Question

A 180 kg satellite is orbiting on a circular orbit 6355 km above the Earth's surface. Determine the speed of the satellite. (The mass of the Earth is 5.97x1024 kg, and the radius of the Earth is 6370 km.) Submit Answer Tries 0/12

Answer 1

Given that the satellite is in a circular orbit, so the gravitational force experienced by the satellite is equal to the centripetal force.

$F_{g}=F_{c}$

$\frac{GM_{e}m}{(R_{e}+h)^{2}}=\frac{mv^{2}}{(R_{e}+h)}$

$\frac{GM_{e}}{(R_{e}+h)}=v^{2}$

$\sqrt{\frac{GM_{e}}{(R_{e}+h)}}=v$

$\sqrt{\frac{6.674*10^{-11}*5.97*10^{24}kg}{(6.37*10^{6}m+6.355*10^{6}m)}}=v$

$\sqrt{\frac{6.674*10^{-11}*5.97*10^{24}}{(6.37*10^{6}+6.355*10^{6})}}=v$

$\sqrt{\frac{6.674*10^{-11}*5.97*10^{24}}{12.725*10^{6}}}=v$

ANSWER: ${\color{Red} v=5595.661m/s}$

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