Question

The moon has a mass of 7.4 × 1022 kg and completes an orbit of radius 3.8×108 m about every 28 days. The Earth has a mass of 6 × 1024 kg and completes an orbit of radius 1.5 × 1011 m every year. What is the speed of the Moon in its orbit? Answer in units of m/s.

Answer 1

To solve this problem it is necessary to apply the kinematic equations of movement description, where the speed of a body is defined as the distance traveled in a given time, that is to say

$v = \frac{x}{t}$

where,

x = Displacement

t = time

Since the moon is making a path equal to that of a circle, we know by geometry that the perimeter of a circle is given by

$x = 2\pi r$

$x = 2\pi (3.8*10^8)$

$x=2.39*10^9m$

At the same time we have that time is equal to

$t = 28days(\frac{86400s}{1day})$

$t = 2419200s$

Using the equation for velocity we have finally that

$v= \frac{x}{t}$

$v = \frac{2.39*10^9}{2419200}$

$v = 987.92 m/s$

Therefore the speed of the Moon in its orbit is 987.92m/s