An artificial satellite circling the Earth completes each or

An artificial satellite circling the Earth completes each orbit in 121 minutes. (The radius of the Earth is 6.38 times 10^4m. The mass of the Earth is 5.98 times 10^24 kg. Find the attitude of the satellite. What is the value of g at the location of this satellite?

Solution

a.

the expression for V^2 is, V^2 =(GM/(R+h)

the period is, T = 2 pi (R+h)/V

hence,

T^2=4pi^2(R+h)^3/GM

R+h)^3 = T^2 GM/[4pi^2]

(R+h)^3=121*60*121*60*6.67*10^-11*5.98*10^24 / 4*3.14*3.14

R+h = 8.108*10^6

altitude: h = 8.108*10^6-6.38 *10^6 = 1.728 *10^6 m

b.

acceleration due to gravity:

g = GM/(R+h) ^2

= 6.67*10^-11* 5.98*10^24/(8.108*8.108*10^12)

= 6.07 m/s^2