A Satellite Orbits The Moon

wpid-acd13-0101-001_3.jpg

Image Credit: NASA Ames/Dana Berry

A satellite orbits the Moon in a circular orbit. The radius of the Moon is 1.74×10^6 m , the mass of the Moon is 7.35×10^22 kg. Calculate the speed of a satellite in a circular orbit, very near the Moon’s surface.

 

Solution.

The gravitational force between the satellite and the Moon is in the radial direction and its magnitude is given by the Newton’s equation

F=G*M*m/R^2

where G is the gravitational constant equals  6.67×10−11 m^3kg^−1s^-2, M and m are the masses of the Moon and the satellite respectively and R is the radius of the orbit (radius of the Moon).

In case of the circular motion the net force equals mass times acceleration, where acceleration could be calculated by v^2/R.

Thereby,
F=m*a=m*v^2/R.

Based on the last formula and the Newton’s equation we should get

G*M*m/R^2=m*v^2/R

or

v=√(G*M/R)

Finally,

v=√(G*M/R) = √(6.67×10−11*7.35×10^22/1.74×10^6) = 1678.54 m/s .

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s