Correlation of planet sizes with star sizes?

Correlation of planet sizes with star sizes?

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I did my own amateur Kepler data analysis in May of this year of data from discoveries. I found a strong correlation between star size and planet size (percentages). 37 of the 44 planets confirmed (84.1%) orbiting M dwarfs were less than 2.0 R(Earth) with only one hot Jupiter. 129 of 241 (53.6%) orbiting K dwarfs were less than 2.0 R(Earth) with 9 hot Jupiters (3.7%). 196 of 517 (37.9%) orbiting G dwarfs were less than 2.0 R(Earth) with 49 hot Jupiters (9.5%). 92 of 213 (43.2%) orbiting F dwarfs were less than 2.0 R(Earth) with 23 hot Jupiters (10.8%). I would like to know how much of this correlation is probably real and how much is biased by the limits of the study? Biases I am aware of are the fact that the Kepler study is primarily of systems with "close in" planets, (only 90 of 1015 confirmed as of 4/1/15 are over 0.3 AU) and that only 4.3% of the "Kepler stars" are M dwarfs. I also see biases that might arise from the methods of confirming the planets (Kepler stars from 110 to 405 had planets confirmed by the "multiple candidate" method). It also appears that there may be a greater difference between K and G star systems than between G and F. Where can I find a more professional analysis of this type?

I think there are a number of studies that look at these statistics; I'll try to dig some out. In the meantime I can give you some further things to ponder.

First, let's assume a null hypothesis that the statistics and mass distribution of planets were independent of stellar mass - what would we observe?

Well one selection bias you don't mention is that the likelihood of transit detection depends on the ratio of planet to star size. This means you are less likely to see small planets around F-stars than M-stars. Or to put it another way, you expect the fraction of large planets to increase with stellar mass - as you have found.

It is quite likely that the material available to form planets is correlated with the stellar mass - in other words there is a correlation between stellar mass and protoplanetary disc mass. In which case it could be quite difficult for smaller stars to have the requisite protoplanetary disc density to form giant planets before the disc disperses.

The Sun

  • If the Sun were a front door, the Earth would be the size of a nickel
  • The Sun makes up 99.8% of the mass in our solar system
  • If you combined every planet in the solar system, the Sun would still be 50x larger
  • The Earth could fit inside the Sun 12,000 times


  • Mercury has no atmosphere and is a volcano-rich planet
  • Its orbital speed is 29.7 miles per second
  • For every two orbits around the Sun, Mercury rotates on its axis 3 times
  • Mercury is the second densest planet in our solar system


  • Referred to as Earth’s sister
  • Has no rings or moons
  • Probes cannot land on Venus due to its dense cloud of sulfuric gases
  • This planet rotates clockwise, while all other planets rotate counter-clockwise
  • Venus has a very weak magnetic field


  • An orbit around the Sun takes 365.24 days, and a day lasts 24 hours
  • Surface temperature ranges from -88 to 58 degrees Celsius
  • The Earth’s rotation is gradually slowing, so in 140 million years, the length of a day will increase to 25 hours
  • The Earth tilts approximately 66 degrees on its rotational axis
  • Mars’ average orbiting speed is 14.5 miles per second
  • Mars is the second smallest planet in the solar system
  • Mars is extremely cold with an average temperature of -60 degrees Celsius and down to -125 degrees in winter


  • Jupiter is large enough to encompass all of the other planets combined.
  • Has an ongoing hurricane named the Great Red Spot, and is so big that earth could fit twice within it
  • Jupiter protects earth from meteors
  • Jupiter is comprised of helium and hydrogen
  • Scientists still don’t know if Jupiter has a solid or gaseous core


  • Saturn is the most distant from the Sun that can be seen by the naked eye
  • Saturn is composed of hydrogen, methane, and helium
  • Saturn has 82 moons and 30+ rings
  • Saturn’s surface temperature is -139 degrees Celsius


  • Uranus is the third largest in terms of size and the fourth largest regarding mass, and is one of the lease dense planets in our solar system.
  • Uranus has a tilt of 98 degrees
  • Uranus is the first planet discovered by using a telescope
  • One orbit takes 84 Earth years and one day on Uranus is 18 Earth hours


Neptune is the furthest planet from the Sun, being 4,497.1 million km away. Neptune has a diameter of 49,528 km and a mass of 10.243 (1024). Uranus is composed of hydrogen and helium and is surrounded by a cloud layer with winds faster than the speed of sound (2,100 km per hour). An abundance of methane givens Neptune a brilliant blue colouring. One orbit around the solar star takes roughly 165 Earth years, and one day on Neptune is 19 Earth hours. Here are some interesting facts about Neptune:

  • Officially discovered in 1846 and was the first predicted planet
  • Has 14 moons and a thin collection of rings
  • Fourth largest planet in the solar system
  • Neptune is the coldest planet in the solar system with average temperatures of -200 degrees Celsius


Ah, the "famous planet that is not a planet". Perhaps it is not technically considered a "standard" planet. But we still like to include it in our Solar System model.

Astronomy Picture of the Day

Discover the cosmos! Each day a different image or photograph of our fascinating universe is featured, along with a brief explanation written by a professional astronomer.

2013 June 6
Star Size Comparisons
Video Credit & Copyright: morn1415 (YouTube)

Explanation: How big is our Sun compared to other stars? In a dramatic and popular video featured on YouTube, the relative sizes of planets and stars are shown from smallest to largest. The above video starts with Earth's Moon and progresses through increasingly larger planets in our Solar System. Next, the Sun is shown along as compared to many of the brighter stars in our neighborhood of the Milky Way Galaxy. Finally, some of the largest stars known spin into view. Note that the true sizes of most stars outside of the Sun and Betelgeuse are not known by direct observation, but rather inferred by measurements of their perceived brightness, temperature, and distance. Although an inspiring learning tool that is mostly accurate, APOD readers are encouraged to complete the learning experience -- and possibly help make future versions more accurate -- by pointing out slight inaccuracies in the video.

Why do astronomers use scientific notation to describe sizes?

Astronomers use scientific notation to describe sizes as sizes very a lot. For example, distance to moon is #385,000# kilometers, but distance to Sun is about #150,000,000# kilometers (this is known as AU - Astronomic Unit of distance) and average distance of Neptune, farthest planet is #30# AU or #4,500,000,000# kilometers and it may take just around #4# hours for light to reach Neptune.

Now compare it with the nearest star Proxima Centauri, which is at a distance of four light-years and as in one year there are about #8766# hours, the distance to Proxima Centauri is about #8766# times the one to Neptune or in kilometers it will be

This is still very small as compared to size of universe. For example, the bulge at the center of milky way is about #12000# light years or #3000# times distance to Proxima Centauri.

Further the observable universe spans some #93# billion light-years in diameter, as it is still expanding i.e.

A similar scale may apply to volumes, mass and number of stellar objects. It is for these reasons that astronomers use scientific notation to describe sizes.

Astronomy 102 Specials: The Hertzsprung-Russell Diagram and the Correlation between Temperature and Luminosity

One of the most conspicuous features of a Hertzsprung-Russell (H-R) diagram for any group of stars is the diagonal band running from upper left to lower right where nearly all of the stars are located. This band is called the Main Sequence , and because it's so prominent for any group of stars, it must be important and worthy of further study.

The existence of a Main Sequence in an H-R Diagram indicates that for most stars, there is a correlation between luminosity and temperature. Recall that the x-axis on the H-R Diagram is Temperature and that it's plotted backwards, and that the y-axis on the H-R Diagram is Luminosity, plotted the right way. A correlation is evident because the stars aren't distributed randomly on the plot, but rather in a well-confined region. The plot below shows the Main Sequence as a single line rather than a collection of points. I've done this by calculating the average luminosity for the collection of stars at each temperature, and then plotting only one point to represent all of these stars. Mostly, it makes the plot a bit easier to read.

Note that the correlation between temperature and luminosity is a direct one --- that is, as the temperature increases (i.e., as you go leftward on the plot), the luminosity increases. This direct correlation is somewhat reminiscent of the relationship we learned between the temperature and luminosity of a blackbody emitter. Recall that for a blackbody, the total intensity and temperature are related as follows:

where I is the intensity, and T is the temperature. Furthermore recall that the power, or equivalently, the luminosity emitted by a blackbody is:

where S is the surface area of the emitter. For a sphere (all stars are spherical):

where R is the radius of the sphere. Now, combining these three relations, we get:

and we find that for a blackbody emitter, there is a direct relationship between the temperature and the luminosity. Could this relationship explain the direct correlation between temperature and luminosity seen in the H-R Diagram? It seems pretty plausible, since for a lot of reasons we think that stars emit mostly like blackbodies.

Let's find out. The way to do this is to create a model of how a star would emit if it behaved exactly like a blackbody. The simplest model is to assume that all stars are the size of the Sun, since the Sun is the one star whose size we know. Then our model gives us a direct relationship between the temperature and the luminosity as follows:

= 4 x 3.14 x 5.67 x 10 -8 x (6.96 x 10 8 ) 2 T 4

We can plot this relationship directly onto the H-R Diagram by calculating the luminosity we'd get for a bunch of different temperature model stars. This will give us a line on the H-R Diagram.

If our model line and the Main Sequence were one and the same, we could conclude that our model "fits" the data, and that our simple blackbody model explains the correlation between temperature and luminosity in real stars. However, these two lines don't overlap, and so we can't claim to have explained the correlation.

In fact, our model does a pretty lousy job of predicting the luminosity of Main Sequence stars based on their temperature. For example, when we plug 11220 K for a temperature into the model, we get out a luminosity of about 14 times the luminosity of the Sun, or 14 L o (as indicated by the blue plus in the above figure). However, real stars with surface temperatures of 11220 K have luminosities of nearly 100 L o , or about a factor of five or so higher. Therefore, we have a lot more work to do before we can claim a fit.

Even though the model doesn't fit very well, we would still like to keep some parts of it because they make sense. The first and perhaps most important is that stars behave like blackbodies. There are a lot of reasons we believe this to be so, including the fact that the broadband spectra of stars have the characteristic blackbody shape, and that the temperatures derived from spectral line observations agree with the temperatures derived from fitting the broadband spectrum with e blackbody curve. So, it's worthwhile to try to keep the blackbody assumption if at all possible.

However, we've made another assumption in our model which is almost completely unjustified. We just chose a size for all stars based on our knowledge of the size of the Sun. While this is probably a good starting point, since the Sun is the only stellar object for which we can measure a size, there's no reason all stars have to have the same size as the Sun. What if there exist stars whose sizes are three times larger than that of the Sun? What kind of temperature-luminosity relation might those stars have?

Well, for a given temperature, a larger star will have a larger luminosity. Why? Because while the temperature determines the intensity of the surface of the star, the larger star will have more surface area and therefore will radiate more luminosity, even if the temperatures and therefore the intensities of the two stars are the same (you had a question on this in Problem Set #2 now you know why). So we might expect that the blackbody model for larger stars might appear higher on the H-R Diagram than the line for Sun-sized stars. Likewise, the blackbody model for stars smaller than the Sun would appear lower on the H-R Diagram, since smaller stars have less surface area for radiating.

And that's exactly what you get:

All three model curves have the same slope, and this slope is not the slope of the Main Sequence, so individually, none of these models is going to fit the Main Sequence. This says that stars on the Main Sequence aren't all of the same size, which when you think about it is just fine. After all, why should all stars be the same size anyway?

Although these models individually don't match the Main Sequence, together they span much of the Main Sequence. That is, as long as you don't mind using different star sizes for different parts of the Main Sequence, we can explain all of the stars with a blackbody model where the temperature and star size increase together. Low temperature Main Sequence stars can be best explained by our blackbody model if their sizes are also smaller than the Sun, and high temperature Main Sequence stars can be best explained if their sizes are also larger than the Sun.

Thus we can explain the apparent correlation between temperature and luminosity in the HR Diagram in terms of a blackbody model and another correlation -- the correlation between temperature and size -- for Main Sequence stars. In addition, we can also see that position on the H-R Diagram can tell us the size of the star stars in the upper right are much larger than the Sun, and stars in the lower left are much smaller than the Sun. The stars of the Main Sequence fall in a relatively narrow range of sizes, with radii ranging from about 30% of the Sun's radius to about 10 times the Sun's radius.

We'll see in later sections of the course that this new correlation between surface temperature and star size is a result of yet another more fundamental parameter --- the star's mass.

Astronomy Picture of the Day

Discover the cosmos! Each day a different image or photograph of our fascinating universe is featured, along with a brief explanation written by a professional astronomer.

2018 June 12
Star Size Comparison 2
Video Credit: morn1415 (YouTube) Images Credit: NASA (typically) Music: Alpha (Vangelis)

Explanation: How big is our Sun compared to other stars? In dramatic and popular videos featured on YouTube, the relative sizes of planets, stars, and even the universe are shown from smallest to largest. The featured video begins with Earth's Moon and progresses through increasingly larger moons and planets in our Solar System. Soon, the Sun is shown and compared to many of the brighter stars in our neighborhood of the Milky Way Galaxy. Finally, star sizes are shown in comparison with the Milky Way Galaxy, galaxies across the observable universe, and speculatively, regions of a potentially greater multiverse. Note that the true sizes of most stars outside of the Sun and Betelgeuse are not known by direct observation, but rather inferred by measurements of their perceived brightness, temperature, and distance. Although an inspiring learning tool that is mostly accurate, APOD readers are encouraged to complete the learning experience -- and possibly help make future versions more accurate -- by pointing out slight inaccuracies in the video.

Solar System Size and Distance

How big are the planets and how far away are they compared to each other? See how the sizes of planets and the distances between them compare. And find out why it's so hard to create a scale model of the solar system that accurately represents both size and distance on a single screen or the page of a book.

Watch en Español: Seleccione subtítulos en Español bajo el ícono de configuración.

Video Transcript

If you could drive around the entire planet, it would take more than sixteen days of non-stop driving at highway speeds.

But, compared to some of the planets in our solar system, it’s pretty small.

We often see planets displayed as similar in size, like this, to make details on smaller planets easier to see.

In reality, the size of planets compared to each other looks more like this.

Even though this shows the sizes of planets accurately, they aren’t that close together.

Because of the great distances between planets, and the planets relatively small sizes compared to those distances, it’s practically impossible to create a visual representation on a screen or the page of a book that realistically represents the sizes of the planets and the distance between them.

As a result, the best we can usually do is show the accurate sizes of planets or the accurate distances between the planets.

Remember, they’re not actually lined up like this.

In space, the planets’ positions are constantly changing as they revolve around the Sun.

SOLVED-Scope Sizes and Star Magnitudes

With each respective telescope size, what star magnitude is it capable of?

Edited by StarTrooper, 23 July 2020 - 10:00 PM.

#2 coopman

#3 coopman

This is very dependent on your amount of light pollution, of course.

#4 ShaulaB

If you are not fully dark adapted, you won't get to the limits visually. That's the problem with using a phone, tablet, or laptop while observing. An app might come up that undoes the red-screen, and oops, dark adaption is gone for another 20 minutes.

#5 Redbetter

Naked eye in dark sky I still go to 7.0 mag without correcting my myopia. When I was in pristine skies 25 years ago I could reach 8.0. so there is a lot of room above 8.5 mag for a 6" in dark sky. (I can take 6" into the 15's on a good night with a good scope.) Of course naked eye is totally different than single eye telescopic. Binocular vision helps naked eye, but wide pupils have more aberration (astigmatism primarily). Meanwhile, telescopic limiting magnitude is achieved at small exit pupil/high magnification which improves contrast several fold.

I recover rapidly from deep red LED chart reading, more slowly from less red sources. The eye has to adapt anyway going from ambient 21 to 22 MPSAS conditions to 25-27 MPSAS+ in the eyepiece in dark sky conditions. Even if you are perfectly dark adapted to 22 MPSAS, the background of the eyepiece in dark sky will be far dimmer at high power. From my own tests my eye can still distinguish a difference at 28 MPSAS or a bit beyond, which is

250x dimmer background. This is one of the reasons why it takes some time at the eyepiece before you see the faintest details and your ability to go deeper plateaus. The eye adapts for the darker background. [Note that the background thermal isomerization of rhodopsin in the eye results in a background glow in the 25-26 MPSAS range if I recall correctly. I have worked through the numbers in the past.]

A bigger factor as aperture increases is seeing. My 20" is usually operating about 1 mag below what it can do for my eye, because the sky is not steady enough and magnification has to be kept lower so as not to blur stellar images to the point they are harder to detect, rather than easier. The image, even in the best moments, is of reduced contrast rendering it harder to detect an 18 mag star on anything but the best nights. On what I consider good nights, mid 17's is typical Mediocre nights top a little over 17.0. While small unobstructed apertures are less impacted, I still find it more difficult to detect to the limits with a 60mm refractor in poor or mediocre seeing, and end up handicapped to some degree compared to what it does in good seeing.

In stable skies with a decent refractor I exceed the Method 1 calcs above by about 1 mag or a little more. The last half magnitude is very challenging and requires some experience and good conditions. The half magnitude before that requires some effort and healthy eyes.

17 New Planets – Including Earth-Sized World – Discovered by Astronomy Student

University of British Columbia astronomy student Michelle Kunimoto has discovered 17 new planets, including a potentially habitable, Earth-sized world, by combing through data gathered by NASA’s Kepler mission.

Over its original four-year mission, the Kepler satellite looked for planets, especially those that lie in the “Habitable Zones” of their stars, where liquid water could exist on a rocky planet’s surface.

The new findings, published in The Astronomical Journal, include one such particularly rare planet. Officially named KIC-7340288 b, the planet discovered by Kunimoto is just 1 ½ times the size of Earth — small enough to be considered rocky, instead of gaseous like the giant planets of the Solar System — and in the habitable zone of its star.

“This planet is about a thousand light-years away, so we’re not getting there anytime soon!” said Kunimoto, a Ph.D. candidate in the department of physics and astronomy. “But this is a really exciting find, since there have only been 15 small, confirmed planets in the Habitable Zone found in Kepler data so far.”

UBC astronomy student Michelle Kunimoto. Credit: UBC

The planet has a year that is 142 ½ days long, orbiting its star at 0.444 Astronomical Units (AU, the distance between Earth and our Sun) — just bigger than Mercury’s orbit in our Solar System, and gets about a third of the light Earth gets from the Sun.

Of the other 16 new planets discovered, the smallest is only two-thirds the size of Earth — one of the smallest planets to be found with Kepler so far. The rest range in size up to eight times the size of Earth.

Kunimoto is no stranger to discovering planets: she previously discovered four during her undergraduate degree at UBC. Now working on her Ph.D. at UBC, she used what is known as the “transit method” to look for the planets among the roughly 200,000 stars observed by the Kepler mission.

“Every time a planet passes in front of a star, it blocks a portion of that star’s light and causes a temporary decrease in the star’s brightness,” Kunimoto said. “By finding these dips, known as transits, you can start to piece together information about the planet, such as its size and how long it takes to orbit.”

Kunimoto also collaborated with UBC alumnus Henry Ngo to obtain razor-sharp follow-up images of some of her planet-hosting stars with the Near InfraRed Imager and Spectrometer (NIRI) on the Gemini North 8-meter Telescope in Hawaii.

“I took images of the stars as if from space, using adaptive optics,” she said. “I was able to tell if there was a star nearby that could have affected Kepler’s measurements, such as being the cause of the dip itself.”

In addition to the new planets, Kunimoto was able to observe thousands of known Kepler planets using the transit-method, and will be reanalysing the exoplanet census as a whole.

“We’ll be estimating how many planets are expected for stars with different temperatures,” said Kunimoto’s Ph.D. supervisor and UBC professor Jaymie Matthews. “A particularly important result will be finding a terrestrial Habitable Zone planet occurrence rate. How many Earth-like planets are there? Stay tuned.”

Reference: “Searching the Entirety of Kepler Data. I. 17 New Planet Candidates Including One Habitable Zone World” by Michelle Kunimoto, Jaymie M. Matthews and Henry Ngo, 25 February 2020, The Astronomical Journal.
DOI: 10.3847/1538-3881/ab6cf8

Watch the video: Επικη συγκριση Συμπαντος (August 2022).