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Concept

Problem: A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.01 x 104 m/s, and the radius of the orbit is 2.76 x 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 9.09 x 106 m. What is the orbital speed of the second satellite?

FREE Expert Solution

The general relationship between the orbital distance and speed can be found by equating the centripetal force with gravitational force.

$\overline{)\begin{array}{rcl}\frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}& {\mathbf{=}}& \frac{\mathbf{G}\mathbf{M}\mathbf{m}}{{\mathbf{r}}^{\mathbf{2}}}\\ {\mathbf{v}}& {\mathbf{=}}& \sqrt{\frac{\mathbf{G}\mathbf{M}}{\mathbf{r}}}\end{array}}$

The radius of the second orbit increases by a factor of 9.09/2.76 = 3.29

Therefore, the orbital speed will change by a factor of sqrt (1/3.29) = 0.55

Problem Details

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.01 x 104 m/s, and the radius of the orbit is 2.76 x 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 9.09 x 106 m. What is the orbital speed of the second satellite?