Need some help with Astronomy homework

[llamatoes]

I was set the task of proving that the earth's orbit is heliocentric in my astronomy homework, (one of the greta things about being on the register of people that are good ats science at my school and living in Greenwich, London, I can attend the Royal observatory's astronomy course through my school, free of charge).

I have done the whole thing about the parallax of star, and I was tempted to write a basic description of a Hohman transfer, in order to explain.

Is there anything else I should include?

[Winter Man]

Retrograde motion of the planets. That was the original proof, IIRC.

[check]

Retrograde motion of the planets. That was the original proof, IIRC.

Well, Ptolemy had an explanation for that which still allowed for a geocentric solar system. The Ptolemy model had to become more and more complex with each refinement in measurement...

Edit: But yeah llamatoes, Winter Man is right; you might want to mention retrograde motion of the planets, and how that the more accurately they were able to measure the motion of the planets, the more complex the model had to become, and they could never get it quite right. A heliocentry model, on the other hand, explained everything nicely and was much simpler.

Edited October 15, 2013 by check

[Idobox]

What about a high precision gyro?

Assuming you're on the equator, if it is set up to be perfectly vertical at noon the first day, after 3 months it will be horizontal at the same hour, and you can show the direction 'turns' at one rotation per year, consistent with the heliocentric model. Especially since it won't move relative to distant stars.

[Nikolai]

Stellar aberration.

http://en.wikipedia.org/wiki/Stellar_aberration

[Mr Shifty]

Retrograde motion was accounted for in the Ptolomaic model by having the planets rotating around an epicenter. In fact, the Copernican model was no more accurate for predicting the positions of celestial bodies than the Ptolomaic model was. Observations that started to shatter geocentrism were the observation of all the phases of Venus by Galileo, which didn't fit into the Ptolomaic model (though Tycho Brahe's geocentric model accounted for them.) But the real killers were Kepler's laws of motion, which gave far more accurate predictions than either the Copernican model or any of the geocentric models, because they accounted for eccentricity. Kepler, for instance, was able to accurately predict a transit of Venus, which had never been done before. Newton's reduction of Kepler's laws to a single law of gravitation convinced most astronomers, but it wasn't until stellar paradox was measured in 1838 that there was definitive proof.

In short, it's actually pretty difficult to prove, as an observer from the Earth, that the solar system is heliocentric. But, if you've got the parallax of the stars down, you're pretty much there.

[Idobox]

Still about the gyro.

You can use it to show the sun doesn't move significantly during the day, but that the Earth spins. That already one part of geocentrism broken. Foucault's pendulum does the same, but is a bit more difficult to explain to the layman.

The angle between the sun and the direction the gyro points at should change by about 1° per day, which should be measurable with a decent gyro.

[K^2]

There isn't really such a thing as proving that Heliocentric model is right. You can prove that it's a simpler model than the Geocentric one, but Geocentric model is no less valid. The problem is to make Geocentric work, you have to introduce several new forces that act on all bodies in heaven. These are the laws of physics in Geocentric model.

1) All bodies attract each other with a force proportional to product of their masses and inverse square distance between them. (Gravity)

2) All bodies are repelled from Earth by a force proportional to the mass of the body and inverse distance to Earth's reference axis. (Centrifugal)

3) All bodies are pushed into retrograde spin by a force proportional to their mass and sinus of an angle to a reference axis. (Coriolis)

4) All bodies are pushed along the direction connecting Sun to Earth with a force proportional to their mass and inverse square distance between Earth and Sun. (Accelerated frame.)

With the right choice of constants that go with these forces, these equations are precise and result in Earth remaining at the center of the universe and everything else revolving around it in perfect consistency with observations.

[Mr Shifty]

There isn't really such a thing as proving that Heliocentric model is right. You can prove that it's a simpler model than the Geocentric one, but Geocentric model is no less valid. The problem is to make Geocentric work, you have to introduce several new forces that act on all bodies in heaven. These are the laws of physics in Geocentric model.

1) All bodies attract each other with a force proportional to product of their masses and inverse square distance between them. (Gravity)

2) All bodies are repelled from Earth by a force proportional to the mass of the body and inverse distance to Earth's reference axis. (Centrifugal)

3) All bodies are pushed into retrograde spin by a force proportional to their mass and sinus of an angle to a reference axis. (Coriolis)

4) All bodies are pushed along the direction connecting Sun to Earth with a force proportional to their mass and inverse square distance between Earth and Sun. (Accelerated frame.)

With the right choice of constants that go with these forces, these equations are precise and result in Earth remaining at the center of the universe and everything else revolving around it in perfect consistency with observations.

This is pretty fascinating. I'd be very interested to see a paper that lays this out in detail, if you've got one. Does this model account for stellar parallax? How does it handle the Earth's axial tilt?

[-Velocity-]

In addition to what others have said, you could also use the phases of Venus and Mercury, and the lack of any phases but gibbous and full on Mars on the more distant planets. That shows that Mercury and Venus orbit the Sun, and that all the other planets are more distant from the Sun than Earth. I don't think that, by itself, proves heliocentricity though, but it's rather strong evidence, and the simplest model you can make that agrees with that evidence is the heliocentric model.

[Brotoro]

You observe annual stellar parallax shifts.

You observe annual changes in the lines in stellar spectra because of the Doppler shift as we alternately move toward and away from the those stars.

[K^2]

This is pretty fascinating. I'd be very interested to see a paper that lays this out in detail, if you've got one. Does this model account for stellar parallax? How does it handle the Earth's axial tilt?

I don't know if anybody ever wrote a paper on this, even as a bit of a joke, but it's basically just a shift to an accelerated coordinate system. We know how the Earth moves relative to Sol System's baricenter, and any object with known trajectory can be shifted to be a center of your coordinate system so long as you add some forces to account for the new coordinate system being accelerated one.

Stelar paralax is accounted for rather simply. You'll note that the last force added does not depend on distance from Earth or Sun. So even the most remote stars will experience it causing them to wobble about at one cycle per year. And indeed, if you observe parallax, it means that relative to Earth, the stars are moving/accelerating. In Heliocentric model, this is due to Earth's annual motion around the Sun. Here, we shift this motion to the stars themselves. So every star out there ends up making a 1AU circle every year. Which, of course, seems weird, but that's the cost of making Earth the center of the Universe.

[Mr Shifty]

I don't know if anybody ever wrote a paper on this, even as a bit of a joke, but it's basically just a shift to an accelerated coordinate system. We know how the Earth moves relative to Sol System's baricenter, and any object with known trajectory can be shifted to be a center of your coordinate system so long as you add some forces to account for the new coordinate system being accelerated one.

I presume this is a consequence of general relativity, about which I know nearly nothing. And here I reveal my ignorance with with is probably a silly question: if you have to posit extra forces for the accelerated reference frame, is there a reference frame with a minimum number of forces? Isn't simplicity a valid criterion to use for privileging one reference frame over another?

[Brotoro]

When I first learned about relativity, I told my science teacher that obviously *I* was stationary at the center of the universe, and the Earth would roll under my stationary body as I push it along with my feet, and the whole heavens would spin around me as I applied a torque to the Earth with my feet.

He told me this was the Egocentric Universe Model.

Edited October 15, 2013 by Brotoro

[K^2]

I presume this is a consequence of general relativity, about which I know nearly nothing. And here I reveal my ignorance with with is probably a silly question: if you have to posit extra forces for the accelerated reference frame, is there a reference frame with a minimum number of forces? Isn't simplicity a valid criterion to use for privileging one reference frame over another?

General Relativity is the ultimate generalization of the concept, but Classical Mechanics includes treatment of accelerated reference frames via fictitious forces (aka inertial forces). Centrifugal force is the most (in)famous example.

And yes, the coordinate systems in which no fictitious forces appear are the inertial coordinate systems. You can always chose more than one. In General Relativity, you can only ensure that the coordinate system is inertial locally. In Classical Mechanics, however, it is a global property. Of course, this comes at a price of gravity being a real force in Classical Mechanics. In General Relativity, gravity itself is a fictitious force, and all inertial coordinate systems are in free fall.