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Keplers 3rd law and derivations of it.

Attached are three questions. the first relates to kepler's 3rd law and calculating the maxima and minima of acceleration of a planet around a Sun. The second asks for this equation to be conbined with newtons law of universal gravitation to find the mass of the sun and the third asks for the period of another planet with a larger radius. i am a bit rusty and can't remember how i should approach these, i have included in orange typeface my thoughts and ideas of how i should be going about answering these questions. Please can you confirm if i was heading in the right direction and show me how i should answer them? thank you

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Solution Preview

The correct solutions are explained in the attached pdf file.

For the formulae on Kepler's laws, you should have all that are needed in your textbook(s) or lecture notes, however, just in case, here is a page where you can look up the 3rd law of Kepler:

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

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Here is the plain TEX source

centerline{bf Kepler laws}

In the formula you quote at the start, $r_1$, is the bf semi-major rm axis.
Therefore
$$
r_1 = {d+1.4dover 2} = 1.2 ...

Solution Summary

The solution examines Keplers 3rd law and the derivations of it.

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