# Newton's third law of motion

Let's say there are two bodies with equivalent mass. The first one orbits the second, and the second one orbits the first. What kind of orbital pattern would result? Assume that the only force considered here is gravity. I know that the centripetal and centrifugal forces are the result of action and reaction, but I don't know how to determine how the bodies would stay in motion or if they would eventually come in contact.
I'm thinking that the shape would be similar to Fermat's spiral, but I'm not quite sure.

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diazona
Homework Helper
Ellipses. Assuming they don't come close enough to crash into each other, that is (and if they do, it will be on the very first orbit).

It sounds like you're asking about something like a binary star system. There are zillions of those out in space, many of them have been observed and their orbits measured, and they do appear to be elliptical. Or equivalently, a planet-moon system, e.g. Pluto and Charon. (Earth's moon actually orbits the Sun more than it does the Earth, so that's not the best example)

If the orbit is elliptical then the two bodies wouldn't be orbiting around each other.

rcgldr
Homework Helper
The two bodies would orbit about a common center. To make things simple assume a circular path for each.

If there was no gravity, and instead the two bodies were connected by a string, then at each end of the string, the string would exert a centripetal force on the body coexistant with the body exerting an equal and opposing outwards force, sometimes called a reactive centrifugal force. Wiki includes an explanation of this using a single twirling body in diagram #3:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force

However in the original post, there is no string to interact with, and since gravity is the only force, the newton third pair law of forces is the gravitational force each body exerts on the other, and both forces are centripetal and oriented towards the common center of mass.

russ_watters
Mentor
If the orbit is elliptical then the two bodies wouldn't be orbiting around each other.
What do you mean by that? All orbits are elliptical. For two objects mutually orbiting a common center of mass, both objects follow elliptical paths. And even if you assume one object is so much larger that it's center is the center of mass, the orbit of the other object around it is still an ellipse.

My astronomy prof used it in class all the time, and I think it's great.

Last edited by a moderator:
the bodies will revolve around the common center of gravity.

My astronomy prof used it in class all the time, and I think it's great.
wow! the simulator is great! Last edited by a moderator:
wow! the simulator is great! There are a ton of them on their website. http://phet.colorado.edu/en/simulations/category/new

In total, I've probably clocked 100 hours on them, haha.

cool!!! I like it!!