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# 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

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###### 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?