Question

a satellite orbits the earth at a height of 400 km above the surface. how much energy must be expended to rocket the satellite out of the earth's gravitational influence ? mass of the satellite 200kg , mass of the earth is 6.0 × 10^24 kg​

Answer 1

Given :

Height of the satellite = 400 km = 0.4 × 10⁶ m

Mass of the earth = 6.0 × 10²⁴ kg

Mass of the satellite = 200kg

To find :

The energy expended to rocket the satellite out of the earth's gravitational influence.

Solution :

We know that,

The total energy of the satellite is given by,

$\dashrightarrow \sf E = - \dfrac{GMm}{2r}$

By substituting the values in the above Formula,

$\dashrightarrow \sf E = - \dfrac{GMm}{2(R + h)}$

$\dashrightarrow \sf E = - \dfrac{6.67 \times {10}^{ - 11} \times 6.0 \times {10}^{24} \times 200}{2(6.4 \times {10}^{6} + 0.4 \times {10}^{6} )}$

$\dashrightarrow \sf E = - 5.89 \times {10}^{9} J$

$\dashrightarrow \sf E =0 - ( - 5.89 \times {10}^{9})$

$\dashrightarrow \sf E = 5.89 \times {10}^{9}J$

Therefore, The energy expended to rocket the satellite out of the earth's gravitational influence is 5.89 × 10⁹ J