A satellite with a mass of 8000 kg must be moving at a velocity of 27,700 km/hr

Question

A satellite with a mass of 8000 kg must be moving at a velocity of 27,700 km/hr to achieve an orbit 100 km above the surface of the Earth. How much work does the rocket it is launched on do to put the satellite in orbit assuming that it starts on the ground (6400 km from the center of the Earth) with zero velocity? Explain how each of these factors that you are not accounting would increase or decrease the work needed and explain which part of your calculation it would be included in:
• The air resistance against the rocket as it accelerates.
• The rotation of the Earth. (Is the rocket really at zero velocity before it launches?)
• The rocket the satellite is on also has mass that decreases as it burns fuel.
It takes 2.45 x 1011 J of energy to launch the rocket.

Explanation / Answer

final speed of satellite , u = 27700 km/hr

as 1 kmph = 5/18 m/s

u = 7694.44 m/s

radius of orbit , R = 6371 + 100 = 6471 Km

work needed = increase in kinetic energy+ increase in potential energy

work needed = 0.5 * 8000 * 7694.44^2 + 6.673 *10^-11 * 8000 * 5.98*10^24 *(1/(6371 *10^3) - 1/(6471 *10^3))

work needed = 2.445 * 10^11 J

work done by the rocket to take the satellite in the orbit is 2.445 * 10^11 J

Air resistance will increases the amount of workdone

Rotation of earth INCREASES the amount of workdone

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