Undergrad Astronomy in a Simple Solar System

[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.

 

[Ibix]

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

You are missing the point.

Detailed quantitative observations will indeed reveal complexities that are much more efficiently explained in a heliocentric model. However, qualitative statements like "you can see the Sun move relative to the stars" are wholly explicable in either a heliocentric or a geocentric model (as evidenced by the Moon). That's a part of why geocentrism clung on as a mainstream model for so long.

The OP was asking for a simple experiment that children could do. Observing that the stars and the Sun move relative to one another isn't simple (there are major safety hazards in solar observation) and, unless accompanied by detailed measurement and analysis (not simple either), it doesn't differentiate a heliocentric model from a geocentric model of the type illustrated in #28 anyway.

Edit: I should note that "the stars change with the seasons" is a safe way of observing that the Sun moves relative to the stars, known since antiquity. If it disproved geocentrism we wouldn't be having this conversation.

 

[oriel36]

The OP was asking for a simple experiment that children could do. Observing that the stars and the Sun move relative to one another isn't simple (there are major safety hazards in solar observation) and, unless accompanied by detailed measurement and analysis (not simple either), it doesn't differentiate a heliocentric model from a geocentric model of the type illustrated in #28 anyway.

Edit: I should note that "the stars change with the seasons" is a safe way of observing that the Sun moves relative to the stars, known since antiquity. If it disproved geocentrism we wouldn't be having this conversation.

Let's face it, the easiest way to determine that the Earth orbits the Sun is to appreciate that the stars will transition from left to right of the central/stationary Sun and parallel to the orbital plane. I personally feel that it is from the most unappreciated satellite out there.

The stars in the region of space known as the constellation Scorpius are now transitioning to the right of the central Sun due to the orbital motion of the Earth just as anyone who drives around a traffic circle will see background objects change position from one side of the roundabout to the other as the car travels/orbits the centre.

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

https://theskylive.com/planetarium

The old geocentric astronomers marked the transition of the stars from an evening to morning appearance as heliacal risings but, with a satellite out there free of daily rotational influences, that transition can now be described in heliocentric or Sun-centred perspectives as the Earth's orbital motion is responsible for that transition.

It is a matter of a more expansive view so try not to be caught between two stools.

 

[saddlestone-man]

Referring back to #45 ... I love those Ptolemy Epicycles.

 

[saddlestone-man]

A simple experiment that a child could conduct would be to estimate the brightness of Venus over say 18 months. During this time its distance from the Earth would vary between about 38Mkm and 260Mkm, and its brightness would vary accordingly.

The same observation could be made with Mars.

Is there any way to explain this variation in the brightness of Venus and Mars with a geocentric model? Surely their brightness would be constant.

 

[oriel36]

Do yourself a favour and match the actual time-lapse from the year 2000 with actual models from the same year which see the planets come and go within the range of the C3 camera. The Sun is a fixed, stationary and central reference for all motions and especially around the end of April and into June when most of the planets make an appearance.

 

[oriel36]

A simple experiment that a child could conduct would be to estimate the brightness of Venus over say 18 months. During this time its distance from the Earth would vary between about 38Mkm and 260Mkm, and its brightness would vary accordingly.

The same observation could be made with Mars.

Is there any way to explain this variation in the brightness of Venus and Mars with a geocentric model? Surely their brightness would be constant.

No there isn't and Galileo commented on how perceptive Copernicus was in this respect where Venus gets larger as it approaches the slower moving Earth but its phases modify the luminosity over that 18 month period -

https://www.popastro.com/images/planetary/observations/Venus-July 2010-January 2012.jpg

"SALV.But the telescope plainly shows us its horns to be as bounded and distinct as those of the moon, and they are seen to belong to a very large circle, in a ratio almost forty times as great as the same disc when it is beyond the sun, toward the end of its morning appearances. "

SAGR. 0 Nicholas Copernicus, what a pleasure it would have been for you to see this part of your system confirmed by so clear an experiment [telescope]!

SALV. Yes, but how much less would his sublime intellect be
celebrated among the learned! "

Galileo ,Dialogue Concerning the Two Chief World Systems, 1632

 

[Ibix]

Is there any way to explain this variation in the brightness of Venus and Mars with a geocentric model? Surely their brightness would be constant

The brightness need not be constant, since the distances between the Sun, Earth, and planet need not be constant and the angles change, even in a model like your #28. So this model does predict phases of the inner planets and not the outer.

But it cannot predict correct phases, because you could only have Venus being full when it's in opposition to the Sun. Yet in reality, Venus is always close to the Sun and is occasionally seen to be nearly full. So you probably can conclude that Venus and Mercury circle the Sun if you have a telescope good enough to resolve Venus as a disc and enough patience to log the phases.

But that doesn't mean that the Earth goes round the Sun. To see that, you need to track the position of planets in the sky and show that their positions are consistent with both us and them orbiting the Sun (i.e., that their apparent path across the distant stars is explicable in terms of two elliptical orbits).

I think that gathering this data - a several months long careful nocturnal observation project - is probably more than most children would be willing to do. Certainly just to win an argument with a classmate. That's why I suggested finding tables of the positions of the planets in the sky. You can verify that they are where the tables say they should be at leisure, and you can use the tables to plot the planets' track on the sky and show that it's complex epicyclic motion. That is convincing evidence, with a bit of geometry. But it's based on detailed data and calculation, not on qualitative statements, and you do need the detail.

 

[andrew s 1905]

Ptolemy epicycles always struck me as an precursor to Fourier decomposition.
Regards Andrew.

 

[DrStupid]

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.

We do that because we know the physics behind it. But this thread is about building a model without this knowledge on the basis of simple observations only and the history of astronomy tells us that turning this

https://tinyurl.com/y4yae5j3

into this

https://tinyurl.com/y5sesuno

is not obvious.

 

[hmmm27]

Even if there were no other celestial bodies hanging about to make it "easy", all you need to immediately shoot down "The Sun orbits the Earth once a day" , and establish declination and 1yr orbital period, is a gimballed gyroscope.