Question

A satellite of mass mS orbits the Earth (with mass mE and radius RE) with a velocity v and an
altitude h. The gravitational force FG and the centripetal force FC are given by:
FG = G
mS · mE
(RE + h)
2
, FC =
mS · v
2
RE + h
, G = const.
Based on the kinetic energy, how much liquid hydrogen (energy density: 106
J/Litre) is at least
needed to bring a small 1 kg satellite in an orbit of 400 km. (Use literature to find mE, RE, G.)

Answer 1

Answer:

If the satellite is at height "h" then the Kinetic energy will be K.E = GMm/r + h

Explanation:

Question statement:

Find an equation for the kinetic energy Ekin(h) of a satellite with an altitude h.?

Solution:

The kinetic energy of an object in orbit can easily be found from the following equations:

Centripetal force on a satellite of mass m moving at velocity v in an orbit of radius r = mv^2/r

F =GMm/r^2 and so mv^2 = GMm/r

But kinetic energy K.E = mv^2 and so:

Kinetic energy of the satellite K.E = GMm/r

If the satellite is at height "h" then the Kinetic energy will be K.E = GMm/r + h

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