are very complex. Some planets are also tidally locked to their stars. This means that the same side of the planet is always facing the star (our moon is almost tidally locked, which is why you only ever see the near side of the Moon). Could there be life on a planet that is tidally locked? We really don’t know. On Earth a lot of life uses the night and day but is this true of other planets with life? We also have to think about the importance of moons for making a planet habitable. Could having a moon make a planet more likely to have life? Computer modeling shows that having a large moon could be beneficial for a planet to have life because the planet doesn’t wobble as much. A planet whose axial tilt changes a lot likely also faces extreme climate change. The Earth goes through ice ages due to changes in its orbit eccentricity, axial tilt, and axial direction. However, life has always survived these changes. A planet without a large moon will have extreme axial tilt changes that could include a complete covering of ice or varying ice bands on the planet, both of which could be too harsh for life to survive.

Considering all of these factors helps us to narrow down possible worlds that might be habitable for life as we know it. Whether or not they’re in the Goldilocks Zone or are tidally locked, whether or not they have thin or thick atmospheres, and if they have moons and the shapes of their orbits are all important factors. However, there are also other worlds in our solar system that don’t meet some of these criteria for potentially habitable worlds and yet they may have had life a long time ago or may even have life on them right now. These are places like Mars, Titan, Europa, and Enceladus. Mars is at the outer edge of our Goldilocks Zone, it has a really thin atmosphere and is very cold, and it only has two very small moons, and yet we know that Mars once had potentially habitable environments. Likewise, Titan, a large moon of Saturn, has incredible complex organic molecules going through many processes. Could there be something alive in the organics of Titan that isn’t quite like life as we know it? Also, there are moons in our solar system like Europa and Enceladus that have oceans of liquid water below their icy crusts. Could there be living things in the oceans of Europa or Enceladus? What might be required for those environments to be habitable? As astrobiologists search for life out there they need to consider all of the possible places where life is most likely to survive and flourish.

#### Disciplinary Core Ideas

PS3.A: Definitions of Energy: Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (HS-PS3-1, HS-PS3-2) *At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. (HS-PS3-2, HS-PS3-3)

LS1.C: Organization for Matter and Energy Flow in Organisms: The process of photosynthesis converts light energy to stored chemical energy by converting carbon dioxide plus water into sugars plus released oxygen. (HS-LS1-5) *The sugar molecules thus formed contain carbon, hydrogen, and oxygen: their hydrocarbon backbones are used to make amino acids and other carbon-based molecules that can be assembled into larger molecules (such as proteins or DNA ), used for example to form new cells. (HS-LS1-6)

PS3.D: Energy in Chemical Processes: The main way that solar energy is captured and stored on Earth is through the complex chemical process known as photosynthesis.

ESS1.A: The Universe and Its Stars: The star called the Sun is changing and will burn out over a lifespan of approximately 10 billion years. (HS-ESS1-1) *The study of stars’ light spectra and brightness is used to identify compositional elements of stars, their movements, and their distances from Earth. (HS-ESS1-2, HS-ESS1-3)

ESS1.B: Earth and the Solar System: Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the Sun. Orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system. (HS-ESS1-4)

ESS2.C: The Roles of Water in Earth’s Surface Processes: The abundance of liquid water on Earth’s surface and its unique combination of physical and chemical properties are central to the planet’s dynamics. These properties include water’s exceptional capacity to absorb, store, and release large amounts of energy, transmit sunlight, expand upon freezing, dissolve and transport materials, and lower the viscosities and melting points of rocks. (HS-ESS2-5)

ESS2.D: Weather and Climate: The foundation for Earth’s global climate systems is the electromagnetic radiation from the Sun, as well as its reflection, absorption, storage, and redistribution among the atmosphere, ocean, and land systems, and this energy’s re-radiation into space. (HS-ESS2-2)

#### Crosscutting Concepts

Scale, Proportion, and Quantity: The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs. (HS-ESS1-1) Stability and Change-Much of science deals with constructing explanations of how things change and how they remain stable. (HS-ESS1-6)

Big Idea: The Goldilocks Zone is the area around a star where a planet can maintain the temperature necessary for liquid water to exist. The Earth is 93 million miles from the Sun and within a habitable zone that supports life. Because Earth is in the Goldilocks Zone of the Sun, it is the right temperature to have the liquid water necessary for life. While there are billions of planets in the galaxy, planets that are in the Goldilocks Zone around their stars are of particular interest in the search for life beyond Earth because of their potential for liquid water. Planetary systems are categorized by whether or not they are in the Goldilocks Zone or are tidally locked, whether they have thin or thick atmospheres, if they have moons and the shapes of their orbits. There are other worlds in the solar system, like Mars, that do not meet some of the criteria for potentially habitable worlds and yet they show promising signs of habitability. These are places like Mars, Titan, Europa, and Enceladus.

Boundaries: Students in this grade band use basic algebraic expressions or computations to calculate the change in energy in a system. (HS-PS3-1) Students use mathematical representations for the gravitational attraction of bodies and Kepler’s Laws of orbital motions but do not involve calculus.

5-9 Project Spectra: Planet Designer: Martian Makeover. This is an activity (two 50-minute lessons) about the atmospheric conditions (greenhouse strength, atmospheric thickness) Mars needs to maintain surface water. Learners use a computer interactive to learn about Mars past and present before exploring the pressure and greenhouse strength needed for Mars to have a watery surface as it had in the past. This lesson is part of Project Spectra, a science and engineering education program focusing on how light is used to explore the Solar System. University of Colorado, Boulder/NASA. http://lasp.colorado.edu/home/wp-content/uploads/2013/06/martian_makeover_teacher_20130617.pdf

6-8 or 9-12 Mars Image Analysis. In this one-three hour lesson, students analyze and interpret the accompanying large-format images of Mars taken by NASA’s Mars Thermal Emission Imaging System ( THEMIS ) camera. The analysis involves identifying geologic features, calibrating the size of those features, and determining surface history. The lesson culminates in students conducting in-depth research on questions generated during their analyses. Can be used independently or part of the Mars Science Imaging Project through Arizona State University. NASA /Arizona State University. http://marsed.asu.edu/mars-image-analysis

6-9 Planet Hunters Education Guide. Lesson 3: Finding the habitable zone (page 41). This activity explores four types of stars and their characteristics, such as color, temperature, size, and lifespan. These characteristics are then used to determine the conditions for planets around each of them. Next, students compare and contrast their results to develop ideas about where it is reasonable to expect that life could be found outside our own solar system. This lesson is part of a nine lesson unit that takes learners through engaging activities that feature habitability, identifying and characterizing exoplanets, and citizen science. NASA . https://s3.amazonaws.com/zooniverse-resources/zoo-teach/production/uploads/resource/attachment/122/Planet_Hunters_Educator_Guide.pdf

6-9 Rising Stargirls Teaching and Activity Handbook: A public service announcement ( PSA ) for Life (page 57). Students work cooperatively in teams to solidify the concept of what life needs to survive. Each team pursues an in-depth study of a particular planetary environment and its prospects for life, then presents this information as a PSA to the larger class. Rising Stargirls is a 10-day workshop dedicated to encouraging girls of all backgrounds to learn, explore, and discover the universe through interactive astronomy using theater, writing, and visual art. This provides an avenue for individual self-expression and personal exploration that is interwoven with scientific engagement and discovery. Rising Stargirls. https://static1.squarespace.com/static/54d01d6be4b07f8719d7f29e/t/5748c58ec2ea517f705c7cc6/1464386959806/Rising_Stargirls_Teaching_Handbook.compressed.pdf

6-12 Astrobiology Math. This collection of math problems provides an authentic glimpse of modern astrobiology science and engineering issues, often involving actual research data. Students explore concepts in astrobiology through calculations. Relevant topics include Habitability Zones and Stellar Luminosity (page 57) and The Greenhouse Effect and Planetary Temperature (page 41). NASA . https://www.nasa.gov/pdf/637832main_Astrobiology_Math.pdf

6-12 Extreme Planet Makeover. This online interactive allows students to change the settings of a planet’s size, distance to star, age, and type of star it orbits in order to understand the habitability zone. The habitability zone is a very important concept in astrobiology and is tied to CLQ1.2 in terms of the creation of Earth as a habitable environment. NASA . https://exoplanets.nasa.gov/interactable/1/index.html

6-12 (3-5 adaptable) Project Spectra! – Goldilocks and the Three Planets. In this lesson (two class periods), students determine what some of Earth, Venus, and Mars’ atmosphere is composed of and then mathematically compare the amount of greenhouse gas and CO2 on the planets of Venus, Earth, and Mars, in order to determine which has the most. Students brainstorm to figure out what things, along with greenhouse gases, can affect a planet’s temperature which can determine its habitability. University of Colorado, Boulder/NASA. http://lasp.colorado.edu/home/wp-content/uploads/2011/08/Goldilocks.pdf

6-12 Ocean Worlds. In this web interactive, students learn about water on Earth, in the cosmos and on other planetary bodies. It tells the story of water from its creation and its delivery to the Earth, as well as up-to-date information about water on planetary bodies within the Solar System such as Mars, Europa and others and far away in a variety of places such as planet formation nebulae and exoplanets. The learner comes away with a true sense of how common water is in the universe. NASA . https://www.nasa.gov/specials/ocean-worlds/

8-10 SpaceMath Problem 124: The Moon’s Atmosphere! Students learn about the moon’s very thin atmosphere by calculating its total mass in kilograms using the volume of a spherical shell and the measured density. [Topics: volume of sphere, shell density-mass-volume unit conversions] https://spacemath.gsfc.nasa.gov/moon/4Page26.pdf

8-10 SpaceMath Problem 292: How Hot is That Planet? Students use a simple function to estimate the temperature of a recently discovered planet called CoRot-7b. [Topics: algebra II evaluating power functions] https://spacemath.gsfc.nasa.gov/astrob/6Page61.pdf

8-10 SpaceMath Problem 264: Water on Planetary Surfaces. Students work with watts and Joules to study melting ice. [Topics: unit conversion, rates] https://spacemath.gsfc.nasa.gov/astrob/Astro3.pdf

8-10 SpaceMath Problem 263: Ice or Water? Whether a planetary surface contains ice or liquid water depends on how much heat is available. Students explore the concepts of specific heat and latent heat of fusion to better understand and quantify the energy required for liquid water to exist under various conditions. [Topics: unit conversion, scientific notation] https://spacemath.gsfc.nasa.gov/astrob/Astro1.pdf

9-11 SpaceMath Problem 181: Extracting Oxygen from Moon Rocks. Students use a chemical equation to estimate how much oxygen can be liberated from a sample of lunar soil. [Topics: ratios scientific notation unit conversions] https://spacemath.gsfc.nasa.gov/moon/5Page28.pdf

9-12 SpaceMath Problem 287: LCROSS Sees Water on the Moon. Students use information about the plume created by the LCROSS impactor to estimate the (lower-limit) concentration of water in the lunar regolith in a shadowed crater. [Topics: geometry volumes mass=density x volume] https://spacemath.gsfc.nasa.gov/moon/6Page66.pdf

9-12 SpaceMath Problem 352: Exponential Functions and Atmospheric ‘Scale heights’. A study of the way a planet’s atmosphere changes as its temperature is changed using exponential functions. [Topics: scientific notation evaluating exponential functions optional calculus] https://spacemath.gsfc.nasa.gov/astrob/7Page15.pdf

9-12 SpaceMath Problem 349: Exoplanet Orbits and the Properties of Ellipses. Given the formula for the orbits of newly-discovered planets, students determine the basic properties of the elliptical orbits for the planets. [Topics: properties of ellipses] https://spacemath.gsfc.nasa.gov/astrob/7Page13.pdf

9-10 Voyages through Time: Planetary Evolution. This comprehensive integrated curriculum helps students address the question, “What makes it possible for Earth to have life?” The Earth is literally filled with life and yet our neighbors Mars, Venus and the Moon have developed so differently. Through the planetary evolution module students address that main question through a series of activities. There is a sample lesson on the website and the curriculum is available for purchase. SETI . http://voyagesthroughtime.org/planetary/index.html

### Storyline Extensions

#### A tale of three planets:

Venus and Mars are both on the edges of the Goldilocks Zone in our solar system, but why don’t they show liquid surface waters and large apparent biospheres like we have here on Earth?

Venus is has the hottest planetary surface in our solar system. It’s about 850°F there and the pressure is about 92 times more than what we have at sea level here on Earth. That makes Venus a very different place. Venus may have once had oceans (and maybe even a biosphere!), but it appears that the entire surface of Venus heated up high enough that all of the rocks melted and turned into lava at some point long ago. On top of that, Venus has what we call a “runaway greenhouse”, where the buildup of greenhouse gases (especially CO2) in the Venusian atmosphere made it get hotter, which caused more greenhouse gases to build up, which made it warmer, and so on. Venus is a very interesting place!

We think early Mars likely had lots of water, in rivers and lakes and maybe even in an ocean. That’s because early Mars likely had a much thicker atmosphere. But, these days, the surface of Mars is very cold, very dry, and the pressure is very low. Without a thick enough atmosphere, Mars cannot sustain liquid water at its surface, even though it’s within the Goldilocks Zone.

Even though Venus and Mars are on the edges of the Goldilocks Zone, they don’t have abundant biospheres that we can see on their surfaces. This tells us that being within the Goldilocks Zone alone probably isn’t enough to guarantee that a world will have liquid water or life. However, it’s still an important place for us to look around other stars when trying to find Earth-like worlds in our galaxy.

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## Planetary Satellites, Natural

### IV.C.4 Ganymede

The icy moon Ganymede , which is the largest Galilean satellite, also shows evidence for geologic activity as recently as a billion years ago. A dark, heavily cratered terrain is transected by more recent, brighter grooved terrain (see Fig. 6 ). Although they show much diversity, the grooves are typically 10 km wide and 1 3 to 1 2 km high. They were implaced during several episodes between 3.5 and 4 billion years ago. Their formation may have occurred after a melting and refreezing of the core, which caused a slight crustal expansion and subsequent faulting and flooding by subsurface water.

FIGURE 6 . A high resolution (∼80-M) Galileo image of the Uruk Sulcus regim placed on an earlier Voyager image. Bright grooved terrain, older darker terrain, and bright impact craters are visible in the Voyager image. The four boxes show the entire Galileo coverage.

The grooved terrain of Ganymede is brighter because the ice is not as contaiminated with rocky material that accumulates over the eons from impacting bodies. The satellite is also covered with relatively fresh bright craters, some of which have extensive ray systems. In the cratered terrain there appear outlines of old, degraded craters, which geologists called palimpsests. The polar caps of Ganymede are brighter than the equatorial regions this is probably due to the migration of water molecules released by evaporation and impact toward the colder high latitudes. HST detected a thin atmosphere of molecular oxygen, similar to that of Europa.

The author gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC). This research has made use of NASA's Astrophysics Data System.

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Keywords: stars: evolution, stars: interiors, stars: mass-loss, stars: oscillations, stars: rotation, stars: variables: general, stars: magnetic

Citation: Lovekin CC (2020) Challenges in 2D Stellar Modeling. Front. Astron. Space Sci. 6:77. doi: 10.3389/fspas.2019.00077

Received: 18 January 2019 Accepted: 09 December 2019
Published: 09 January 2020.

Markus Roth, Albert Ludwig University of Freiburg, Germany

Marcella Marconi, Astronomical Observatory of Capodimonte (INAF), Italy
Petri Käpylä, University of Göttingen, Germany

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