What orbital pattern occurs when two bodies of equal mass orbit each other?

In summary, when two bodies with equivalent mass orbit each other, the resulting orbital pattern would be elliptical, assuming that they do not come in contact with each other. This is due to the force of gravity being the only force considered, resulting in the Newton Third Law of Motion where the bodies exert equal and opposite centripetal forces towards the common center of mass. The orbital pattern can be visualized using simulations such as the one provided by phet.colorado.edu.
  • #1
ionowattodo
11
0
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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  • #2
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)
 
  • #3
If the orbit is elliptical then the two bodies wouldn't be orbiting around each other.
 
  • #4
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.
 
  • #5
ionowattodo said:
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.
 
  • #6
Maybe http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html" will help.

My astronomy prof used it in class all the time, and I think it's great.
 
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  • #7
the bodies will revolve around the common center of gravity.
 
  • #8
Archosaur said:
Maybe http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html" will help.

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

wow! the simulator is great! :smile:
 
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  • #10
cool! :smile: I like it!
 

What is Newton's third law of motion?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object will exert an equal force in the opposite direction on the first object.

How does Newton's third law of motion apply to everyday life?

Newton's third law of motion can be observed in many everyday situations, such as when you push a door open, the door pushes back on you with an equal force. It also explains how rockets are able to move forward in space by pushing exhaust gases out the back in the opposite direction.

Does Newton's third law of motion apply to both objects at rest and in motion?

Yes, Newton's third law of motion applies to both objects at rest and in motion. Even if an object is not moving, it still exerts a force on another object and receives an equal and opposite force in return.

Can Newton's third law of motion be violated?

No, Newton's third law of motion is a fundamental law of physics that has been proven through countless experiments and observations. It cannot be violated or proven wrong.

How does Newton's third law of motion relate to momentum?

Newton's third law of motion states that forces always occur in pairs, meaning that the total momentum of a system is always conserved. This means that the momentum of one object will always be equal and opposite to the momentum of the other object in the pair.

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