Question

if a satellite transfers to an orbit that is farther away from a planet, what happens to its velocity and period? (1 point)
the period is shorter because the satellite moves faster.
the period is shorter because the satellite moves slower.
the period is longer because the satellite moves slower.
the period is longer because the satellite moves faster.

Explanation:

Step1: Use the formula for orbital velocity

The orbital velocity formula is \(v = \sqrt{\frac{GM}{r}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the planet, and \(r\) is the orbital radius. As \(r\) increases (satellite moves to a farther orbit), the value of \(v\) decreases (since \(v\) is inversely proportional to \(\sqrt{r}\)).

Step2: Use the formula for orbital period

The orbital period formula is \(T = 2\pi\sqrt{\frac{r^{3}}{GM}}\). As \(r\) increases, the value of \(T\) increases (since \(T\) is proportional to \(\sqrt{r^{3}}\)).

Answer:

The period is longer because the satellite moves slower.