Planet-X has a mass of 4.33×10 24 kg and a radius of 7520 km. What is the First

Question

Planet-X has a mass of 4.33×1024 kg and a radius of 7520 km. What is the First Cosmic Speed i.e. the speed of a satellite on a low lying circular orbit around this planet? (Planet-X doesn't have any atmosphere.)

What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet?

If the period of rotation of the planet is 17.5 hours, then what is the radius of the synchronous orbit of a satellite?

I am espeacailly confused on how to find G

Explanation / Answer

G = universal constant = 6.67 x 10^-11

part a )

v = sqrt(GM/r )

v = 6197.2347 m/s

part b )

1/2* mv^2 = GMm/r

v = sqrt(2GM/r)

v = 8764.21338 m/s

part c )

using kepler 3rd law

r^3 = GMT^2/4pi^2

T = 17.5 hours = 63000 s

r = 3.07 x 10^7 m

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