Question

In order to place a satellite into orbit, it requires enough fuel to supply the necessary mechanical energy. Into what types of mechanical energy does the fuel get transformed?

Answer 1

When a satellite is revolving into the orbit around a planet then we can say

net centripetal force on the satellite is due to gravitational attraction force of the planet, so we will have

$F_g = F_c$

$\frac{GM_pM_s}{r^2} = \frac{M_s v^2}{r}$

now we can say that kinetic energy of satellite is  given as

$KE = \frac{1}{2}M_s v^2$

$KE = \frac{GM_sM_p}{2r}$

also we know that since satellite is in gravitational field of the planet so here it must have some gravitational potential energy in it

so we will have

$U = -\frac{GM_sM_p}{r}$

so we can say that energy from the fuel is converted into kinetic energy and gravitational potential energy of the satellite