Question

We want to place a satellite moving in a circular orbit 500 km above the earth's surface in a circular orbit 1000 km above the earth's surface. To do this, first give the satellite a speed increase of ikenv while it is in the 1st green orbit and place it in the 2nd yellow elliptical orbit, and then, when the elliptical orbit reaches a distance of 1000 km from the ground, it gives it a second Δv 'velocity and allows the satellite to settle in the 3rd red circular orbit. .

a) What is the total speed increase Δvtoplam = Δv + Δv 'to be given to the satellite?

b) How many seconds does the satellite change from 500 km orbit to 1000 km orbit?

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Answer 1

This Problem is based on the Hohmann orbit transfer in which a spacecraft is transferred from a circular orbit to another circular orbit via an elliptical orbit.

Given that

radius of earth = R = 6371 km (say)

= 500 km from the surface of earth = 6871 km

= 1000 km from the surface of earth = 7371 km

From the Concept of Hohmann transfer, we know that

Here a = = semi-major axis of the transfer orbit

- standard gravitational parameter

For earth,

time taken for orbit transfer