Question

Consider a 435 satellite in a circular orbit at a distance of 3.19X10^4 above the Earth’s surface. What is the minimum amount of work W the satellite’s thrusters must do to raise the satellite to a geosynchronous orbit?

Geosynchronous orbits occur at approximately 3.6X10^4 above the Earth’s surface. The radius of the Earth and the mass of the Earth are RE=6.37X10^3 and 5.97X10^24 respectively. The gravitational constant is G = 6.67X10^-11 Assume the change in mass of the satellite is negligible.

Answer 1

let m = 435 kg

we know, relation between Kinetic energy and potential energy,

KE = -PE/2

W = change in mechanical energy

= (KEf + PEf) - (KEi + PEi)

= (-PEf/2 + PEf) - (-PEi/2 + PEi)

= PEf/2 - PEi/2

= -0.5*G*Me*m/(Re + h2) - (- 0.5*G*Me*m/(Re + h1) )

= 0.5*G*Me*m*(1/(Re + h1) - 1/(Re + h2) )

= 0.5*6.67*10^-11*5.97*10^24*435*(1/(6.37*10^6 + 3.19*10^7) - 1/(6.37*10^6 + 3.60*10^7) )

= 2.19*10^8 J <<<<<<<<------------Answer