Astronomy

What causes objects to become tidally locked?

What causes objects to become tidally locked?

I'm trying to write a gravity simulation (suns planets etc), and was hoping tidal locking could be one feature demonstrated.

Using a simple equation for gravity has produced some interesting results, but (unless its emergent behaviour) I see nothing that would encourage tidal locking. But, after some reading it appears tidal locking is quite common, planets and their satellites, planets and suns, suns and other suns (binary stars).

Is it a result of the formation stage of these objects, or is it somehow a function of the equation of gravity?


Tidal locking occurs because the planet deforms the satellite into an oval, with long axis pointing towards the planet. If the satellite is rotating the long axis will move away from being pointing towards the planet, and the gravity of the planet will tend to pull it back, slowing the rotation until one face is permanently facing the planet. Tidal locking isn't a result of the formation processes, but a consequence of satellites not being perfectly rigid.

In order to model the effects of tides on the orbits and rotation periods of satellites you need to know several important pieces of information.

First you obviously need to know the size of the planet and the satellite (both in terms of mass and radius) the shape of the orbit and the rotation rate of both planet and satellite. For many objects, these values are well known.

Next, and this is the tricky bit, you need to know how the satellite and planet will be deformed by the other's gravity, and how much tidal heating will occur. These are the so-called "love number" (after Augustus Love) and the dissipation function, Q.

It is hard to estimate these. For the Earth Moon system the ratio k/Q is known to be 0.0011. (but the Earth is a poor model for other planets, which don't have a substantial ocean, or a liquid core)

For other planets the value of Q varies between 10 and 10000, with larger values for the gas giants, and k can be estimated from the rigidity of the bodies.

A simple gravitation model is not able to capture the subtleties of the gravitational interaction between two mutually deforming bodies, indeed for most simulations, the planets are modelled as points, or at most as spheres, and this is good enough for all but the highest precision calculations.

Tidal locking takes a long time (by human standards) but a relatively short time compared with the age of the solar system. The time taken is very strongly dependent (order 6) on the radius of the orbit.

Direct simulation would be more or less impossible: the deformations are too small, and the time scale of locking is too large. It would be possible (though difficult) to model tidal locking in a simulation with unrealistic values for the rigidity of the satellite, and the size of the planet (think jelly world, orbiting a (Newtonian) black hole) so the deformation is greater and the locking time shorter. However modelling the elastic deformation of a body under gravity is far from trivial.


In Astronomy, what causes tidal / gravitational locking?

I've read what tidal / gravitational locking is, but am wondering why it occurs. Why/how did the Moon end up tidally locked to the Earth, and why will the Earth eventually become tidally locked with the Sun?

Or is it no more complicated than their internal mass is not 100% evenly distributed?

Basically, it's because gravity makes the moon bulge out a little bit on the side facing the earth.

As the moon turns, it takes some time for that bulge to move across the surface and keep facing the earth. If the moon is turning slowly, the the bulge will lag behind a bit, and earths gravity will be pulling on a slightly lop-sided moon, giving it some torque and making the moon spin a bit faster.

Until eventually the moon is spinning exactly fast enough so the bulge can keep up and always face the earth.


Answers and Replies

The more evenly distributed the mass, the weaker the effect of tidal forces will be. Also, if the planet is far from the parent star, tidal forces will be weaker. Remember, the tidal forces are the result of the difference in gravitational pull across the planet. The distance from the center of the star to the near side of the planet vs. the distance from the center of the star to the far side of the planet. The more distant the planet is, the smaller the difference between the near and far side (comparatively).

Of course, in terms of habitability, this brings up a whole new set of problems.

The moon rotating has angular momentum. The process that causes a planet to tidal lock will also cause a moon spiral in. Moons will escape in some cases because the hill sphere shrinks as a planet gets closer to the host star.

Suppose we think of a double planet as a single thing. The process of tidal locking will also be a process of making the double planet into a single planet. Next think of them as two objects orbiting each other. As they spiral in their rotational velocity increases and their orbital period decreases. The end result is a collision but it could be a long time before the collision occurs. Each of the individual planets will initially have their own rotational velocity. As they lock to each other that angular momentum gets converted to orbital momentum.
The planets tidal locking to each other will counter the pair locking with the star. So you can assemble the most extreme case. Two equal mass objects are positioned inside edge of the hill sphere and both are rotating near their breakup velocity. They eventually fall in to each other but that "eventually" could be a long time. Technically Earth would lock to the Sun except but will not happen within the Sun's lifetime. The habitable part is quite debatable. Planets near breakup velocity will lose atmospheres much faster than slow rotators. The closer you are to exact extreme conditions the less likely it will be that such a thing exists or that we will find one. It is possible but it is also very possible that life will adapt to conditions on a tidally locked planet.

Or what if there was a large planet, maybe a mini-Neptune, next to it in orbit? Would that have any effect on the tidal-locking?


Contents

Consider a pair of co-orbiting objects, A and B. The change in rotation rate necessary to tidally lock body B to the larger body A is caused by the torque applied by A's gravity on bulges it has induced on B by tidal forces. [5]

The gravitational force from object A upon B will vary with distance, being greatest at the nearest surface to A and least at the most distant. This creates a gravitational gradient across object B that will distort its equilibrium shape slightly. The body of object B will become elongated along the axis oriented toward A, and conversely, slightly reduced in dimension in directions orthogonal to this axis. The elongated distortions are known as tidal bulges. (For the solid Earth, these bulges can reach displacements of up to around 0.4 metres (1.3 ft). [6] ) When B is not yet tidally locked, the bulges travel over its surface due to orbital motions, with one of the two "high" tidal bulges traveling close to the point where body A is overhead. For large astronomical bodies that are nearly spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid, i.e. an axially symmetric ellipsoid that is elongated along its major axis. Smaller bodies also experience distortion, but this distortion is less regular.

The material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time is required to reshape B to the gravitational equilibrium shape, by which time the forming bulges have already been carried some distance away from the A–B axis by B's rotation. Seen from a vantage point in space, the points of maximum bulge extension are displaced from the axis oriented toward A. If B's rotation period is shorter than its orbital period, the bulges are carried forward of the axis oriented toward A in the direction of rotation, whereas if B's rotation period is longer, the bulges instead lag behind.

Because the bulges are now displaced from the A–B axis, A's gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, whereas the "back" bulge, which faces away from A, acts in the opposite sense. However, the bulge on the A-facing side is closer to A than the back bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational force and torque. The net resulting torque from both bulges, then, is always in the direction that acts to synchronize B's rotation with its orbital period, leading eventually to tidal locking.

Orbital changes Edit

The angular momentum of the whole A–B system is conserved in this process, so that when B slows down and loses rotational angular momentum, its orbital angular momentum is boosted by a similar amount (there are also some smaller effects on A's rotation). This results in a raising of B's orbit about A in tandem with its rotational slowdown. For the other case where B starts off rotating too slowly, tidal locking both speeds up its rotation, and lowers its orbit.

Locking of the larger body Edit

The tidal locking effect is also experienced by the larger body A, but at a slower rate because B's gravitational effect is weaker due to B's smaller mass. For example, Earth's rotation is gradually being slowed by the Moon, by an amount that becomes noticeable over geological time as revealed in the fossil record. [7] Current estimations are that this (together with the tidal influence of the Sun) has helped lengthen the Earth day from about 6 hours to the current 24 hours (over ≈ ⁠4½ billion years). Currently, atomic clocks show that Earth's day lengthens, on average, by about 2.3 milliseconds per century. [8] Given enough time, this would create a mutual tidal locking between Earth and the Moon. The length of the Earth's day would increase and the length of a lunar month would also increase. The Earth's sidereal day would eventually have the same length as the Moon's orbital period, about 47 times the length of the Earth's day at present. However, Earth is not expected to become tidally locked to the Moon before the Sun becomes a red giant and engulfs Earth and the Moon. [9] [10]

For bodies of similar size the effect may be of comparable size for both, and both may become tidally locked to each other on a much shorter timescale. An example is the dwarf planet Pluto and its satellite Charon. They have already reached a state where Charon is visible from only one hemisphere of Pluto and vice versa. [11]

Eccentric orbits Edit

A widely spread misapprehension is that a tidally locked body permanently turns one side to its host.

For orbits that do not have an eccentricity close to zero, the rotation rate tends to become locked with the orbital speed when the body is at periapsis, which is the point of strongest tidal interaction between the two objects. If the orbiting object has a companion, this third body can cause the rotation rate of the parent object to vary in an oscillatory manner. This interaction can also drive an increase in orbital eccentricity of the orbiting object around the primary – an effect known as eccentricity pumping. [12]

In some cases where the orbit is eccentric and the tidal effect is relatively weak, the smaller body may end up in a so-called spin–orbit resonance, rather than being tidally locked. Here, the ratio of the rotation period of a body to its own orbital period is some simple fraction different from 1:1. A well known case is the rotation of Mercury, which is locked to its own orbit around the Sun in a 3:2 resonance.

Many exoplanets (especially the close-in ones) are expected to be in spin–orbit resonances higher than 1:1. A Mercury-like terrestrial planet can, for example, become captured in a 3:2, 2:1, or 5:2 spin–orbit resonance, with the probability of each being dependent on the orbital eccentricity. [13]

Moons Edit

Most major moons in the Solar System, the gravitationally rounded satellites, are tidally locked with their primaries, because they orbit very closely and tidal force increases rapidly (as a cubic function) with decreasing distance. [14] Notable exceptions are the irregular outer satellites of the gas giants (e.g. Hyperion), which orbit much farther away than the large well-known moons.

Pluto and Charon are an extreme example of a tidal lock. Charon is a relatively large moon in comparison to its primary and also has a very close orbit. This results in Pluto and Charon being mutually tidally locked. Pluto's other moons are not tidally locked Styx, Nix, Kerberos, and Hydra all rotate chaotically due to the influence of Charon.

The tidal locking situation for asteroid moons is largely unknown, but closely orbiting binaries are expected to be tidally locked, as well as contact binaries.

Earth's Moon Edit

Earth's Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth, the same hemisphere of the Moon is always seen. The far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft Luna 3. [15]

When the Earth is observed from the Moon, the Earth does not appear to translate across the sky but appears to remain in the same place, rotating on its own axis. [16]

Despite the Moon's rotational and orbital periods being exactly locked, about 59 percent of the Moon's total surface may be seen with repeated observations from Earth, due to the phenomena of libration and parallax. Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity of its orbit: this allows up to about 6° more along its perimeter to be seen from Earth. Parallax is a geometric effect: at the surface of Earth we are offset from the line through the centers of Earth and Moon, and because of this we can observe a bit (about 1°) more around the side of the Moon when it is on our local horizon. [ citation needed ]

Planets Edit

It was thought for some time that Mercury was in synchronous rotation with the Sun. This was because whenever Mercury was best placed for observation, the same side faced inward. Radar observations in 1965 demonstrated instead that Mercury has a 3:2 spin–orbit resonance, rotating three times for every two revolutions around the Sun, which results in the same positioning at those observation points. Modeling has demonstrated that Mercury was captured into the 3:2 spin–orbit state very early in its history, within 20 (and more likely even 10) million years after its formation. [17]

The 583.92-day interval between successive close approaches of Venus to Earth is equal to 5.001444 Venusian solar days, making approximately the same face visible from Earth at each close approach. Whether this relationship arose by chance or is the result of some kind of tidal locking with Earth is unknown. [18]

The exoplanet Proxima Centauri b, discovered in 2016 that orbits around Proxima Centauri, is almost assuredly tidally locked, expressing either synchronized rotation or a 3:2 spin–orbit resonance like that of Mercury. [19]

One form of hypothetical tidally locked exoplanets are eyeball planets, which in turn are divided into "hot" and "cold" eyeball planets. [20] [21]

Stars Edit

Close binary stars throughout the universe are expected to be tidally locked with each other, and extrasolar planets that have been found to orbit their primaries extremely closely are also thought to be tidally locked to them. An unusual example, confirmed by MOST, may be Tau Boötis, a star that is probably tidally locked by its planet Tau Boötis b. [22] If so, the tidal locking is almost certainly mutual. [23] [24] However, since stars are gaseous bodies that can rotate with a different rate at different latitudes, the tidal lock is with Tau Boötis's magnetic field. [ citation needed ]

An estimate of the time for a body to become tidally locked can be obtained using the following formula: [25]

  • ω is the initial spin rate expressed in radiansper second,
  • a is the semi-major axis of the motion of the satellite around the planet (given by the average of the periapsis and apoapsis distances),
  • I ≈ 0.4 m s R 2 R^<2>> is the moment of inertia of the satellite, where m s ,> is the mass of the satellite and R is the mean radius of the satellite,
  • Q is the dissipation function of the satellite,
  • G is the gravitational constant,
  • m p ,> is the mass of the planet (i.e., the object being orbited), and
  • k 2 ,> is the tidal Love number of the satellite.

Even knowing the size and density of the satellite leaves many parameters that must be estimated (especially ω, Q, and μ), so that any calculated locking times obtained are expected to be inaccurate, even to factors of ten. Further, during the tidal locking phase the semi-major axis a may have been significantly different from that observed nowadays due to subsequent tidal acceleration, and the locking time is extremely sensitive to this value.

Because the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one. By assuming that the satellite is spherical, k 2 ≪ 1 , Q = 100 ll 1,,Q=100> , and it is sensible to guess one revolution every 12 hours in the initial non-locked state (most asteroids have rotational periods between about 2 hours and about 2 days)

There is an extremely strong dependence on semi-major axis a .

For the locking of a primary body to its satellite as in the case of Pluto, the satellite and primary body parameters can be swapped.

One conclusion is that, other things being equal (such as Q and μ ), a large moon will lock faster than a smaller moon at the same orbital distance from the planet because m s ,> grows as the cube of the satellite radius R . A possible example of this is in the Saturn system, where Hyperion is not tidally locked, whereas the larger Iapetus, which orbits at a greater distance, is. However, this is not clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic.

Solar System Edit

Parent body Tidally-locked satellites [27]
Sun Mercury [28] [29] [17] (3:2 spin–orbit resonance)
Earth Moon
Mars Phobos [30] · Deimos [31]
Jupiter Metis [32] · Adrastea · Amalthea [32] · Thebe [32] · Io · Europa · Ganymede · Callisto
Saturn Pan · Atlas · Prometheus · Pandora · Epimetheus · Janus · Mimas · Enceladus [33] · Telesto · Tethys [33] · Calypso · Dione [33] · Rhea [33] · Titan · Iapetus [33]
Uranus Miranda · Ariel · Umbriel · Titania · Oberon
Neptune Proteus · Triton [30]
Pluto Charon (Pluto is itself locked to Charon) [11]

Extra-solar Edit

  • The most successful detection methods of exoplanets (transits and radial velocities) suffer from a clear observational bias favoring the detection of planets near the star thus, 85% of the exoplanets detected are inside the tidal locking zone, which makes it difficult to estimate the true incidence of this phenomenon. [34]Tau Boötis is known to be locked to the close-orbiting giant planetTau Boötis b. [22]

Solar System Edit

Based on comparison between the likely time needed to lock a body to its primary, and the time it has been in its present orbit (comparable with the age of the Solar System for most planetary moons), a number of moons are thought to be locked. However their rotations are not known or not known enough. These are:


Tidal Forces 101 | Earth’s Tides & More Cool Effects!

A tidal force is the result of the gravitational interaction between two objects in space. Most commonly it is due to the difference in strength of gravity between a small and large body such as the Earth and the Moon. Tidal forces result in Earth’s daily tides, moons to be ‘tidally locked’, tidal acceleration and even the breakup of comets and the formation of planetary ring systems!

So What Exactly Are Tidal Forces?

A tidal force is the result of the non-uniform gravitational field between two objects, often of very different mass. This results in the side closest to the other body experiencing a stronger force of attraction than the far side, thus effectively stretching each body!

The Earth and Moon is the best example of this effect. The influence of the Moons gravity deforms Earth’s surface resulting in a slight bulge and the formation of our daily ocean tides! This same effect is also slowing Earth’s rotation very slightly, resulting in longer days!

Tidal forces don’t just form the Earth’s tides, they are also responsible for other phenomena too. These include tidal locking of moons, tidal acceleration, and the disintegration of moons or comets within the Roche limit, which can lead to the formation of ring systems.

Tidal Locking

Tidal forces are responsible for the major moons of the solar system to be tidally locked to their planet. This means that the same side of the moon always faces the planet as it rotates on its axis, exactly once per orbit of the planet! This is why we can never see the far side of the Moon!

Tidal locking is caused by a moons rotational energy being lost (over a long period of time) as frictional heating due to the tidal forces and subsequent warping and squeezing. This loss of rotation energy stops once the moons rotational period matches its orbital period. This tidal heating from the gravitational warping of a moon produces dramatic volcanic effects on Jupiter's inner moon Io causing it to be the most volcanic body in the solar system!

Typically, only the moons become tidally locked and not the planets. However, if the distances are close and the difference in mass between the two bodies is close enough, they may both become tidally locked to each other over time. This is the case for the dwarf planet Pluto and its moon Charon.

Tidal Acceleration

Tidal acceleration occurs between a moon and a planet. Over time, tidal acceleration causes a moon to slowly move away if it is orbiting in the same direction as the planet's rotation. This also gradually slows the planet's rotation and lengthens its day. This is slowly happening between the Earth and Moon.

Tidal Deceleration

Tidal deceleration also occurs between a moon a larger body like a planet and results in the eventual breakup of the moon or impact with the planet’s surface.

There are two scenarios under which this occurs, first, when there is a fast orbiting inner moon, such as Phobos, which orbits Mars faster than the planet rotates. The tidal bulge Phobos raises on Mars acts to slow Phobos. Over millions of years, moons like Phobos will be slowed to the point where they will either strike the planet or cross within the planets ‘Roche limit’ and be tidally torn apart into fragments!

The other scenario where tidal deceleration causes a moon to breakup or be absorbed by the planet is where the moon orbits in a retrograde direction (i.e. opposite to the planets rotation). There is only one major moon in the solar system which orbits like this, that is Neptune's moon Triton. All the other retrograde moons orbit their planet at a great distance where the tidal forces are negligible.

Destructive Power Of The Roche Limit

As an orbiting body gets closer to the larger body, such as a planet, the tidal forces increase. If the body crosses a point called the ‘Roche Limit’ the distorting tidal forces are so strong to cause an body (such as a moon or comet which strays too close) to disintegrate. This is because the warping and stretching force of the gravity gradient exceeds the body’s internal attraction.

This effect can be seen around Saturn where the tidal forces within the planets Roche Limit prevent the material in the rings from accreting into moons resulting in a planetary ring system. Tidal forces are also believed to have torn the comet Shoemaker-Levy 9 apart as it passed close to Jupiter in 1994.


Ep. 54: Questions Show #6

It’s been a while, so let’s catch up with the listener questions. We’ve got some easy ones, some hard ones and probably some impossible ones. We talk about our universe as a black hole, tidal locking of planets like Uranus, colours of stars at different ages, our universe’s birthday and more.

Shownotes

Our archive is full of background information. Don’t forget to check out these shows from the past!

Pamela will be giving a remote presentation to the Astronomical Association of North Carolina on Saturday September 30.

Transcript: Questions Show #6

Fraser Cain: It’s been a while, so let’s catch up with the listener questions. We’ve got some easy ones, we’ve got some hard ones, and I think we’ve got some impossible ones, so… I won’t tell you which is which ahead of time.

We actually get this question a lot. I’ve got two different people, Steven Williams and Lon Blumenthal asked this question: “has it occurred to anyone that we live inside a black hole?”

Dr. Pamela Gay: The question has occurred, and the answer is no.

Fraser: Why do people think we might live in a black hole? That seems kind of crazy to me.

Pamela: It’s a lot of science fiction. There’s this idea in science fiction that you can fly into a black hole and emerge in a completely different part of our universe, in an alternate universe… and so from these fiction writings, the idea has gotten into the zeitgeist that you fly into a black hole and you fly into a different universe – which means a universe can be inside of a black hole.

The problem is real black holes just lead to death.

Fraser: I guess that’s the question – it’s like a frog asking if I hop into that blender, will it lead me to another universe?

Fraser: No, no it won’t – a universe of pain.

Pamela: It will lead to death, and yeah – where death leads to is a personal question not based in facts and not addressable in this show.

So no. We know we don’t live in a black hole because we have atoms that are whole atoms with spaces between them. In black holes, atoms can’t exist. The densities are so high that not even neutrons can hold themselves apart.

An example I like to use is a normal universe is fridge with a bunch of randomly displayed cans of Coke in it and you have to dig around the butter to find the soda. A white dwarf is where all of the cans of soda have been packed in using the Coca-Cola shipping cases to completely pack your refrigerator and you can’t fit one more can of Coke inside.

A neutron star is what happens when you put all those cans of soda in a can crusher and make them really small (and the soda sprays in all directions). Neutron star formation gets you a supernova.

If you then squish those leftover remains of cans such that every single molecule in the cans has now been broken, you’re nowhere near as dense as a black hole. You have to keep squishing until the atoms in the cans fall apart in order to get to a black hole.

So yeah – real life can’t exist in those conditions.

Fraser: Right, so it’s almost like it’s become a kind of philosophical question and it goes back to that extra-dimensional conversation we had in a well-received episode we did back in the day. I guess it’s kind of like it’s different – could it be so different that it’s not really a devastating matter crusher? Could it be a bold new universe we could explore? (Says the frog hopping into his blender.

Fraser: All right. I’m sure we’ll get this question more, so maybe we’ll address it again later on.

Pamela: We’re not going to do any experiments to test this one. Really – you will die if you enter a black hole.

Fraser: But if you do, let us know how it goes.

Next up, Nathan Dye wants to know (this is based on our tidal-locking episode): “would it be possible for a planet with an axis like Uranus to become tidally locked with its star?”

First I want to say I’m going to say urAnus – I don’t care what anyone says, that’s how I say it.

I know it’s one of the legitimate ways to say it, and there’s the more “family-friendly” URanus version, but this is how I’m saying it.
So I can imagine you’ve got a planet like Uranus and it is spinning, unlike the rest of the planets, it’s actually spinning like it’s been pushed on its side and it’s kind of rolling around the solar system. Could an object like that become tidally locked to the star?

Pamela: Only if it agreed to have its axis rotated again – and that’s actually possible.

You can start off with a top happily spinning with its bottom facing the table and its top facing the ceiling and over time it will flop on its side and commence rolling around on the surface of the table. That’s because gravity exerted a torque, it became unstable, and it fell over. It was rotating about its axis the entire time, but how that axis was aligned changed.

In order to tidally lock a planet like Uranus, you have to rotate its axis of rotation you have to pivot it around so it looks more like a normal planet. As long as its axis of rotation isn’t perpendicular to its orbit, as long as its equator and its orbit aren’t lined up, you can’t really tidally lock it. There’s nothing to really grab onto and slow down.

We’ve learned in studies of planets like Venus that it’s possible for distributions of material on planets to cause the planets axes to pivot. There are people who have gotten computer models to actually flip Venus over on its head just using gravity.

Now, since Uranus is a gas giant, it’s kind of unlikely that you could flip Uranus enough to tidally lock it, but if you had a rocky planet that got knocked on its side through some sort of collision and it had the right distribution of mountains and it was close enough to a star, (if, if, if, if, if…) it’s possible that you could end up torquing the planet (that’s another really fun word to say).

So we’re torquing Uranus (and we still manage to be a family friendly show). If you torque Uranus correctly, and if it had a mountain or something (which it doesn’t have), you could tidally lock it.

Fraser: Isn’t the question kind of meaningless? Think of the case of a tidally locked planet. Its rotation period is exactly the same as its orbital period. So one big lumpy bulge is always facing toward the star, and it’s always facing that way as it goes around the star. I guess if you’re up above looking down, you’re going to see the planet slowly make that orbit, but if you’ve got the planet on its side, and yet it’s got that one face – it’s very top – aiming toward the star, couldn’t it still be almost rolling around the solar system?

Pamela: This is where it starts to become a two-step process. As long as Uranus (or a planet like it) is oriented such that its north pole always faces the Sun and Santa Claus is always experiencing sunburn… in that situation you can’t just tidally lock the planet.

You actually have to find a way to pivot the planet so it looks like all the other planets. Step one is change the axis of rotation. Step two is tidally lock it.

Fraser: I imagine I’ve got a ball on a string, and I’m spinning it around my head. The ball is tumbling as it goes around, but its north pole is still going to be facing me as I’m spinning this ball around. Wouldn’t there be irregularities around the top of the planet so that it would eventually slow down its rotation, because it’s always getting grabbed in certain ways, until it stops and is on its side and always facing the exact same face to me. At that point it doesn’t matter anymore.

Pamela: So what you’re envisioning is the north pole always facing the Sun, and equatorial Africa is always facing the north star?

Fraser: Yeah. And then it doesn’t matter anymore, because it stopped moving because it’s turned into a tidally locked planet. With a tidally locked planet, one chunk of it has to be aiming toward the star, and that’s that.

Pamela: The problem here is if you start off with a situation where now we have knocked the planet Earth over so the north pole is facing the Sun, but it’s still rotating around. At the beginning of this problem we have equatorial Africa facing the north star and then twelve hours later (or some period of time later) we have some place in equatorial south America facing up toward the north star. So the planet is still rotating about its axis, but the axis is pointed toward the Sun.

If I want to tidally-lock the Earth to the Sun in this situation, I somehow have to be able to grab the Sun at its equator and slow it down. That requires a force that’s either up toward the north star or down toward where the current south polar area is.

Fraser: What if the most mass is at the north pole?

Pamela: If the most mass is at the north pole, the Sun may be able to knock the planet over so the rotation axis is facing the Sun. It’s not going to be able to grab onto that and stop the rotation, because there is symmetric torque all the way around. It doesn’t slow down the rotation, it just pivots the planet around.

It’s sort of like if I want to close a door, pushing on the door along the door – sticking my hand on that little catch that keeps the door closed – if I push on that catch, the door is not going to move left or right, it’s just going to hang out going “you’re pushing me into my hinges, what are you trying to accomplish?”

So you can’t really torque a rotating planet that has its rotational axis pointing at the Sun, to get it to stop rotating. You have to exert the force from either below the planet or above the planet. So it’s one of these things where the angles don’t work in your favour.

Fraser: I guess the point is in the end the Star will wrench the planet into its happiest place, and that will be that.

Pamela: Exactly. Sometimes rotations are allowed to keep on happening.

Fraser: Okay! This is going to be the whole episode just on this one question, so let’s move on.

Pamela: But it’s a good, complicated question!

Fraser: It is a good question, yes – I like it, that’s why I had more to talk about.

Okay, so Damon asks us, “why are young stars blue? Why are there red giants, blue giants and dwarfs of different colours? What determines a star’s colour? Was our Sun born blue?”

Pamela: This is one of these things where I have to admit I’m one of the people that have helped get the concept out there that young stars are blue.

Now, not all young stars are blue, but all blue stars are young. A star’s colour is determined strictly by its temperature. Really hot objects are really blue, and cold objects are really red (the exact opposite of when you draw a thermometer). To get a really, really hot star, you have to be blowing through fuel at huge rates.

So when you look at a population of stars, if that population of stars has blue stars in it, you can say the population is young. Some blue stars only last a couple of million years. A little tiny baby red star can live for tens of billions of years.

That little baby dwarf red star is born red. It stays red, it just keeps going red. That blue star was born blue, it will go through phases of different colours as it gets rid of mass and all sorts of other craziness. It lives for only a brief period of time.

So if you look at a population and there are blue stars in the population, the whole population is young. If you see a population where all the stars are red, that means all the hot stars have died. Colour comes strictly from temperature.

Fraser: So our star, did it start out yellow?

Pamela: Our star started out more blue than it is currently, but it didn’t start out blue, blue, blue. It went through a period where it was warmer than it is today (so it was blue-er than it is today), and settled down to the current colour. It’s heating up again such that it’s slowly going to get a little more yellow. We’re never going to get to be a true blue star like Rigel, we’re just going to vary through different shades of yellow or orange depending on how your eyes perceive colour.

We’re also going to eventually bloat up, cool off and become a red giant star. Cool stars are red. It’s through these different processes – how much light a star gives off and what colour it is – that the names come from. So a big, bloated star that’s not burning through a lot of fuel but is burning helium in its core, that’s a red giant star. A star that’s burning hydrogen in its core and has a red colour is a red dwarf.

“Giant” refers to what’s being burned in the core. Giants can be burning helium or carbon – but they’re not burning hydrogen. Dwarfs, they’re burning hydrogen in their core. The colour is telling us how much stuff they’re burning. Blue giants are burning huge amounts of stuff – it’s like a really well stocked fire will get yellow-er, and whiter and if you stock it hot enough (not that I’ve ever done it), you can get a fire white-hot/blue-hot.

Fraser: Is there a limit? Could you have the perfect star burning at the hottest possible thing that it shifts right out of the visible spectrum and straight into ultraviolet? Would it disappear from our eyes?

Pamela: Not so much, because stars are actually giving off not just one colour, but a whole variety of colours in what’s called a blackbody spectrum. When we talk about the star’s colour, that’s the colour of photon that comes off in the highest number. So, our Sun is currently giving off light in the infrared, the ultraviolet but most of it’s light in the visible spectrum. That’s why we perceive it as a yellow-orange star – but all those colours are present, just in lesser numbers.

You can conceivably have a star that’s gotten so hot that it’s giving off most of its light in the ultraviolet. We can’t see that in our eyes, but we can see the other colours it’s giving off. We can see the blues, the reds, and the infrareds. Because our eyes cut off in the blue, we’ll perceive that star as being blue.

Fraser: All right. So it’s an average, but it’s the average of what we see most of the time. Okay.

Pamela: Yes. It’s a weighted average – if you look at a room with 80 brown-haired girls in it, you might say the room is full of brown-haired girls even though you might have one red-headed boy, three brown-headed boys and one red headed girl… what we perceive is what there’s the most of.

Fraser: Moving on, we’ll get another question here. This one is going to break everyone’s brains – I guarantee this ahead of time. So if someone asks you why you’re looking a little numb, blame this question. Dave Stites asks, “my birthday is September 30th. (happy birthday, Dave). Can the universe be said to have a birthday, or due to the deformation of space-time, does it transcend this notion?”

So I guess what Dave’s getting at is we know that relativity means people experience time at different rates. Even though the big bang occurred in one moment, has the movement of all of the objects in the universe through relativity changed the time? Could there be a time that would be considered the birthday or is that lost in motion?

Pamela: This is such a wonderful question. I’m going to walk up to someone who does a lot of relativity later today and ask this question and watch the twitchy-ness occur.

What’s so cool about this question is there’s two different ways to look at it. First of all, there’s the question of when do I celebrate the universe’s next birthday, when does Andromeda celebrate it?

If I assume the Milky Way and Andromeda Galaxies have been chewing through space side-by-side for the past 13.7 billion years, then as long as both systems have been moving at the same velocities the whole time, my individual perception of time and the individual perception of time of someone in Andromeda, should be the same.

But it takes time for light from Andromeda to get here. I might decide I’m going to celebrate the universe’s birthday on one day. If someone made the identical decision in Andromeda, and celebrated on the exact same day I did, I wouldn’t know that for over 2 million years, because it takes time for the light from Andromeda to get here.

So we can’t watch people celebrate at the same time, because we can never see anyone else as they are in the moment that they are.

So that’s the way it breaks you once.

Fraser: Sure, but let’s go with a theoretical thing. Say I’m running around in circles at close to the speed of light and you’re standing there, and we decide to celebrate the universe’s birthday from our relative positions.

Pamela: This is the way it breaks you twice.

Andromeda and the Milky Way may have been ploughing through the universe at the same rate for the past 13.7 billion years, but there are other systems out there that have been orbiting faster. There are individuals, presumably, somewhere out there on planets that are orbiting high-mass stars that are orbiting systems where they orbit significantly faster than we do. The faster you move, the slower you perceive time. There are all these different potential motions, and every time you change your velocity compared to somebody else, you change how time is ticking for you compared to somebody else.

So a part of space that has been orbiting a supermassive black hole, or a part of space that’s just been orbiting a neutron star, those parts of space are going to perceive the passage of time at a different rate, so they’ll be ready to celebrate the anniversary of the big bang at a different point in time, than somewhere else in the universe that is maybe completely isolated and sitting there going, “the universe is expanding around me but I’m not going to move.”

Fraser: Wouldn’t they be celebrating before we did? And be sending us their happy birthday celebration announcement, and we’d be all “what’re you talking about? We’ve got to wait another billion years.”

Pamela: The dude who’s not moving is the one that celebrates it first. Then it’s the people who are moving faster and faster and faster – for them time is slowing down. So they’ll be ready to celebrate a little bit later.

It’s all a matter of how fast you have been moving that tells you when you’re ready to celebrate the anniversary of the big bang or the birthday of the big bang, however you want to look at it.

Pamela: It’s very cool.

Fraser: All right. Moving on. Damon Harvey asks “whenever I see a re-enactment of the big bang on TV science shows, they always show the familiar explosion with lots of light. Was visible light – or any light – a real component of the big bang at the time before the release of the cosmic microwave background radiation?”

In other words, if I was inside the big bang while it was going off, would I be able to see anything with my eyeballs?

Pamela: This is actually a really cool question. What’s wrong with these depictions of the big bang as an explosion, but that they convey the idea that the universe is expanding away from a single point. It’s not. All of space is simultaneously expanding – not away from anything, just expanding. Light was a real part of it.

In the original moments of the universe, everything was pure energy: quarks, photons and no atoms. Slowly, during a period called baryogenesis, we started getting matter and anti-matter forming and colliding and exploding off of each other. Then we had these nuclear reactions going on and all of these processes are producing more and more light… but it couldn’t go anywhere.

An example I recently used with a bunch of schoolchildren was imagine a living room packed with 25 little girls, 25 little boys, and 25 hyperactive little yappy dogs. They’re all trying to run around as fast as they can. None of these critters can get very far before they collide, knock into each other and have to change their paths. They can’t run in a straight line.

When the CMB happened it was like all of a sudden a teacher said “grab your partner!” and all of the human children grab onto a human child and stand really close to one another. At that moment, all the little yappy dogs escape from the room entirely.

Those escaping yappy dogs were just like the cosmic microwave photons escaping in all directions. All of space was all of these different rooms, such that one room’s yappy dogs, one area of space’s bits of photon, are now getting to me. The photons that were created in our part of the universe are now getting to somebody else.

So all that light was already there, it just couldn’t get anywhere until the CMB occurred.

Fraser: It’s almost like if you were inside that ball, the distance from the front of your eye to the back of your eye would be an enormous distance, the likes of which the universe had never known before.

Everywhere else in the universe is completely cram-packed full of photons mashing into each other. If you were actually able to stick your little eyeballs into the universe at that point, it would be the largest space in the universe, which would instantly fill with photons. The point being it’s kind of hard to describe or imagine what it would look like to look. It’s like looking when you’re in the bottom of tar – everywhere you look is just black (or the opposite, I don’t know).

Pamela: Here, everywhere you look is light.

Pamela: What’s cool is the universe was expanding so fast that in the first gazillionth of a second, yeah – it’s smaller than your eyeball, but within seconds it’s bigger than a galaxy. The universe was expanding faster than anyone can really conceive except using computers. Today we can only see a few percent of the universe – and we can see an awfully huge distance. But the universe expanded so much during the epic of inflation during the first few seconds, that it carried everything amazingly far apart. Space itself was expanding such that two non-moving objects would see the space between them grow so much they’d see each other as moving faster than the speed of light (they’re not moving, just hanging out on their grid of space, but the grid of space was expanding faster than the speed of light).

Fraser: I know we’re going to get a million questions about this. We are going to do a separate show just on inflation and explain how the universe can expand faster than the speed of light.

So I think the amount of time you would have while everything was light, was just a fraction of a second. If you were there for that moment, it would all just be light.

Pamela: Everything would be light. But after that, for the next 300 thousand years, you could still be hanging out looking around and the light was so dense that it would still be bombarding your eye. It would be so energetic that your eyes would be forced to re-emit it after being completely destroyed.

Fraser: Right, right, right – I’m imagining I have these invulnerable superman eyes.

The point being that you’ve got light moving. Imagine every photon’s got a trajectory it’s on, and then normally if I was going to bump up and that other photon was going to bump down, left or right and the universe expanded… you’ve got all these photons trying to continue on that trajectory. Normally they would’ve bumped into something else, but now space has opened up so they can continue on those trajectories. If you’re standing out there in the middle of it, you’ve got these photons that were on these trajectories finally getting a chance to go somewhere and your eyes happen to be what’s in front of them.

Let’s move on, because I don’t want to ruin our inflation show.

This is great too – we get this question a lot as well. Robert Roland asks, “if we assume the universe began in a hot, dense situation, what mechanism prevented it from becoming or remaining a black hole, the most super-massive one possible?”

I’ll add that I can imagine if you took all of the mass and light in the universe and somehow brought it to one location, it would turn into a supermassive black hole containing all of the mass of the universe. What is the difference between that and the big bang, which contained all the mass and energy of the universe?

Pamela: This is a really wonderful question. The first time someone asked me this, my brain actually stopped. Then it realised the answer.

In our modern universe, if you throw a whole bunch of mass together without giving it some way to support itself, it’ll collapse. If you put enough of it in one place, it will collapse into a black hole. What’s happening here is mass, within the framework of space around it, collapses compared to space, and it can drag in stuff around it.

In the beginning of the universe, everything was as dense as a black hole. So one chunk of space can’t really pull on any other chunk of space because they’re all the same density. There’s no place that has a higher gravitational pull than some other place. Everything’s about the same density, and the space that all of this stuff is embedded within is what’s carrying it apart.

Fraser: So that’s the extra ingredient.

Pamela: That’s the extra ingredient: the space is pulling everything apart.

Fraser: If you made a supermassive black hole now, you wouldn’t be cramming space into it.

Pamela: Yeah, it’s just a single point in a vast universe.

Fraser: But in the big bang, the extra ingredient was love – no, the extra ingredient was space itself that was jammed into the big bang singularity as well.

Pamela: So what was able to overcome the gravity, was the expansion of space. So yes, you have this huge, dense area where the conditions would’ve been as dense for a period of time as the centre of a black hole, but then space itself carried all of that energy and matter apart and spread it out thin enough and it spread it out thin enough that instead of forming a supermassive black hole, it was able to form stars, galaxies and us.

I think that’s it – that’s the answer. I’ve got nothing else. The difference is that it had space, and that made all the difference in the universe.

Let’s move on then. Joshua Leviton asks, “although gamma rays pass through all matter, would an organism be able to have eyes that could see wavelengths of gamma rays, or is this impossible because gamma rays pass through all matter and can mutate DNA?”

I know that gamma rays don’t hit us down here on Earth, thanks to the Earth’s atmosphere, so it almost seems like it’s not something an organism would evolve. Let’s pretend that we had organisms that wanted to keep safe distances away from a nuclear reactor – would they be able to evolve some kind of gamma ray detectors? And what’s a gamma ray detector?

Pamela: Gamma rays don’t really pass through everything. They can pass through stuff: they’re really high-energy particles of photons, and I think this person may be combining the ideas of gamma rays and neutrinos.

Gamma rays do pass rather well through different things. X-rays will actually pass straight through a wall – in fact they’ll pass through your hand. Gamma rays are even higher energy than x-rays, and they will pass through you unless they hit just the right part of a piece of your DNA and cause cancer (which is a bad thing).

We do have things on the planet Earth that create gamma rays. There are different nuclear reactions. You can have a bit of nuclear material that lets off a gamma ray when it decays. Inside of nuclear reactors you can have different things that give off gamma rays. The way we detect this is we have crystals that are scintillation materials. When a gamma ray hits part of this crystal, it will give off normal light we can detect with normal detectors.

You can imagine some sort of science fiction creature that developed with eyes that instead of having normal lenses to focus light, the lenses instead are made of some sort of scintillation material such that when a gamma ray hits it, the material radiates off light the detectors of the eyes are able to see.

The problem is we really don’t know how to focus gamma rays very well. They don’t like to be focused, you can’t use a normal lens – they’ll just fly through it. We have to use all sorts of crazy reflection techniques to try and figure out where gamma rays are coming from. So you’re really looking at having a creature that has giant eyes that are somehow able to funnel the gamma rays in a meaningful way.

I’m not sure why such an organism would exist, but I see a great sci-fi plot emerging out of this with some sort of crazy creature out in space (I don’t know what it would eat, or how it would survive, but it has really cool eyes).

Fraser: Right, I think we always make that comment – if you could just look up into space with gamma ray eyes, the brightest object would be this or that. Imagine if we could have some actual life form that could see it. It’s important as well because the way they detect gamma rays is different from the way we detect regular light. You can’t have a great big mirror, you’ve got to have something completely different – a crystal detector.

Pamela: It’s just cool to think about. All the normal ways of designing eyes we have (a lens that focuses light, a retina that detects the light) you have to throw out the window. If a gamma ray hit your retina (and hit it just right) it would destroy your retina. That’s generally a bad thing.

The scintillation material doesn’t really focus it, it just transforms the gamma ray light into a different type of detectable light. You still have to come up with a way to focus it using reflections, after detecting it with scintillation crystals before it can get to a normal retina.

Fraser: So it’s unlikely.

Fraser: We’ll call that life form unlikely, here in our gamma ray protected atmosphere.

We’ve run out of questions.

Fraser: Well, we haven’t completely run out of questions – we have mountains of questions still to get through, so we may get a couple more questions shows bunched up here as we continue our tour through the solar system.

If you have any questions about the universe, space, astronomy, previous shows, please feel free to email us your question, or even better send us an audio question and we’ll incorporate it into a future show.

This transcript is not an exact match to the audio file. It has been edited for clarity.


What causes objects to become tidally locked? - Astronomy

It wasn't always this way with the moon -- the moon _used_ to rotate relative to earth, so that an observer on earth would have seen different faces of the moon as it spun. But it gradually stopped spinning due to something called "tidal locking".

You know that the moon causes the tides in the ocean, right? The moon's gravity pulls on the earth, and it pulls most strongly on the face of the earth that is facing the moon. The land on earth doesn't particularly care about this extra tug, but the oceans do. Water is "lifted" towards the moon, and flows to make a bulge that faces the moon. (There is a bulge in the back of Earth too, pointing away, which is related.) As the earth turns, this "bulge" flows through the oceans, always approximately facing the moon we see it as tides moving up and down.

Well, the earth does the same thing back to the moon -- tidal forces from the Earth are about 80 times stronger than the moon's tidal forces on us (because the Earth mass is 80x that of the moon). However, there are no oceans on the moon -- so no liquid sloshes around like it does on earth. Believe it or not, the earth's tidal forces _do_ deform the moon itself, though, ever so slightly. Back when the moon used to rotate relative to us, there was a little "land bulge" on the moon's surface, which "wants" to face the earth. When the moon used to rotate, though, the rotation would tend to carry the "bulge" along with it. This set up a tug of war -- the moon's rotation pulls the bulge away, and the earth pulls back on the bulge, against the rotation. This, then, basically acted like a bicycle brake: the earth's tidal forces constantly acted to pull against the rotation, hereby slowing the rotation down until it stopped. So now -- the "bulge" just points right at us. It's not very big -- but it is still there.

The moon is not the only heavenly body that is tidally locked. Mercury is tidally locked to the sun -- meaning if you lived on Mercury, it would either always be day or always be night, depending on which side of Mercury you lived on.

A longer description can be found at
tidal-locking

They give an estimate for the time it takes for the locking to happen -- my quick math said something like 300,000 years for the moon. Check my math -- I wasn't very careful about it, and may be completely wrong!

The moon revolves around the earth AND also ROTATES on its axis once per month.

So you can do an experiment or demonstration. Imagine the MOON did NOT rotate on its own axis (that is that the moon did not spin around its own axis but ONLY REVOLVED around the Earth. If you do this using a simple demonstration you will note that if THAT was the case, then we would see the entire moon after one revolution.

Now do the demonstration again, but this time allow the moon to rotate on its axis in exactly the same amount of time it takes the moon to revolve around the Earth. you can get a friend plus you as earth and actually demonstrate this to convince yourself.

What a great question! The Moon rotates about its axis every 29.5 days(just like the Earth rotates around its axis every day)--this is why the moon has phases, as different parts of its surface are exposed to the Sun over the course of a month. It also takes the Moon 29.5 days to complete its orbit around the Earth (this is relative to the Earth--from the Sun's perspective, it only takes 27.3 days for the Moon to complete its orbit, but during this time the Earth has been moving along in its orbit around the Sun, and the Moon needs an extracouple of days to "catch up"). Because the time it takes for the Moonto orbit the Earth is the same as it takes for it to rotate about its axis, we always see the same face of the Moon. (You can try this out for yourself--if you walk in a circle around a friend, you will have to rotate at the same rate as you are walking if you want to stay facing your friend.)

It's not just a coincidence that these two things happen at the same rate--we think that a long time ago the Moon actually rotated more quickly than it orbited, so if we had been around then, we would have been able to see different faces of the Moon. The Moon's rotations lowed down, however, due to what are called tidal forces: the side of the Moon that's closer to the Earth feels a slightly stronger pull due to the Earth's gravity than does the side of the Moon away from the Earth, so it deforms a little bit--it gets a little bit longer in the direction facing the Earth. As different sides of the Moon faced the Earth, different parts of the Moon would get deformed, and all of this deformation produced a lot of friction. This friction slowed down the Moon's rotation over a long time, until eventually the same side always faced the Earth, and the deformed part did not have to move anymore.

The Moon's gravity does the exact same thing to the Earth: the waters in the ocean on the side of the Earth that faces the Moon are more strongly attracted to the Moon than are those part-way round the Earth, which in turn are more strongly attracted to the Moon than those that are on the opposite side of the Earth. This is what produces the cycle of low and high tides that you can see in the ocean. The friction of these tides is slowing down the Earth's rotation as well--in the past the Earth rotated about is axis much more quickly, so billions of years ago, days were only a few hours long.

Tides - the moon pulls on the side of the Earth closest to it more strongly than it pulls on the opposite side of the Earth, which effectively stretches the Earth as it is being pulled on from one side but not the other and the Earth is ever-so-slightly flexible. This is what causes the ocean to come up on land on the side facing the moon and the side being (relatively) pulled away, because water is more fluid and flexible than land is, because it is liquid. However, this also exerts a pull on the Earth against the Earth's rotation, just as if you pull on a long projection on something, it will rotate toward the direction you are pulling (imagine pulling on the end of a spoon sitting on the table - the body of the spoon will rotate to be opposite the direction you're pulling). But the Earth is already spinning on its own axis, so the moon's tides are actually slowing the Earth's rotation. This is very slow, but 400 million years ago, the year had about 400 days instead of 365.

Just as the moon exerts tides on the Earth, so does the Earth exert tides on the moon, except the moon has no oceans to get sloshed up and down as this happens. Because the Earth is so much more massive than the moon, the moon inevitably loses more angular momentum in its own rotation. Put simply, it has become tidally locked, with its rotation period being the same as its orbital period, because the Earth is basically dragging it along as it orbits the planet. Because one side of the moon happens to be being pulled on by the Earth, just like the spoon on the table, that side follows the Earth around as it is pulled, and always stays pointed toward the Earth. Thus, we never see the far side of the moon.

A way to visualize why we only see one side of the moon is to walk in a circle while always facing the middle of the circle. While it may not feel like it, you are actually rotating your body while revolving around the circle. The key here is that the period of revolution is equal to the period of rotation. When you have walked halfway around the circle, you face the exact opposite direction compared to when you started. You complete 1/2 revolution in 1/2 rotation, meaning the same rate of revolution and rotation.

The moon's revolution and rotation periods are about 29.5 days. If you want to model the earth and moon together, have a friend stand in the middle of the circle and spin in place 29.5 times for every time you complete a full circle as the moon. Just don't get too dizzy! Your friend in the middle will see you "rising" and "setting" each time he spins in place. This is why we see the moon rise and set each day--the earth spins in place once a day, a rate 29.5 faster than the moon's rate of revolution.

We always see the same side of the Moon because it takes the same amount of time (about 29.5 days) for the Moon to complete one orbit around the Earth as it does for the Moon to complete one rotation about its axis.

Now you're probably wondering why it takes the same amount of time for the Moon to complete one revolution around the Earth as it does for it to complete one rotation about its axis. This is a phenomenon known as tidal locking. The force of Earth's gravity pulling on the Moon causes it to bulge slightly in the direction of the Earth. Now imagine that the rotation of the Moon about its axis were faster (or slower) than its orbit around the Earth. Because the force of gravity is inversely proportional to the square of the distance between two bodies (F=GMm/r 2 , where M and m are the masses of the 2 objects, G is the gravitational constant, and r is the distance between the two objects), the force on the bulge closer to the Earth is greater than the force on the bulge farther from the Earth. Thus the force of Earth's gravity pulling on the bulge would produce a torque (a force that causes rotation) on the Moon, causing the Moon's rotation to slow down (or speed up), until the period (amount of time to complete one cycle) of the rotation of the Moon about its axis and the orbit of the Moon around the Earth are the same.


Why is the moon leaving us?

Earth’s Moon. Credit: James Lennie.

We had a good run, us and the Moon. Grab your special edition NASA space tissues because today we're embarking on a tale of orbital companionship, childhood sweethearts and heartache.

You could say we came from the same part of town. A long time ago the Mars-sized object Theia, collided with the Earth and the Moon was formed out of the debris from the collision.

We grew up together. Counting from the very beginning, this relationship has lasted for 4.5 billion years. We had some good times. Some bad times. Gravitationally linked, arm in arm, inside our solar family sedan traversing the galaxy.

[SNARK:We even still like to go "exploring" the Moon's "surface" once in a while]

But now, tragedy. The Moon, OUR Moon, is moving on to brighter horizons. We used to be much closer when we were younger and time seemed to fly by much faster. In fact, 620 million years ago, a day was only 21 hours long. Now they've dragged out to 24 hours and they're just getting longer, and the Moon is already at a average distance of 384,400 km. It almost feels too far away.

If we think back far enough to when we were kids, there was a time when a day was just 2 – 3 hours long, and the Moon was much closer. It seemed like we did everything together back then. But just like people, massive hunks of rock and materials flying through space change, and their relationships change as well.

Our therapist told us it wasn't a good idea to get caught up on minutiae, but we've done some sciencing using the retroreflector experiments placed by Apollo astronauts, and it looks as though the Moon has always had one foot out the door.

Today it's drifting away at 1-2 cm/year. Such heartache! We just thought it seemed like the days were longer, but it's not just an emotional effect of seeing our longtime friend leaving us, there's a real physical change happening. Our days are getting 1/500th of a second longer every century.

I can't help but blame myself. If only we knew why. Did the Moon find someone new? Someone more attractive? Was it that trollop Venus, the hottest planet in the whole solar system? It's really just a natural progression. It's nature. It's gravity and tidal forces.

And no, that's not a metaphor. The Earth and the Moon pull at each other with their gravity. Their shapes get distorted and the pull of this tidal force creates a bulge. The Earth has a bulge facing towards the Moon, and the Moon has a more significant bulge towards the Earth.

[SNARK:We're pointing our bulges at each other.]

These bulges act like handles for gravity, which slows down their rotation. The process allowed the Earth's gravity to slow the Moon to a stop billions of years ago. The Moon is still working on the Earth to change its ways, but it'll be a long time before we become tidally locked to the Moon.

A series of photos combined to show the rise of the July 22, 2013 ‘super’ full moon over the Rocky Mountains, shot near Vail, Colorado, at 10,000ft above sea level in the White River National Forest. Moon images are approximately 200 seconds apart. Credit: Cory Schmitz

[SNARK:We're not giving up our motorcycle or our unsavory friends any time soon..]

This slowing rotation means energy is lost by the Earth. This energy is transferred to the Moon which is speeding up, and as we've talked about in previous episodes the faster something orbits, the further and further it's becomes from the object it's orbiting.

Will it ever end? We're so attached, it seems like it'll take forever to figure out who's stuff belongs to who and who gets the dog. Fear not, there is an end in sight. 50 billion years from now, 45 billion years after the Sun has grown weary of our shenanigans and become a red giant, when the days have slowed to be 45 hours long, the Moon will consider itself all moved into its brand new apartment ready to start its new life.

What about the neighbors down the street? How are the other orbital relationships faring. I know there's a lot of poly-moon-amory taking place out there in the Solar System. We're not the only ones with Moons tidally locked. There's Phobos and Deimos to Mars, many of the moons of Jupiter and Saturn are, and Pluto and Charon are even tidally locked to each other, forever. Now's that's real commitment. So, in the end. The lesson here is people and planets change. The Moon just needs its space, but it still wants to be friends.

What do you think? If you were writing a space opera about the Earth and the Moon break-up, what was it that finally came between them? Tell us in the comments below.


Nick and Geoff explain why there are two tidal bulges on the Earth – one below the Moon and one on the other side

The cause of tides has been known since the days of Isaac Newton (1642-1727), but it is sufficiently complex to have become a matter for debate amongst the astronomers at Sydney Observatory in recent weeks. Here Nick and Geoff try to explain why the Earth has two tidal bulges due to the Moon – one below and one on the other side.

INTRODUCTION

Consider the sad fate of Astronaut Fred who is falling head-first into a black hole and towards oblivion. As indicated in the instantaneous picture above there is a larger force on his head than on his body and less on his feet. So we can say that his head is being pulled away from his body and his body from his legs.

Astronaut Fred falling into the black hole, in a frame of reference that accelerates at the same rate as Fred’s centre of mass. Drawing Nick Lomb

We can look at Astronaut Fred in a more sophisticated way. If we choose a frame of reference that falls with Fred’s centre of mass (CoM). Then, as Fred’s fall is largely taken care of by the frame of reference, what we are left with on the above diagram are the remaining forces that are slightly different from the main gravitational force on Fred’s CoM. As his head is accelerating towards the black hole even in this frame of reference, it experiences a force away from his CoM. Similarly, Fred’s legs are accelerating away from the black hole in this frame of reference, they experience a force away from the CoM.

These forces that represent differences from the main force acting on a body’s CoM are called tidal forces.

A simple instantaneous picture explaining tides, drawing Nick Lomb

Now let us consider tides on the Earth’s oceans caused by the Moon under the simple instantaneous picture. The forces on the Earth’s CoM must be balanced. Gravity is pulling towards the Moon and so we have to introduce the fictitious centrifugal force (connected with rotation) away from the Moon.

On the side of the Earth directly below the Moon gravitational pull from the Moon is stronger as the distance is shorter while centrifugal force is less. This unbalance leads to bulge towards the Moon. On the other side of the Earth gravitational pull towards the Moon is less as the distance is greater while centrifugal force is more. Again there is a bulge, this time away from the Moon.

A more sophisticated picture of tides on Earth in a frame of reference co-moving with the Earth’s centre of mass. Drawing Nick Lomb

As with Astronaut Fred we can look at tides in a more sophisticated way if we choose a frame of reference that co-moves with the Earth’s CoM. Again that accounts for the main acceleration towards the Moon and what we are left with in the diagram above are the tidal forces, that represent slight differences to the main force on the CoM.

The oceans below the Moon are accelerating less towards the Moon than they would need to according to the greater gravitational pull they experience than the CoM. Hence there is a tidal force towards the Moon and a tidal bulge. Similarly on the other side of the Earth acceleration is too much according to the gravitational pull at that location. Hence there is a tidal force away from the Moon and a tidal bulge.

DETAILED EXPLANATION

Although rather simplistic, a force is simply a push or a pull and throughout the Universe there are only four types(1). From the rotation of galaxies to the inside of the atom, four simple types of force reign supreme. They are in order of decreasing strength:

1. The Strong Nuclear Force
2. The Weak Nuclear Force
3. The Electromagnetic Force, and
4. The Force of Gravity.

Amazingly, the Strong Nuclear Force is 10 to the power of 40 times stronger than gravity yet its range is stunningly small and limited to the realm of the nucleus. Gravity however, a mere wimp in comparison acts over unlimited distances with ever diminishing strength as we shall see.

Along with Einstein, one of the greatest contribution to the study of gravity occurred in the period of 1665 to 1667 when plague forced Sir Isaac Newton (1642-1727) to flee London. Most of us have heard the story that he was struck upon the head by a falling apple and wondered what made it fall. It is very likely this is apocryphal, but perhaps he did see an apple fall whilst in a contemplative mood. By applying his second law of motion which states “The acceleration of an object is proportional to the net force applied to it and inversely proportional to its mass” Newton realised that some force must pull or push the apple down. Might this same force act on objects a long way away like the Moon?

He eventually devised the theory of Universal Gravitation in which gravity is the force of attraction between all objects of mass to every other object of mass. His formula for Universal Gravitation is as follows:

In it, the force of gravity between two objects of mass (m) and (M) is equal to their product multiplied by the constant of Universal Gravitation (G) divided by the distance between them squared. If the mass of the objects does not change then we can see that the force between them is inversely proportional to the square of their distance from one another. Using this formula alone, the Sun exerts more than 170 times the force of gravity on the Earth than does the Moon, after all the Earth orbits the Sun. So why is the tidal influence of the Moon so much more noticeable than that of the Sun? Consideration of the above formula reveals that objects other than point sources such as voluminous planets and stars will experience a difference in gravity potential from one side to the other. Algebraically we can derive that tidal forces, a difference in force across an object due to gravity, follows an inverse cubed relationship. Clearly distance becomes much more critical in this case.

Where (M) and (m) are the mass of the primary object and its satellite with a radius (R) at distance from one another of (r) and assumes that R/r is very small. The difference in gravity potential or the gravitational field across the object is the key to tides and not simply the magnitude of the force. As a result the influence of the Sun on tides drops to 46% of the effect of the nearby Moon.(2)

The tidal pull of the moon raises and lowers the rocky surface of the Earth by about 0.3m (3) every day while the more elastic water can be raised by up 15m depending on surrounding terrain but in which direction?

At this point we need to turn to Kepler’s Third Law.

Where (P) is the period, (a) is the semi major axis and (k) is a constant. Therefore for any orbiting object the period of its orbit squared multiplied by the semi major axis of its orbit cubed equals a constant.

Kepler’s Third Law in Action, drawn by Geoff Wyatt

In the above diagram Geoff is in a stable orbit of (O) to the left. (B) is the centre of the planet and describes the orbit. As the planet is a solid object (A) according to Kepler’s third law is orbiting too quickly for its orbital radius (O to B- [B to A]) and tends to push inwards creating a bulge. (C) is orbiting too slowly for its orbit (O to B + [B to C]) and the resulting force tends to push or bulge planet outwards.

A more detailed analysis utilizing Newton’s gravitation which can be derived from Kepler’s Laws also explains two tidal bulges as the result of differences in forces caused by a distant object.

Vector Analysis of Tidal Forces 1, from Donald Simanek

In this image taken from Donald Simanek’s page on “Misconceptions about Tides” vector analysis for four points A,B, H and D reveals the following.(4)

Object (G) exerts a gravitational force on (M) that follows the inverse cube law as stated above. All vectors are directed towards (G).
Consider a person standing at (H). There will be a greater force on their head than their toes and the tidal force (T), will be given by the difference, TH = FH1 – FH2. The net force is shown by the vector subtraction on the lower left with the resultant force towards (G).
Now consider a person on the other side of (M) at (A). The force on their toes is greater than on their head and the difference in forces is TA = FA1 – FA2 but as can be seen by the vector diagram on the upper left the resultant force is away from (G).

For a person at (D) the forces are almost identical and parallel as a result the tidal force points towards the centre of (M) and at (B) the resultant vector is tangential to (M).

Vector Analysis of Tidal Forces 2, from Donald Simanek

If this process were conducted for many points on the surface the above diagram would result. Two tidal bulges are clearly seen on (M), one on the side toward the attracting mass and the second on the far side of (M).

A wonderful example of tides and their uses can be seen at Mont St Michel in France where the incoming tide completely surrounds the island even protecting its inhabitants from invaders in the past.

Curiously some scientists believe we owe our very existence to the tides. For without them the seas would not rise and fall several times a day creating an opportunity for sea creatures to gain foothold on land in the tidal zone between high and low tide.(5)

Apart from the rising and falling of the each objects surface the other major tidal force effect is that the Moon was gravitationally locked to the Earth when in a molten state and remains so locked. Being tidally locked the Moon has reached its lowest energy state and rotates once on its axis every rotation around the Earth.

Tidal recession of the Moon

As both objects bulge towards the other but not in a perfectly straight line as a result of the Earths rapid rotation, a torque or turning force due to tidal friction arises that slows the Earth’s rotation and pushes the Moon away from the Earth in order to conserve angular momentum. The diagram above shows that as the Earth’s tidal bulge leads the Moon by about 6 hours the forces between the Moon and the bulge balance as per Newton’s Third Law. However the overall effect of the two forces is to slingshot the Moon ahead hence pushing it out while at the same time opposes the Earth’s rotation and slows it down. Yes the days are getting longer!

A crater chain on the Moon

The Moon is also, clearly, a long suffering victim of tidal forces from other places in the Solar System. In the image below of Davy Crater, a crater chain has most likely been caused by the tidal disruption of a loosely bound comet, which then collided with the Moon. Pre impact, the comet passed by a more massive object, quite probably Jupiter, and was subjected to tidal forces which pulled it apart. The loosely bound objects then peppered the Moon in quick succession.

Comet Shoemaker-Levy 9 collisions with Jupiter

A more recent and spectacular example of a similar event was the tidal disruption of Comet Shoemaker Levy No.9 in 1992, before colliding with Jupiter in 1994. As the comet approached Jupiter, the leading side was subjected to a stronger force than the trailing side. As it was comprised of loosely bound particles, it simply fell apart under the tidal difference and formed a train of 21 large pieces. Two years later, after it passed the Sun, its altered orbit put it on a collision course with Jupiter and led to a spectacular series of impacts.

Tidal forces, by the very nature of gravity, are seen throughout the Solar System. The second largest object in the Solar System, Jupiter, has at least 63 moons (6). Its inner most moon, Io, is subject to the most violent volcanic activity witnessed because of the changing gravitation fields or tidal forces. A complex gravitational dance between Jupiter and the other large nearby moons subject Io to constantly changing forces. As Io flexes between 50 and 100m over short periods enough friction is generated to heat the interior to the point of volcanism.

Another large moon, Europa, is also tidally heated (7) to a point where, just a few metres below its icy surface, alkaline liquid water is known to exist which would otherwise be frozen. Earth does not, therefore, have exclusivity on liquid water.

Even large scale features such as galaxies can be affected by tides. If they get too close to one another they can be subject to disruptive tidal forces with perhaps the most beautiful example being the Antennae galaxy.

The Antennae, galaxies in collision, Hubble Space Telescope image

In this Hubble Space Telescope Image, the preceding and following arms are the result of tidal forces between the two galaxies. As they approach one another stars are being drawn ahead into a leading arm, while others across the galaxy, where the tidal force is less, are left behind at the same time. Eventually, tidal forces will drive them to be roughly spherical in nature, a shape that would have pleased Aristotle immensely.(13)

Geoff Wyatt and Nick Lomb, Sydney Observatory

BIBLIOGRAPHY

(1) http://cnx.org/content/m14044/latest/
(2) http://en.wikipedia.org/wiki/Tide
(3) http://www.astronomycast.com/solar-system/episode-47-tidal-forces/
(4) http://www.lhup.edu/

DSIMANEK/scenario/tides.htm
(5) http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0102-1- phase/TIDESONLIFE.htm
(6) http://www.nineplanets.org/jupiter.html
(7) http://www.resa.net/nasa/europa_life.htm
(8) http://physics.fortlewis.edu/Astronomy/astronomy%20today/CHAISSON/GLOSSARY/GLOSS_R.HTM
(9) http://www.britannica.com/eb/article-9063949/Roche-limit
(10) http://en.wikipedia.org/wiki/Roche_limit
(11) http://en.wikipedia.org/wiki/Roche_limit
(12) http://www.astronomycast.com/solar-system/episode-47-tidal-forces/
(13) http://www.astronomycast.com/solar-system/episode-48-tidal-forces/

IMAGE CREDITS

Sir Isaac Newton http://www.virtualmuseum.ca/Exhibitions/Annodomini/THEME_15/IMAGES/J991825.jpg
Johannes Kepler http://www.nasa.gov/vision/universe/starsgalaxies/kepler_prt.htm
Vector Analysis of Tidal Forces 1 http://www.lhup.edu/

DSIMANEK/scenario/tides.htm
Vector Analysis of Tidal Forces 2 http://www.lhup.edu/

DSIMANEK/scenario/tides.htm
Mont St Michel http://www.gites-de-bretagne.com/images/montstmichel_lge.jpg
Tidal Recession of the Moon http://odin.physastro.mnsu.edu/

eskridge/astr102/spinslow.gif
Davy Crater Chain http://www.lpi.usra.edu/publications/slidesets/3dsolarsystem/slide_17.html
Shoemaker Levy 9 and Jupiter http://www2.jpl.nasa.gov/sl9/
Antennae Galaxy http://hubblesite.org/newscent er/archive/releases/1997/34/image/a/format/large_web/
Plato and Aristotle http://en.wikipedia.org/wiki/Image:Sanzio_01_Plato_Aristotle.jpg


NASA Blueshift

So here we are, two souls bound by the gravity of our hearts, orbiting each other’s thoughts as the universe sets on the cosmic ocean. The universe seems to slow as we drift around the quasar, and millennia seem to pass. Stars shoot across the void, and our eyes connect. Your gaze meets mine, and we are tidally locked. I grab your hand. “I have something to show you,” I whisper. You follow me towards the constellation Cancer.

And that is where I insert my foot into my mouth, because I am about as smooth as mashed potatoes. But why am I interested in the constellation Cancer? Because in 2004, astronomers discovered a planet orbiting the star 55 Cancri, a star very similar to the Sun. 55 Cancri, also known as Rho Cancri, is part of a binary star system just at the end of the ”Y” shape in Cancer, about 40 light years away. The Planet was named 55 Cancri e. Astronomers have adopted a standard in naming planets outside of our solar system that uses the host star’s name followed by a letter that corresponds to the order in which a planet was found. So 55 Cancri e is the 5 th (and most recent) of the 5 planets discovered around 55 Cancri (the two stars in the binary system use a capital “A” and “B” in their names to differentiate them).


Visualization of the Cancri system
Credit: NASA/JPL-Caltech/T. Pyle (SSC)


55 Cancri e is incredibly close to its star, which causes the planet’s temperatures to rise to about 9200 degrees Fahrenheit (add my smoothness and incredibly good looks and romance is in the air). How close is this planet to its host? We are talking 25 times closer than Mercury is to the Sun! Mercury‘s orbit averages 35,980,000 miles from the Sun and lasts roughly 87 days on Earth. 55 Cancri e is 3,532,320 miles from its star (more than 30,000,000 miles closer than Mercury’s orbit to the Sun), and makes a full orbit in around 18 hours. Let’s think about this for a moment. Mercury has an 87 day orbit, and 55 Cancri e has an 18 hour orbit. It takes Earth a year to orbit the Sun and 24 hours to rotate. Could Cancri e’s years be shorter than its days? No – because 55 Cancri e has no days! In fact, 55 Cancri e is tidally locked with its star. Remember that hunk of rock that orbits Earth? That’s right I’m talking about you, Moon! Have you ever noticed that you always see the same face? Well the Moon is tidally locked with the Earth, so as it orbits Earth, its rotation is such that the same face is always staring right at us, watching and judging. (But let’s not confuse ourselves here – the Moon is tidally locked with the Earth, not the Sun, so it still has day and night as the Earth-Moon system orbits the Sun.) 55 Cancri e is so close to its star that the same situation is happening, and one face is getting perpetual scorching heat from the star. So half of the planet is always facing the star in a permanent day, and the other half is shrouded in perpetual darkness. Night and day changes from a reference of time… to a reference of place.


Visualization of “Super Earth” 55 Cancri e
Credit: NASA/JPL-Caltech

What’s really exciting about this planet is that it is believed to be made mostly of diamond (and this is why I brought you here). And by mostly diamond, I mean the value of the planet has been theorized to be around $26.9 nonillion. I can hear the gears in everyone’s head grinding. A nonillion is 1,000,000,000,000,000,000,000,000,000,000 (30 zeroes). To give you a bad example of a nonillion (there aren’t any good ones), if I covered the Earth in a nonillion one dollar bills, the bills would create a layer 12 million miles thick – nearly half the distance from Earth to Venus’ orbit. The World Bank estimates the value of Earths GDP to be a meager $70 trillion (12 zeroes). To be fair, 55 Cancri e is double the radius of Earth’s 3,959 miles and is 8 times more massive, which puts 55 Cancri e in the criteria to be called a super-Earth. After estimating the planet’s mass and radius, and studying its host star’s composition, scientists think the rocky world is composed mainly of carbon (in the form of diamond and graphite), as well as iron, silicon carbide, and potentially silicates.


Artist’s concept of Earth vs 55 Cancri e
Credit: NASA/JPL-Caltech/R. Hurt (SSC)

Understandably, scientists are not going to these places and taking samples or pictures. How do we know what we do about this planet? Originally it was thought that 55 Cancri e had originated with a composition similar to Earth, and that being so close to its star, the immense heat and pressure caused a lot of super-critical fluids to ooze out of the nooks and crannies of the planet. Super-critical fluids behave in ways that are similar to gases and liquids. However as scientists studied the light from the host star, we’ve been able to tell that the metallicity of the star is uniquely high, meaning that there is an abundance of elements greater than helium within the star, specifically carbon. In turn, this shows that the planet is likely to be composed of carbonaceous material as well. And with the immense heat and pressure, we get the diamonds we are so fond of. But let’s not be so narrow-minded. This planet may be a very diverse system with many more things to observe and appreciate… but that is a lot of diamond. A small piece wouldn’t hurt. My imagination is proving rather fruitful as of late!

Now that I am a galactic super power with more money than I can possibly fathom, let’s not overstay our welcome. Maybe we should find some place to hold out a bit, reflect on the excitement for awhile – and since we are probably wanted for interstellar robbery, perhaps somewhere like the largest void in the known universe? As always, leave a comment or two or three and we’ll see what else the universe has in store for us!