I Astronomy in a Simple Solar System

[saddlestone-man]

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

 

[russ_watters]

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.

 

[Vanadium 50]

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

Parallax.

 

[russ_watters]

Parallax.

Wanna bet on whether the OP deletes the stars from this scenario too? After the fact...

 

[saddlestone-man]

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?

 

[Ibix]

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.

 

[saddlestone-man]

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?

 

[Janus]

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.

 

[Vanadium 50]

conclusive

What's conclusive?

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

 

[PeroK]

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.

 

[saddlestone-man]

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.

 

[Ibix]

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.

 

[russ_watters]

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.

 

[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.

That might be more to do with the Earth's spinning on its axis every day!

 

[Ibix]

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.

 

[Vanadium 50]

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?)

 

[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.

 

[saddlestone-man]

How about:

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?

 

[saddlestone-man]

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?

 

[Vanadium 50]

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.

 

[Vanadium 50]

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.

 

[PeroK]

How about:

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.

 

[Ibix]

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.

 

[Ibix]

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.

 

[saddlestone-man]

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?

 

[Ibix]

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.

 

[andrew s 1905]

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

 

[saddlestone-man]

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?

 

[Ibix]

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.

 

[andrew s 1905]

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

 

[Ibix]

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

 

[Vanadium 50]

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.

 

[Ibix]

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.

 

[saddlestone-man]

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?

 

[andrew s 1905]

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.

Yes I agree and understand all that, and it is the "obvious choice" but that's still an example of a particular choice motivated by simplicity of the equations of motion i.e. the point I am making. Theory leads to it being the "obvious choice" not raw observation.

Kepler found he could simplify things based on his theory that the planets moved in eclipses with the Sun as a focus, then Newtonian explained this in terms of gravity.

To the OPs question pure observation can't prove the Earth orbits the sun it. You have to have an agreed theory to interpret them.

Regards Andrew

 

[saddlestone-man]

I presume you are referring to any observation I make from the Earth. If I launched a rocket out to say the orbit of Jupiter (without looking at Jupiter itself and its moons) and I looked back towards Earth for a year. Wouldn't I clearly see the Earth complete one orbit around the Sun?

It's a complex 'observation' but I don't need to invoke any theory, do I?

 

[DrStupid]

If I launched a rocket out to say the orbit of Jupiter (without looking at Jupiter itself and its moons) and I looked back towards Earth for a year.
[...]
It's a complex 'observation' but I don't need to invoke any theory, do I?

How are you going to launch a rocket to the orbit of Jupiter without having any theory?

 

[andrew s 1905]

I presume you are referring to any observation I make from the Earth. If I launched a rocket out to say the orbit of Jupiter (without looking at Jupiter itself and its moons) and I looked back towards Earth for a year. Wouldn't I clearly see the Earth complete one orbit around the Sun?

It's a complex 'observation' but I don't need to invoke any theory, do I?

You would still need a reference frame. If you centred it on the Earth the Sun would orbit it and vice versa. If you used the fixed stars then yes your right the Earth would orbit Sun but the theory is then then stars are fixed. You can't escape motion is relative.
Regards Andrew

 

[Ibix]

It's a complex 'observation' but I don't need to invoke any theory, do I?

Depends what you mean. In the complex non-inertial frame that @andrew s 1905 is using, your rocket and the Sun are under the influence of the "fictitious forces" I mentioned so that they both move in identical circles. That exactly cancels out the motion of the Sun in your observations.

It's much easier to use an inertial system where your rocket floats with constant speed when its engine is off, and most of physics is much simpler when you do that. But if you are willing to pay the steep mathematical price of doing so, you can transform to a frame in which the Earth is at rest.

Note that this model is still heliocentric - nothing is orbiting the Earth except the Moon. It's just heaped a layer of complexity on top of it to disguise it.

 

[DrStupid]

Note that this model is still heliocentric - nothing is orbiting the Earth except the Moon.

That depends on the definition of "orbit". If you accept epicycles as orbits than all planets and the Sun orbit Earth in the geocentric frame.

 

[andrew s 1905]

Note that this model is still heliocentric - nothing is orbiting the Earth except the Moon. It's just heaped a layer of complexity on top of it to disguise it.

You have repeated this several times but I don't understand it. In an Earth centerd model the all solar system bodies orbit the Earth in the sense the perform circuits. Yes the are very complex but so is the motion of the moon around the Sun it is not a simple ellipse.

Don't get me wrong I am not trying to argue the heliocentric is not the best one it certainly is. I agree the Earth centered is unnecessary complex etc.

Regards Andrew

 

[Ibix]

That depends on the definition of "orbit". If you accept epicycles as orbits than all planets and the Sun orbit Earth in the geocentric frame.

We normally describe the Moon as orbiting the Earth, although it follows a path around the Sun of the kind you are talking about here. So I'd say that certainly Venus and Mercury orbit the Sun and the Sun orbits the Earth. Not sure about what the orbits of the outer planets look like, now I think about it.

The point I was attempting to make (somewhat inexactly) is that this coordinate transformation doesn't turn the heliocentric model into post #28.

 

[saddlestone-man]

Perhaps one thing worth mentioning is we now know the masses of the Sun, Earth, etc and therefore we can predict that although the solar system may have been 'created' as #28, it would soon rearrange itself into a heliocentric system, presumably completely destroying all the current planets and fashioning new ones.

 

[Ibix]

We normally describe the Moon as orbiting the Earth, although it follows a path around the Sun of the kind you are talking about here. So I'd say that certainly Venus and Mercury orbit the Sun and the Sun orbits the Earth. Not sure about what the orbits of the outer planets look like, now I think about it.

Complicated, seems to be the answer. This is a crude model of the solar system out to Jupiter, for fifteen of your Earth years, in an Earth-centered frame:

The yellow circle is the Sun's path
The grey overlapping it is Mercury's path
The orange overlapping that is Venus' path
Earth is unmarked at the center
The red is Mars' path
The brownish at the outside is Jupiter's path

Note that the paths don't close, which is why the inner planets' paths are such a mess. I haven't drawn the rest of the outer planets because the scale makes the inner planets' orbits tiny. The rest of the planets wouldn't add a lot to the picture anyway - their paths just look like variants on Jupiter's.

When I say "crude" - the model simply has all the planets starting in conjunction and moving (in the heliocentric frame) in Sun-centered circles in the same plane. Orbital radii and periods copy-pasted from the first two columns of the table here. So it's pretty much to scale, but the orbits are simplified and probably each have different wrong phase offsets.

 

[andrew s 1905]

@Ibix Ptolemy would be proud of you! Regards Andrew

 

[Vanadium 50]

Epicyclospirograph!

 

[oriel36]

Parallax.

Something far easier and far more important.

https://sol24.net/data/html/SOHO/C3/96H/VIDEO/

The stars transition from left to right of the stationary Sun as seen from a satellite tracking with the Earth around the Sun. The time-lapse from the C3 camera has the central/stationary Sun as a foreground reference for the change in position of the stars minus any daily rotational influence which swamps observations of the orbital motion of the Earth using the stars -



Parallax is for those who are out of touch.

 

[Ibix]

The stars transition from left to right of the stationary Sun as seen from a satellite tracking with the Earth around the Sun.

But that would happen in a geocentric model too. For example a video of the Moon (Earth/Moon being a decent approximation to a geocentric system) would show stars disappearing behind it and reappearing on the other side.

 

[oriel36]

But that would happen in a geocentric model too. For example a video of the Moon (Earth/Moon being a decent approximation to a geocentric system) would show stars disappearing behind it and reappearing on the other side.

There is no geocentric model and a great deal of damage has been done by assigning Kepler's observations of Mars over a 16 year period as geocentric when they represent observations seen from the orbital motion of the Earth -

https://upload.wikimedia.org/wikipedia/commons/e/e9/Kepler_Mars_retrograde.jpg

"Copernicus, by attributing a single annual motion to the earth, entirely rids the planets of these extremely intricate coils, leading the individual planets into their respective orbits, quite bare and very nearly circular. In the period of time shown in the diagram, Mars traverses one and the same orbit as many times as the 'garlands' you see looped towards the centre, with one extra, making nine times, while at the same time the Earth repeats its circle sixteen times " Kepler Astronomia Nova 1609

The reference for the orbital motion of the slower moving planets and only the slower moving planets was the stationary field of background stars (hence the constellations on the rim of the diagram) so that their looping or direct/retrograde motions could be accounted for by the moving Earth overtaking them thereby causing them to fall behind in view as Jupiter and Saturn are seen to do in the following time-lapse -

https://apod.nasa.gov/apod/image/0112/JuSa2000_tezel.gif

To account for the direct/retrogrades motions of the faster moving Venus and Mercury requires an entirely different framework that is now available through the SOHO satellite tracking with the Earth around the Sun where the stars transition from left to right while the Sun is stationary and central.

https://sol24.net/data/html/SOHO/C3/96H/VIDEO/

That change in position of the background stars to the foreground central Sun represents a demonstration of the Earth's orbital motion.

There is a lot of work to do using satellite data.