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A satellite is executing a circular orbit around the Earth (M = 5.98x1024 kg) with an...

A satellite is executing a circular orbit around the Earth (M = 5.98x1024 kg) with an orbital speed of 7700 m/s. What is the value of g at this orbital radius?

  1. 9.8 m/s2
  2. 8.8 m/s2
  3. 9.3 m/s2
  4. 9.1 m/s2
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Answer #1

orbital speed = sqrt(GM/R)

where G = gravitational constant

M = mass of the earth

R = radius

7700 = sqrt(6.67*10^-11*5.98*10^24 / R)

R = 6.727*10^6 m

g = GM/R^2

= 6.67*10^-11*5.98*10^24 / (6.727*10^6)^2

= 8.81 m/s^2

so second option 8.8 m/s^2 is the correct answer

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