Who is rotating around whom in the solar system?

[bhanukiran]

hai, now iam uder a deep problem.
Be patient!
if all the motion is relative, and so all rotation is relative.i am very much convienced with this.but the problem is that ...taking solar system as an example,who is rotating around whom.
indeed i don't understand why ptolamey's geocentric is abonded. who knows whether sun is rotating around earth? one may say...sun is so massive that it cann't be bounded by Earth's gravitational field...wait ..wait...who knows whether gravitational theory is right? indeed my argument may look stupid.but iam now in this position after a long thought process.see... if there were a force called
BRAVITATION (hee hee haa haa) and which might not be a central force.who knows?
ok ok if ur not conveinced with my arguement...leave it.because it is not that easy to say such things. here is different doubt that i have to ask you can you please tell good mathematical method for calculate the trajectories of other planets using geocentric theory..actually i tried it for mercury and venus.its fine. but the problem is arising when i consider some other ones like jupiter.
HOW DOES JUPITER'S ORBIT APPEAR TO US.I HAVE SEEN THE TRAJECTORY IFROM PTOLAMEY'S THEORY.BUT I AM NOT ABLE TO DERIVE IT MATHEMATICALLY.
CAN ANY BODY HELP ME??

 

[Clausius2]

if all the motion is relative, and so all rotation is relative.

Celestial Mechanics isn't my main area of knowledge. But I cannot help thinking of rotation is not relative at all. We know we rotate around the Sun, and not the inverse. Why? because the existence, here on the Earth, of the centrifugal force. If you travel to the Sun you will not feel any force due to the rotation around the Earth, in part because the Sun is not rotating around nothing (excuse me for imagining such a simple model, we know galaxies rotates, and surely the Sun rotates around something).

The fact is an inertial frame is differentiable of one non inertial and viceversa, and rotational frames are non inertial.

 

[Jenab]

I don't know much about Ptolemaic astronomy, except that it proposes that the planets and the sun move around Earth in circles, except that actually each planet does not so much travel on the circle as orbits a central point that does travel around the circle. This secondary orbit is called an epicycle, and it is also a circular orbit. I have heard that getting accurate Ptolemaic ephemerides requires the use of tertiary circular orbits: little epicycles on the big epicycles. A planet moves around a circle whose center moves around a larger circle whose center moves around an even larger circle whose center is the Earth. And even this may not give results precise enough for finicky Ptolemaic astronomers. Maybe even higher-order epicycles will be needed.

What all these epicycles seem to be doing is approximating elliptical motion through the sum of motions of traveling loci on circles. The more complicated the theoretical system is, the more precise the calculated ephemerides are.

But there's a simpler way to get answers that are even better. Forget the epicycles and circular orbits and geocentrism. Instead, assume that the sun is the center of the solar system, around which all the planets move in ellipses, and use the mathematical principles discovered by Kepler and Newton to calculate the ephemerides.

It's simpler. It has better accuracy. And it sort of makes sense that the biggest object in the solar system should govern the motions of the other objects nearby. Ptolemaic astronomy pandered to primate egoism and religious sentiment: man thought he was so special that God made his home the center of the universe. Egoism does not always lead to wrong conclusions: occasionally when someone is proud or smug about something, he has reason to be. But it does pay to be suspicious when one's answers tend to gratify one's pride.

Jerry Abbott

 

[selfAdjoint]

Your conclusion is the one Kepler came to, but only after he had falsified one of the main tenets of Ptolemaic astronomy. The outer planets' motion was represented by
1. A circle surronding the earth, called a deferent.
2. A little circle with center on the deferent, called an epicycle, that turns at a uniform speed.
3. A point inside the deferent, called the equant, which is not at the center of the deferent, but offset, around which the center of the epicycle moves uniformly.

Now Ptolemy could prove by the motions that the three points, center of the deferent, equant, and center of the Earth lay in a straight line, with the equant between the other two. And he ASSUMED that the equant was exactly half way between the other two. Given that restriction, he could work out the dimensions of the deferent and epicycle from just three observations of the planet when it was at opposition to the sun. And his book the Almagest tells you how to do that.

But Kepler wanted not to make Ptolemy's assumption (called "the bisection of the equant"), so he took four oppostions that Tycho had recorded and laboriously calculated the ratio center-equant:equant-earth. Essentially he had to solve two simultaneous trig equations, and he knew no better method to do that but cut and try. Eventually he got an answer, hurrah! But here is where he proves he is a great scientist; he took four DIFFERENT oppositions and did the calculation all over again. And he got a different answer from the first time. Now he reached the correct conclusion: there is no correct ratio for the equant because there is no equant; The planetary motions CANNOT BE FACTORED INTO CYCLES IN WHICH ONE OF THE CYCLES IS IN UNIFORM MOTION ABOUT SOME FIXED POINT. Kepler was then left to find out what was the law of motions of the planets and he eventually found the equal areas in equal times rule which became his second law.

 

[pervect]

if all the motion is relative, and so all rotation is relative.i am very much convienced with this.but the problem is that ...taking solar system as an example,who is rotating around whom.

1) If rotation were completely relative, there would be no way to tell who is rotating and who is not, by definition. You set up a system of coordinates to describe the universe, who is rotating and who is not depends on which coordinates you adopt.

2) Rotation is, however, not relative. We can detect absolute rotation via physical means, such as ring-laser gyroscopes, or via the centrifugal forces that an observer in a rotating coordiante system experiences.

 

[spacetime]

Imagine its only sun and Earth in the universe.

If you choose to observe from the earth, add an inertial force and the sun revolves around the earth.

If you choose to observe from the sun, add an inertial force and the Earth revolves around the sun.

If you choose to observe from an inertial frame, they both revolve around there center of mass ( which, incidentally, lies very close to the center of mass of the sun ).

 

[Clausius2]

Imagine its only sun and Earth in the universe.

If you choose to observe from the earth, add an inertial force and the sun revolves around the earth.

It's not correct. Adding imaginary forces (centrifugal) is needed when the 2nd Law of Motion as F=ma does not fit in your frame. If you add a centrifugal force at the Sun, an observer situated at the Sun won't see the 2nd Law as a true law of motion. The Sun does not revolve around the Earth at all.

 

[spacetime]

O.k. practically Clausius is right. But to be precise,
Sun is not an inertial frame of reference even if there's just Earth affecting it. They both revolve around there center of mass. So, if you add an inertial force, it makes your calculations accurate. It is just that the differences in masses is too large so you make very less error if you assume the sun to be at rest.

 

[Clausius2]

Right Spacetime. Anyway, I'm getting into something I don't know very well.