Question

1. the model below represents two satellites, a and b, which have approximately the same mass. these satellites are orbiting mars at different distances. using your knowledge of the factors that affect gravitational attraction, describe the relative orbital speeds of both satellites a and b. give a reason for your answer using quantitative evidence from each satellite shown in the model. description of speeds: reason with quantitative evidence:

Explanation:

Gravitational force \(F = \frac{GMm}{r^{2}}\) (where \(G\) is the gravitational constant, \(M\) is the mass of Mars, \(m\) is the mass of the satellite, and \(r\) is the distance from the center of Mars to the satellite). This gravitational force provides the centripetal force \(F = \frac{mv^{2}}{r}\). Equating the two: \(\frac{GMm}{r^{2}}=\frac{mv^{2}}{r}\), so \(v=\sqrt{\frac{GM}{r}}\). Since \(v\propto\frac{1}{\sqrt{r}}\), a smaller \(r\) (distance) means a larger \(v\) (orbital speed). Satellite \(A\) is at \(r_{A}=200\space km\) from Mars and Satellite \(B\) is at \(r_{B} = 500\space km\) from Mars.

Answer:

Description of speeds: Satellite \(A\) has a faster orbital speed than Satellite \(B\).
Reason with quantitative evidence: Using the formula \(v=\sqrt{\frac{GM}{r}}\) (where \(v\) is orbital speed, \(G\) is gravitational constant, \(M\) is mass of Mars, and \(r\) is distance from Mars - satellite). Since \(r_{A}=200\space km\) and \(r_{B}=500\space km\) (\(r_{A}