Question

Assume that the Moon is in circular orbit around the Earth. The distance between the Moon and the Earth is approximately 3.56 × 106 km. The period of the Moon’s orbit is approximately 28 days. What is the acceleration of the Moon in km / h2?

Answer 1

Acceleration = 311.2 Km/hr²

Step-by-step explanation:

Given: Radius of the Orbit r= 3.56 × 10⁶ km

Period of the orbit = 28 days = 672 hrs

Sol: We have Fc = MV²/r

⇒M ac = MV²/r

⇒ac = V²/r

First we have to Speed V so for this we have to find the circumference ( distance covered by the moon in one orbit)

⇒ Circumference= 2 π r

= 2 × 3.13149 × 3.56 × 10⁶ km

= 22,368,139.69 Km

Now Speed = Distance /time

Speed = 22,368,139.69 Km / 672 hrs

Speed V = 33,285.92 Km/Hr

Now

ac = V²/r = (33,285.92 Km/hrs)² / 3.56 × 10⁶ km

ac = 311.2 Km/hr²