Question

A 1000-kg satellite in circular orbit around the Earth is moving at a speed of 7

Answer 1

let h is the initial height above the ground.

Orbital speed, v1 = sqrt(G*M/(Re+h))

v1^2 = G*M/(Re+h)

Re+h = G*M/v1^2

h = G*M/v1^2 - Re

= 6.67*10^-11*5.98*10^24/7000^2 - 6.38*10^6

= 1.76*10^6 m

now new orbital speed,

v2 = sqrt(G*M/(Re+2*h))

= sqrt(6.67*10^-11*5.98*10^24/(6.38*10^6 + 2*1.76*10^6))

= 6347 m/s

initial total mechanical energy, TE1 = -KE1/2

= 0.5*m*v1^2/2

= -0.5*1000*7000^2/2

= -1.225*10^10 J

final total mechanical energy, TE1 = -KE1/2

= 0.5*m*v2^2/2

= -0.5*1000*6347^2/2

= -1.007*10^10 J

Workdone = TE2 - TE1

= -1.007*10^10 - (-1.225*10^10)

= 2.18*10^9 J -------------->>>>>>>>>>>>>>Answer