what is the minimum energy required to launch a satellite of mass M from the surface of a Planet of mass m and radius R in a circular orbit of the altitude of 2R
Answers
Let’s assume you are launching from the pole, so the rotational velocity of the launch site with respect to the planet’s center is zero. The basic equation for rotational velocity in orbit is:
2=2
So
=‾‾‾‾√
The kinetic energy of a body at radius is then
()=2
The potential energy is just:
()=−
So the total energy required is:
(2)+(2)−()−()=4−2−0−(−)=44+4−24=34
More generally, if the planet has a rotation rate , the velocity of the surface at latitude is cos, so the initial kinetic energy would be 22cos22, and the energy required would be
6−32cos28
This is minimized when =0, which is why launches close to the equator are preferred for orbits with a low degree of inclination to the equator.
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This is very basic orbital mechanics. LEARN HOW!!!
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