Relativity of motion and astronomy

[ViolentCorpse]

Greetings,

One of the basic postulates of relativity is that the laws of physics hold equally well in all frames of references. This got me wondering about the geocentric model of solar system which necessarily gives rise to motions of peculiar kinds. For example, the epicycles, which are needed in this model to explain the motion of our planets. This kind of motion seems irregular with regard to the laws of motion and a possible violation of these laws. Hence, my question: Is there anything in special/general relativity, that could account for the motion of planets as observed from the Earth's frame of reference?

Thank you!

 

[Ibix]

The laws of physics hold, but do not necessarily have the same form in all frames of reference. There are classes of frames where the laws take a simple form - inertial frames. There are other frames where the laws have more complex forms, including so-called fictitious forces like the Coriolis force and centrifugal forces. These account for the complex motion of the planets if you decide to take an Earth-centered frame.

 

[ViolentCorpse]

Thanks, Ibix. I knew I was missing something. Appreciate it! ^_^

 

[ViolentCorpse]

Hello again everyone,

I had a follow-up question of sorts. I was thinking about the frame of reference of Earth and Newton's laws and did some calculations. In the Earth's frame of reference, the sun orbits the Earth. I used Newton's law of gravitation to find the force of attraction between the Earth and the sun. From that, I used the formula of centripetal force to obtain the velocity with which the mass of the sun would move under the influence of Earth-sun gravitational attraction and used that to determine the time the Sun would take to orbit the Earth at that velocity. I got a figure of 188657.4 days i.e a year would be 188657.4 days long if it were the Sun orbitting the Earth...

Now what the hell have I done here? Am I applying the wrong laws in the wrong frame of reference?

I was embarrassed to ask this because this is a stupid result obtained from my very flawed understanding of mechanics, but then I decided I'd rather be embarrassed than remain a fool..

Would you guys be so kind to explain this to me. I'd extremely grateful.

Thank you!

 

[Nugatory]

What you have calculated is the orbital period of a sun-sized mass attracted to a fixed point in space by a force equal to the gravitational force between Earth and sun. That's a completely different problem with a completely different solution.

To calculate the sun's "orbit" in a frame in which the Earth is not moving, there are two correct procedures:
1) For an exact solution, note that the sun and the Earth are actually rotating about their mutual center of gravity. Solve that problem in any frame you please (the one in which that common center of mass is at the origin and not moving is by far the easiest) and then transform to coordinates in which the Earth is at rest.
2) For a quite good enough approximate solution, the only one that any non-masochist would use, take advantage of the fact that the sun's mass is so much greater than the Earth's that for all practical purposes the common center of mass is at the center of the sun so we can say that the sun is fixed. That's the standard assumption behind the centripetal force equation you used, and it gives you the expected 365-day orbital period for the earth. Now transform that into coordinates in which the Earth is at rest.

 

[Nugatory]

This thread might be happier in Classical, as it's basically about classical Galilean relativity.

 

[ViolentCorpse]

What you have calculated is the orbital period of a sun-sized mass attracted to a fixed point in space by a force equal to the gravitational force between Earth and sun. That's a completely different problem with a completely different solution.

To calculate the sun's "orbit" in a frame in which the Earth is not moving, there are two correct procedures:
1) For an exact solution, note that the sun and the Earth are actually rotating about their mutual center of gravity. Solve that problem in any frame you please (the one in which that common center of mass is at the origin and not moving is by far the easiest) and then transform to coordinates in which the Earth is at rest.
2) For a quite good enough approximate solution, the only one that any non-masochist would use, take advantage of the fact that the sun's mass is so much greater than the Earth's that for all practical purposes the common center of mass is at the center of the sun so we can say that the sun is fixed. That's the standard assumption behind the centripetal force equation you used, and it gives you the expected 365-day orbital period for the earth. Now transform that into coordinates in which the Earth is at rest.

Thank you, Nugatory. I understand now.

the only one that any non-masochist would use

That made me chuckle. Good one! :D