Kepler's laws and orbits question?

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The discussion revolves around calculating the gravitational field strength at the surface of an imaginary planet with a diameter twice that of Earth. Given the moon's orbital radius and period, the user applies Kepler's laws and gravitational equations to derive the gravitational constant (GM) and subsequently the gravitational field strength (g). The calculated value of g is approximately 40,597,576.67 N/kg, which is deemed excessively high, prompting the user to question the accuracy of their calculations. Responses confirm that the calculations appear correct, highlighting the extreme nature of the planet's gravity. The conversation emphasizes the implications of such a high gravitational field on potential habitation.
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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?
 
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Your calculation looks fine. I wouldn't want to live there!
 

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