Question

two satellites, x and y, are orbiting earth. satellite x is 1.2×10⁶ m from earth, and satellite y is 1.9×10⁵ m from earth. which best compares the satellites? satellite x has a greater period and a faster tangential speed than satellite y. satellite x has a greater period and a slower tangential speed than satellite y. satellite x has a shorter period and a faster tangential speed than satellite y. satellite x has a shorter period and a slower tangential speed than satellite y.

Explanation:

Step1: Recall the formulas for period and tangential speed of a satellite

The period \(T\) of a satellite in orbit around Earth is given by \(T = 2\pi\sqrt{\frac{r^{3}}{GM}}\), where \(r\) is the distance from the center of the Earth, \(G\) is the gravitational constant, and \(M\) is the mass of the Earth. The tangential speed \(v\) is given by \(v=\sqrt{\frac{GM}{r}}\).

Step2: Analyze the effect of \(r\) on \(T\) and \(v\)

From \(T = 2\pi\sqrt{\frac{r^{3}}{GM}}\), we can see that \(T\) is directly proportional to \(\sqrt{r^{3}}\). Since \(r_X=1.2\times 10^{6}\text{ m}\) and \(r_Y = 1.9\times 10^{5}\text{ m}\) (\(r_X>r_Y\)), \(T_X>T_Y\).
From \(v=\sqrt{\frac{GM}{r}}\), we can see that \(v\) is inversely proportional to \(\sqrt{r}\). Since \(r_X > r_Y\), \(v_X

Answer:

Satellite X has a greater period and a slower tangential speed than Satellite Y.