Question

If the Moon revolves around the Earth in a circular orbit with a period of 27 days, 7 hours, and 43 minutes, and astronomers have clocked it's orbital speed at 1.03 km/s, what is the centripetal acceleration of the Moon due to its orbit around the Earth?

Answer 1

T = (27 da * 24 hr/da + 7 hr + 43 min/60 min/hr) * 3600 sec/hr = 2.36 * 10E6 sec period of moon in sec

C = v t = 2 pi R circumference of orbit where v is orbital speed

ac (centripetal acceleration) = v^2 / R = v^2 / (v t / 2 pi) = 2 pi v / t

ac = 2 pi * 1.03 * 10E3 m/s / 2.36 * 10E6 sec = 2.74 * 10E-3 m /s^2