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This problem is bugging me:

Two satellites are in circular orbits around a planet. The radius of orbit for satellite 1 is 1.0x10^8 m. Satellite 2 is in a higher orbit a distance 1.0x10^4 m from satellite 1 (this is at the instant when both are over the same point on the planet). 10 hours later the distance between the satellites increased to 1.3953x104 m. Determine the mass of the planet.

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    $\begingroup$ Why is it bugging you? Have you done a lot of work trying to figure out the answer? Are you stuck on some part of it? $\endgroup$ – Mike Nov 2 '17 at 19:46
  • $\begingroup$ Yes I tried to use Kepler's laws to find the mass but with no luck. I also tried a way using trigonometry and angles but that didnt seem to work. $\endgroup$ – user63939 Nov 2 '17 at 19:52
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    $\begingroup$ Interesting. Well, maybe you could show us what you tried and where you got stuck. Try to be specific. You might need to read up on how to ask a homework-like question. $\endgroup$ – Mike Nov 2 '17 at 20:25
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By equating $ F_{centripetal} $ to $ F_{gravitational} $, you can get a general formula for angular speed, in the form of $$ \omega = \sqrt{\frac{GM} {r^3}} $$

Also note that the angle covered is $ \phi = \omega t $, so after finding the respective angular speeds of the satellites, you can draw a triangle where the angle between two radii is $ \phi = (\omega_1 - \omega_2)t$ and the side this angle is looking at is the distance given in the question: $ 1.3953 x 10^4 m $. All that remains is basic trigonometry to find the angle $ \phi $ and then equate it back to $(\omega_1 - \omega_2)t$ and solve for $M$.

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