Question

A spaceship is stationed on Mars. How much energy must be expanded on the spaceship to rocket it out of the solar system? Mass of the spaceship = 1000 kg; mass of the Sun = 2 x 10³⁰ kg; mass of Mars = 6.4 x 10²³ kg; radius of Mars = 3395 km; radius of the orbit of Mars = 2.28 x 10⁸ km; G = 6.67 x 10^-11 Nm² kg^-2.

Answer 1

Let M = Mass of the sun

M' = Mass of Mars

R = Radius of the orbit of the Mars

m = mass of the spaceship

The P.E. of spaceship due to gravitional attraction of the sun = -GMm/R

P.E. of the spaceship due to gravitational attraction of Mars = -GM'm/R'

Since, K.E. of the spaceship = 0

Total energy of the spaceship

= -GMm/R - GM'm/R' = -Gm[M/R + M'R']

The energy required to rocket out the spaceship from the solar system,

= -(total energy of spacesh)