Planetary Motion

Question

Given that the moon orbits the earth in 27.3 days compute the centripetal force acting on the moon. 

Answer 1

Hi Jamie,

 

Centripetal force Fc is given by

 

Fc = mv²/r

 

where m is the mass of the orbiting body, v is the orbital speed and r is the radius of the orbit.

 

So, m is the mass of the moon. We can look this up to be 7.348 X 10²² kg

r = 384,402 km = 3.84 X 10⁸ m, the distance from the center of the earth to the center of the moon.

 

The orbital speed is v = 2πr/T, where T is the period of the orbit, or 27.3 days.

T = (27.3 days)(24 hour/day)(60 min/hour)(60 sec/min) = 2.358 X 10⁶ sec.

 

So, v = 2π(3.84 X 10⁸ m)/(2.358 X 10⁶ sec) = 1023 m/s

 

Fc = mv²/r = (7.348 X 10²² kg)(1023 m/s)²/(3.84 X 10⁸ m) = 2.00 X 10²⁰ N