Question

Determine the minimum amount of energy needed to move a satellite from its orbit around the Earth to an infinite distance from the Earth. The mass of the satellite is 7.45 X 10^3 kg and its orbital radius is 7.50 X 10^6 m. Take the mass of the Earth to be 5.97 X 10^24 kg.

Answer 1

Answer:$19.80\times 10^{10} J$

Explanation:

Given

mass of satellite $m=7.45 \times 10^3 kg$

orbital radius $R=7.50\times 10^6 m$

mass of Earth $M=5.97\times 10^{24} kg$

Minimum amount of Energy to move Satellite from its orbit to an infinite distance is sum of Potential Energy + Kinetic Energy of Satellite

$W=U+K.E.$

$U=-G\frac{Mm}{R}$

$U=-6.67\times 10^{-11}\times \frac{5.97\times 10^{24}\times 7.45 \times 10^3}{7.50\times 10^6}$

$U=-\frac{296.658\times 10^{16}}{7.5\times 10^6}$

$U=-39.55\times 10^{10} J$

$K.E.=\frac{1}{2}\times mv^2$

Where $v=orbital\ velocity$

$v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{6.67\times 10^{-11}\times 5.97\times 10^{24}}{7.50\times 10^6}}$

$v^2=5.30\times 10^7 m/s$

$K.E.=\frac{1}{2}\times mv^2$

$K.E.=\frac{1}{2}\times 7.45\times 10^3\times (5.30\times 10^7)=19.74\times 10^{10} J$

$W=-39.55\times 10^{10}+19.74\times 10^{10}$

$W=-19.80\times 10^{10} J$

i.e. $19.80\times 10^{10} J$ Energy is required to provide to move Satellite out of its orbit