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kramer
3 years ago
5

Determine the minimum amount of energy needed to move a satellite from its orbit around the Earth to an infinite distance from t

he 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.
Physics
1 answer:
zmey [24]3 years ago
8 0

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

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