Question

Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.6m/s2. How fast is this spacecraft moving?
A. 53 m/s
B. 75 m/s
C. 1700 m/s
D. 2400 m/s

Answer 1

Spacecraft will be moving in 1700 m/s.

Option C

Explanation:

The diameter of the moon is 3500 km and the free fall acceleration at the surface is given as  $1.6\ \mathrm{m} / \mathrm{s}^2$

The radius will be half of the diameter of the moon that can be written as:  

$r_{\text {moon }}=1.75 \times 10^{6}$

By the application of the equation for orbit speed, we get  

$\begin{aligned}&v_{\text {orbit}}=\sqrt{r \times q}\\&v_{\text {orbit}}=\sqrt{\left(1.75 \times 10^{6}\right) \times\left(1.6\ \mathrm{m} / \mathrm{s}^{2}\right)}\\&v_{\text {orbit}}=1700\ \mathrm{m} / \mathrm{s}\end{aligned}$