The ISS orbits the Earth at approximately 400,000m altitude. Its mass is 419725 kg. The Earth’s average radius and mass are 6.38e6m and 5.97e24kg. What is the orbital velocity of the International Space Station?

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meep26wesley

High School

The ISS orbits the Earth at approximately 400,000m altitude. Its mass is 419725 kg. The Earth’s average radius and mass are 6.38e6m and 5.97e24kg. What is the orbital velocity of the International Space Station?

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skyluke89

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Answer:
7.66 km/s
Explanation:
The force of gravity between the Earth and the ISS corresponds to the centripetal force that keeps the ISS in circular motion around the Earth:
$G\frac{mM}{(R)^2}=m\frac{v^2}{R}$
where
$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant
$m=419725 kg$ is the mass of the ISS
$M=5.97\cdot 10^{24} kg$ is the mass of the Earth
$R=r+h=6.38\cdot 10^6 m + 400,000 m=6.78\cdot 10^6 m$ is the distance between the ISS and the Earth's centre (given by the sum of the Earth's radius, r, and the ISS altitude, h)
$v=?$ is the orbital velocity of the ISS
Re-arranging the equation and substituting numbers, we find the orbital velocity:
$v=\sqrt{\frac{GM}{R}}=\sqrt{\frac{(6.67\cdot 10^{-11})(5.97\cdot 10^{24} kg)}{6.78\cdot 10^6 m}}=7,664 m/s=7.66 km/s$
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