I need some more clarification of the problem, before I spend time and
effort working. I want to make sure that the conditions aren't self-defing
the situation such that I can't do it. Correct any of these
statements/clarifications as need be.
1) I'm to derive the following Kepler law
period^2 = (4 pi (earth-sun distance)^3)/G(M+m)
in a frame of reference where the earth and sun are stationary.
2) Will you allow me to do it for circular orbits, the only case where the
conversion to the inertial frame from the non-inertial frame is relatively
simple(or vice versa); we ultimately have to convert from one frame to other
to compare answers; so we must have knowledge of the two frame in order to
do that.
3) My physicists have figured out the inverse square law of gravity; and
have figured out the centrifugal force law, namely there exists an outward
pointing force on a mass in this frame of reference equal to
mass*const*(distance from coordinate origin) and that the const has been
verified by experiment to be (4 pi^2)/(period). Where period is the time
it takes the stars to orbit the coordinate system.
4) The dynamical law I'll use is the 2nd law in this non-inertial frame:
Namely
applied to any mass in the system of analysis
m*a = sum of forces,
where in this situation described above sum of forces is the sum of our
experimentally determined law of gravity and law of centrifugal force.
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Are the above a well posed statement of the problem, if not how should I
change them?