# Astronomy in a Simple Solar System

• I
The phases of Venus and Mercury are conclusive evidence that they orbit the sun, while the lack of phases on Mars and Jupiter is not conclusive.f

TL;DR Summary
Is there a simple way of proving that the Earth moves around the Sun and not vice versa?
It seems to me that Galileo and his successors benefitted from there being other bodies in the solar system other than the Earth and the Sun to prove that the Earth (and other bodies) orbited the Sun, and not the other way round.

In an imagined solar system where the Earth has no moon, and there are no other planets, asteroids, comets, etc, is there a (relatively) simple way of proving that the Earth orbits the Sun, and not the other way round?

best regards ... Stef

It seems to me that Galileo and his successors benefitted from there being other bodies in the solar system other than the Earth and the Sun to prove that the Earth (and other bodies) orbited the Sun, and not the other way round.

In an imagined solar system where the Earth has no moon, and there are no other planets, asteroids, comets, etc, is there a (relatively) simple way of proving that the Earth orbits the Sun, and not the other way round?
By understanding gravity -- they obit their common center of mass.

etotheipi
is there a (relatively) simple way of proving that the Earth orbits the Sun

Parallax.

andrew s 1905 and etotheipi
Parallax.
Wanna bet on whether the OP deletes the stars from this scenario too? After the fact...

I'm not going to delete the stars ... can you please explain a little the parallax method of proving this.

I guess a civilisation living on an eternally cloudy / foggy planet would see night and day but wouldn't develop any scientific theory as to why this happened?

can you please explain a little the parallax method of proving this.
Just as nearby streetlamps appear to move relative to further away hills as you change position, nearby stars move relative to far ones. Telescopes on opposite sides of the Earth thus see slightly different star positions, which gives you a way to measure distance to those nearby stars if you know the size of the Earth. Also, you see slightly different star patterns when on opposite sides of our orbit, and thus you can use the (now known) distance to the stars to calculate our orbital radius. Then you notice that this is the same as the distance to the Sun, and case closed.
I guess a civilisation living on an eternally cloudy / foggy planet would see night and day but wouldn't develop any scientific theory as to why this happened?
That would be just speculation. In any case, one would expect that eventually they'd be able to build balloons, aeroplanes and rockets.

russ_watters
Many thanks for the explanation of the parallax method, this seems to be reasonable and doesn't depend on there being other bodies in the solar system. Obviously it needs some sophisticated scientific instrumentation.

If I can be permitted to extend my thought experiment ...

Let's say one day your grandson/daughter says to you "You're a clever astronomer, so please help me. I've got a stupid friend at school who is convinced that the Sun goes round the Earth, is there any way I can demonstrate to him/her that this isn't true?".

I'm assuming we're back in the normal solar system, with the moon, other planets, etc. I'm wondering if accessible modern technology that a grandson/daughter would be good at, ie mobile phones, the internet, etc could be used. I'm not allowing Googling the subject and noting that there are a million hits that say that the Earth goes round the Sun. But could you, for example, ask lots of people around the Earth to make a simple observation at the same time and report the results, which would allow us to get to a conclusive result.

It's only recently that easy and cheap communication with millions of people all over the planet has become possible, so has this made the proof easier?

Many thanks for the explanation of the parallax method, this seems to be reasonable and doesn't depend on there being other bodies in the solar system. Obviously it needs some sophisticated scientific instrumentation.
Not really, it just takes a telescope with a high enough resolution, with the ability to take photos.
You take a set of three photos of the same part of the sky six months apart, and then "Flip" between the photos. If a star appears to jump back and forth between photos( compared to the background stars), it is showing parallax.
How big a telescope do you need? A 15 in. telescope should be able to notice a jump in Alpha Centauri, the closest star system.
This would be enough to demonstrate parallax. Of course, if you wanted the accurately measure the amount of parallax you would need better equipment.

conclusive

What's conclusive?

Is the fact the Venus and Mercury have phases and Mars and Jupiter do not conclusive?

I'm not allowing Googling the subject and noting that there are a million hits that say that the Earth goes round the Sun. But could you, for example, ask lots of people around the Earth to make a simple observation at the same time and report the results, which would allow us to get to a conclusive result.
The reason we say the Earth goes round the Sun is not because this is true in some absolute sense, but because it's difficult to explain the solar system otherwise. The problem with the Earth-centric model is to explain the motion of the planets and especially the moons of those planets.

If you study the solar system from a heliocentric frame, then the planets orbit the Sun (according to the law of gravitation) and the moons orbit their planets likewise. And this is all very simple.

Once you have that model, you can explain the motion of all the other objects in the solar system relative to the Earth. You know why, relative to the Earth, the moons of Jupiter have a complicated loop-the-loop motion.

There's not something inherent and absolute about these measurements - it's only when you try to explain your measurements that a heliocentric solar system makes it all a lot simpler.

Getting there, but not easy observations for my grandchild to make.

Does the fact that the moon has phases tell us anything about the relationship between the Earth and sun.

Getting there, but not easy observations for my grandchild to make.

Does the fact that the moon has phases tell us anything about the relationship between the Earth and sun.
I don't think so. The point about phases of the inner planets is that they orbit the sun and are sometimes "dark side" towards us and sometimes "light side" towards us. But the outer planets are always light side towards us because they're never between us and the sun. As PeroK says, the details of such orbits are really hard to explain in the geocentric model but trivial in the heliocentric model. But there's quite a lot of maths needed there, and Janus' 15" telescope to observe stellar parallax is expensive.

There's loads of auxiliary information, though. For example, here is the path on the sky of the recent NEOWISE comet. The dots are at one week intervals - count the dots per loop to see that we are moving in a loop every year. I'm sure you can find tables for the positions of the outer planets (which you can check observationally for Jupiter and Saturn, at least) which will show a similar looping pattern.

PeroK
Do we really need parallax here? If the question is just about motion of the Sun and Earth, the fact that the stars are in a different place every night is also proof it's the Earth going around the Sun and not the other way around. Otherwise you'd need all the stars orbing the Earth too.

davenn
Do we really need parallax here? If the question is just about motion of the Sun and Earth, the fact that the stars are in a different place every night is also proof it's the Earth going around the Sun and not the other way around. Otherwise you'd need all the stars orbing the Earth too.
That might be more to do with the Earth's spinning on its axis every day!

If the question is just about motion of the Sun and Earth, the fact that the stars are in a different place every night is also proof it's the Earth going around the Sun and not the other way around.
I don't think that's right. If the Sun were on a 365 day orbit around Earth then you'd still see different stars at night through the year. You could only see the stars on the side of the Earth where the Sun isn't whichever orbits the other.

Otherwise you'd need all the stars orbing the Earth too.

The stars are fixed on the heavenly sphere. That's because they are tiny holes allowing the celestial radiance to penetrate the firmament. (Man, don't they teach this stuff in school anymore?)

davenn, russ_watters and Ibix
The stars are fixed on the heavenly sphere. That's because they are tiny holes allowing the celestial radiance to penetrate the firmament.
Humour aside, there's a serious point here. The reality is that people have never been stupid (well... there have always been some smart people anyway), so the fact that this kind of thing was a plausible cosmology for a long time tells you that spotting the flaws in it is hard.

Richard Crane, phinds and russ_watters

By looking at the stars we could prove that the Earth spins on its axis every 24 hours. The Sun appears to rotate around the Earth every 24 hours, so this apparent rotation is most likely due to the spin of the Earth than anything else.

Not a proof but surely a strong hint?

PeroK
Part of my motive for asking the question is that it was hard to prove 500 years ago (partly due to the attitude of the Church of course) but it is any easier to prove today?

Not a proof but surely a strong hint?

Well, maybe. The sun "goes around the earth" every 24 hours. The stars "go around the earth" every 23 hours, 56 minutes and 4 seconds.

so the fact that this kind of thing was a plausible cosmology for a long time tells you that spotting the flaws in it is hard.

What you needed was (see message 3) parallax.

By looking at the stars we could prove that the Earth spins on its axis every 24 hours. The Sun appears to rotate around the Earth every 24 hours, so this apparent rotation is most likely due to the spin of the Earth than anything else.

Not a proof but surely a strong hint?
Corroborated by Foucault's pendulum.

sophiecentaur
Not a proof but surely a strong hint?
Depends how attached you are to the notion that the Earth is the center of everything. Why shouldn't everything orbit the Earth more or less as the heavenly sphere V50 mentions? It's actually perfectly plausible until you look at the details of the motions of heavenly bodies and realize it's so much easier to describe as heliocentric.

I think you really do have to look up the path of Jupiter across the night sky and look for the parallax "wobble".
Part of my motive for asking the question is that it was hard to prove 500 years ago (partly due to the attitude of the Church of course) but it is any easier to prove today?
It depends what you are willing to accept as a given. If you accept that NASA and/or various naval observatories are trustworthy sources then it's not too hard to analyse their data. Actually verifying the data takes a degree of experimental skill and long term work (and cash!) that most people wouldn't have the patience for - but it's possible if you want to do the work.

What you needed was (see message 3) parallax.
Just some perspective, really. I agree it's not conceptually all that difficult if you aren't philosophically entrenched in geocentrism, but it does require fairly accurate measurement and logging of planetary positions to prove it experimentally. Stellar parallax is easier (you just need a few photos to see the stars moving relative to one another), but better kit is required.

Aside: if I recall correctly, Tycho Brahe built an observatory and did the logging because he didn't believe this heliocentric nonsense. That backfired a bit, since his student Kepler developed his laws of planetary motion from the data gathered there.

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davenn
Well, maybe. The sun "goes around the earth" every 24 hours. The stars "go around the earth" every 23 hours, 56 minutes and 4 seconds.
Is this correct?

Is this correct?
Yes. Because the Earth advances a little in its orbit the Sun isn't in quite the same place in the sky today as it was at the same time yesterday. Google "siderial day".

It doesn't help you, though, since the same thing would happen if the Sun went round the Earth.

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In reality don't you have to make some assumption about a frame of reference for example the fixed stars otherwise you have to appeal to simplicity of explanation. If you don't, you don't have any reason to choose a particular frame.
Regards Andrew

The point about phases of the inner planets is that they orbit the sun and are sometimes "dark side" towards us and sometimes "light side" towards us. But the outer planets are always light side towards us because they're never between us and the sun.

Isn't this explained by this model?

Qualitatively yes, possibly. Quantitatively no. That's why systematic detailed measurements of the positions of something like Jupiter would be needed - to show that the detailed predictions of heliocentric theory are accurate and the detailed predictions of a geocentric theory like your sketch are not.

Qualitatively yes, possibly. Quantitatively no. That's why systematic detailed measurements of the positions of something like Jupiter would be needed - to show that the detailed predictions of heliocentric theory are accurate and the detailed predictions of a geocentric theory like your sketch are not.
But can't you transform the equations of motion from a barycentric system to an Earth centred one? Yes they would be more complex but would predict the same outcome.
Regards Andrew

But can't you transform the equations of motion from a barycentric system to an Earth centred one? Yes they would be more complex but would predict the same outcome.
Yeah. But the model illustrated in #28 (on which I was commenting) doesn't have anything orbiting the Sun. So it's a distinct model compared to a non-trivial presentation of a heliocentric model, which is what you are talking about.

andrew s 1905
Yeah. But the model illustrated in #28 (on which I was commenting) doesn't have anything orbiting the Sun. So it's a distinct model compared to a non-trivial presentation of a heliocentric model, which is what you are talking about.
I agree but I was trying to reinforce the point I made in post #27. You either need to appeal to "simplicity " or a fixed reference frame ( stars, QSO etc.) to establish a barycentric system.
This is the lesson relativity is it not?
Regards Andrew

Isn't this explained by this model?

That model has been known to be wrong for at least 2300 years. (So you can't blame the Catholic Church - indeed, some of the books of the Hebrew Bible hadn't been written) Among other problems, it fails to predict apparent retrograde motion.

I agree but I was trying to reinforce the point I made in post #27. You either need to appeal to "simplicity " or a fixed reference frame ( stars, QSO etc.) to establish a barycentric system.
This is the lesson relativity is it not?
Regards Andrew
You don't need to invoke fixed stars - the obvious frame to use is one in which the center of mass of the solar system is at rest. That's barycentric (assuming we can use barycenter to refer to the joint orbital center of more than two bodies - I may be abusing the language). You are correct that we can pick an Earth-centered frame, but so-called fictitious forces emerge from the maths to make your life a misery if you do. Not all frames are created equal! But you are correct that, to be pedantic, we should say that an inertial frame of reference says that the Earth orbits the Sun.

But it's important to distinguish a peculiar choice of frame to describe a heliocentric model from a geocentric model. The planets don't orbit the Earth in your frame - they follow the Sun, albeit in some weird cycloid orbit. In a true geocentric model everything goes round the Earth.

One effect from the Sun (and the Moon) we see on the Earth are the tides.

Would there be any measurable difference in the tides between the heliocentric and geocentric models?