Question

What is the speed of a satellite that orbits about a star with a mass of 3.66 X10 to the power of 32 kg along a circular path with a radius of 4.75 x 10 to the power of 14 m?

Answer 1

Answer on Question #43392, Physics, Mechanics — Kinematics — Dynamics —

What is the speed of a satellite that orbits about a star with a mass of 3.66 X10 to the power of 32 kg along a circular path with a radius of 4.75 x 10 to the power of 14 m?

Solution

Centripetal acceleration is caused by gravitational force:

$a_{sat}=\frac{F}{m_{sat}}=\frac{GM_{star}m_{sat}/r^{2}}{m_{sat}}$

$\frac{v^{2}}{r}=\frac{GM_{star}}{r^{2}}$

Hence

$v=\sqrt{\frac{GM_{star}}{r}}=\sqrt{\frac{6.67\cdot 10^{-11}\cdot 3.66\cdot 10^{32}}{4.75\cdot 10^{14}}}\approx 7.17\cdot 10^{3}\,m/s$

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