Is the gravitational force exerted by the Earth on the Moon equal to the centripetal force acting on the Moon?
The moon is revolving around the earth! Then,the gravitational force exerted by earth on moon should be equal to the centripetal force(the force acting inwards when an object is moving in circular path). Is that right?
Thank you for your question, what you say is true, the gravitational force exerted by the Earth on the Moon has to be equal to the centripetal force.
An interesting application of this principle is that it allows you to determine a relation between the period of an orbit and its size. Let us assume for simplicity the Moon's orbit as circular (it is not, but this is a good approximation for our purposes).
The gravitational acceleration that the Moon experience due to the gravitational attraction from the Earth is given by:
Where G is the gravitational constant, M stands for mass, and r is the radius of the orbit. The centripetal acceleration is given by:
acentr=(4 pi2 r)/T2
Where T is the period. Since the two accelerations have to be equal, we obtain:
(4 pi2 r) /T2=G(MEarth+MMoon)/r2
This is the so-called third Kepler law, that states that the cube of the radius of the orbit is propprtional to the square of the period.
This has interesting applications. In the Solar System, for example, if you know the period and the radius of one planet orbit, by knowing another planet's period you can determine its orbit radis. I hope that this answers your question.
Get More 'Curious?' with Our New PODCAST:
- Podcast? Subscribe? Tell me about the Ask an Astronomer Podcast
- Subscribe to our Podcast | Listen to our current Episode
- Cool! But I can't now. Send me a quick reminder now for later.
How to ask a question:
If you have a follow-up question concerning the above subject, submit it here. If you have a question about another area of astronomy, find the topic you're interested in from the archive on our site menu, or go here for help.
This page has been accessed 28061 times since September 27, 2002.
Last modified: June 4, 2003 9:34:30 PM
Ask an Astronomer is hosted by the Astronomy Department at Cornell University and is produced with PHP and MySQL.
Warning: Your browser is misbehaving! This page might look ugly. (Details)