Physics-circular motion questions! help me

Question

A satellite(m=12600kg) was launched into orbit around the Earth.

a) How much is the gravitational force on the satellite if it was orbiting the Earth at an altitude of 625kg?

b) Calculate the orbital period for the satellite.

 

help me :(

Answer 1

a) 

 

Calculate the  gravitational force by using the following formula:

F = G Mm/(r+h)^2

Mass of the earth M =5.97219 × 10²⁴   kg

Universal gravitational constant, G = 6.673*10^-11 m³ kg^-1 s^-2

Mass of the sattelite, m =12600 kg

Radius of the earth, r = 6400 km = 6400000 m

Height of the sattelite from earth orbit, h = 625 km =625000 m

F =(6.673*10^-11) (5.97219*10^24)(12600)/(6400000+625000)^2

  =101749.6 N

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Answer 2

b) 

 

Calculate the orbital period of the sattelite by using the following formula:

T ² / (r+h) ³ = 4 π²/ GM

T ² / (6400000+625000) ³ = 4 π²/  (6.673*10^-11)(5.97219 × 10²⁴  )

T ² / 34.7 × 10¹⁹= 4 π²/  (6.673*10^-11)(5.97219 × 10²⁴  )

T ² = 34308642.33

T = 5857.36 s

Comments

Thank you! but I have a question.

I just culculated the T^2, but it is 10930500,

So, the T should be 3306.13 s,,

Is there something wrong?

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T ² / (6400000+625000)³ = 4 π²/  (6.673* 10^-11)(5.97219 × 10²⁴ )

T ² /  3.46688 X 10²⁰= 9.91413*10^-14

T ² = 9.91413*10^-14 X 3.46688 X 10²⁰

T ² = 34371106.85

T = 5862.6878 s