Question

plz solve this one
The K.E of a satellite in an orbit close to the surface of earth is K.it's maximum KE so as to escape from the gravitational field of earth is _________ .

Answer 1

the gravitational potential energy U1 of the satellite near earth will be U1 = -GMm/r (obtained from Newton's inverse square la for gravitation), with r = radius earth. thus total energy E1 near earth = K + U1.

if E2 = energy at r = infinity (well, far enough away for PE --> 0), then E2 = 0 as U2 = 0 (0 because no gravitational potential as you have moved away from earth), K2 = 0 (0 again 0 because you only had enough energy to escape the earths field in the first place).

thus E2 = E1 = K + U1 = 0

thus K = GMm/r

Answer 2

answer is 2K

Answer 3

In orbit:
mv^2/ r = GMm/ r^2 (balances forces, right?)

It follows that:
K1 (kinetic energy satellite has in orbit ) = 1/2 mv^2 = (1/2) * GMm/r



We conclude that K (energy it needs to escape) = 2 K1

Note the factor of 1/2 in previous post.

I can write that out more sensibly if it matters.

Answer 4

no need to to that now :)