Question

A 4500-kg spaceship is in a circular orbit 190 km above the surface of Earth. It needs to be moved into a higher circular orbit of 380 km to link up with the space station at that altitude. In this problem you can take the mass of the Earth to be 5.97 × 1024 kg.
I am confused how to solve this problem, please show how this answer is obtained.

Answer 1

Answer:

Explanation:

Total energy of a satellite in an orbit , h height away

= -  GMm /2 ( R + h )

When h = 380 km

Total energy of a satellite = $\frac{6.67\times10^{-11}\times5.97\times10^{24}\times 4500}{2\times(6378+380)\times10^3}$

=  - 13.25 x 10¹⁰ J

When h = 190 km

Total energy of a satellite =

$\frac{6.67\times10^{-11}\times5.97\times10^{24}\times 4500}{2\times(6378+190)\times10^3}$

=   - 13.63 x 10¹⁰ J

Diff

= 38 x 10⁸ J Energy will be required.