(Solved): (a) What is the value of \( g_{\text {moon, the acceleration of gravity on the surface of the moon? ...

(a) What is the value of \( g_{\text {moon, the acceleration of gravity on the surface of the moon? (mass of the moon: }} \) \( M_{\text {moon }}=7.35 \times 10^{22} \mathrm{~kg} \); radius of the moon: \( R_{\text {moon }}=1.74 \times 10^{6} \mathrm{~m} \) ) (b) What is the escape velocity from the moon's surface? (c) Suppose you want to put a satellite in a circular orbit \( 100 \mathrm{~km} \) above the surface of the moon. What speed does it need to have? (d) If the satellite's inertia is \( 200 \mathrm{~kg} \). what is the gravitational potential energy of the moon-satellite system for that orbit? (e) Under the same assumptions, what would be the satellite's angular momentum? (Around the center of the moon.) Suppose now that the satellite is placed in orbit starting at that height and with the correct speed, as calculated on part (c), but the angle of insertion is wrong, so the initial velocity has a small radial component: (f) What kind of orbit (circular, elliptic,parabolic, etc.) does the satellite end up in? (g) Is the satellite's angular momentum constant for that orbit? (h) What is the semimajor axis of that wibit? (Hint: think about the total mechanical energy and how it compares to the previous case.)