Physics: For a satellite to be in a circular orbit 590 km above the surface of the earth, what orbital speed must it be given? express your answer with the appropriate units.

For a satellite to be in a circular orbit 590 km

Ответ:

meganwintergirl

15.01.2022

7.57 km/s

Explanation:

The gravitational force on the satellite provides the centripetal force that keeps the satellite in circular orbit, so we can write:

$\frac{GMm}{r^2}=m\frac{v^2}{r}$

where

G is the gravitational constant

$M=5.98\cdot 10^{24}kg$ is the Earth's mass

m is the satellite's mass

r = R+h is the distance of the satellite from the Earth's centre, where:

$R=6371 km=6.37\cdot 10^6 m$ is the Earth's radius,

$h=590 km = 0.59\cdot 10^6 m$ is the altitude of the satellite above Earth

v is the orbital speed of the satellite

Solving the equation for v, we find

$v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{(6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2})(5.98\cdot 10^{24} kg)}{(6.37\cdot 10^6 m+0.59\cdot 10^6 m)}}=7570 m/s=7.57 km/s$

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Ответ:

shiann2002

07.04.2021

Physics

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For a satellite to be in a circular orbit 590 km above the surface of the earth, what orbital speed must it be given? express your answer with the appropriate units.

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