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A space-craft is at a distance of 100; 000 km from the Earth’s centre and is moving

with a speed of 4 km/s, as measured in the assumed inertial frame of the Earth, with no

thrust from its engines. It is currently moving along a direction that passes the Earth

by a perpendicular distance of 25,000 km from the Earth’s centre.

1.The space-craft continues to travel in the gravitational field of the Earth with

no thrust from its engines. Calculate the parameters associated with the spacecraft’s

orbit. What is the closest distance between the space-craft and the Earth’s

centre? Will it hit the Earth? If not, will the orbit cause it to return to the Earth

again?

2. Suppose the space-craft fires its engines in a radial direction with respect to the

Earth’s centre to try to get into a circular orbit about the Earth. Could this be successful

and, if so, at what radius would it orbit the Earth? Neglect any reduction

in mass of the space-craft on firing its engines.