Kepler's laws and orbits question?

  • Thread starter Kratos321
  • Start date
  • #1
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Homework Statement



An imaginary planet has a diameter twice that of our earth. The planet has one moon with an orbital radius of 5.0x10^7 km and orbital period of 10 earth days.
Determine the strength of the gravitational field at the surface of the planet.

Radius of earth = 6.38 x 10^6m
Orbital radius of moon = 5x10^10m
orbital period = 8.64 x 10^5 s

Homework Equations



r^3/T^2 = GM/4pi^2
g = GM/r^2

i think that's all..?...

The Attempt at a Solution



GM = (4pi^2(5x10^10)^3)/(8.64x10^5)^2
= 6.61 x 10^21

g = 6.61x10^21/(12.76x10^6)^2
= 40597576.67N/kg

this number is massive!!! I must be doing something wrong. any help?
 

Answers and Replies

  • #2
gneill
Mentor
20,826
2,805
Your calculation looks fine. I wouldn't want to live there!
 

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