I'm trying to rewrite Newton's law - GMP(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}= 4(pi)^{2}r^{3}as P^{2}= a^{3}under these conditions: that the mass M is the sun's mass, the radius is 1 AU, and G being converted to the appropriate units.

I get stuck on this problem, and I'm hoping you guys are willing to help me out.

To begin with, to make things easier, I set this problem up as a ratio:

P^{2}/a^{3}= 1 and P^{2}/r^{3}= 4(pi)^{2}/GM

and then I compare the two. In an elliptical orbit, the radius r can be equaled to a, so I get:

P^{2}/r^{3}= P^{2}/a^{3}= 4(pi)^{2}/GM.

Does this look right to you guys so far? I was told that if I did it correctly, my answer should come out to 1, but I'm not getting that once I work things out. I thought that I wouldn't have to worry about the units of G in this setup, but maybe I'm wrong? I'm not sure.

To clarify, I'm using 1.98 x 10^{30}kg for M and 6.67 x 10^{-11}m^{3}/kgs^{2}for G.

Any help would be very much appreciated.

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# Relating Newton's universal law of gravitation with Kepler's 3rd law

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