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

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Discussion Overview

The discussion centers on the orbital patterns of two bodies of equal mass that orbit each other under the influence of gravity. Participants explore the nature of these orbits, considering various shapes and dynamics involved in the interaction between the two bodies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the orbital pattern might resemble Fermat's spiral, expressing uncertainty about how the bodies would maintain motion without colliding.
  • Another participant asserts that the orbits would be elliptical, referencing binary star systems as examples, while noting the condition that they do not come too close to each other.
  • A different viewpoint questions the elliptical nature of the orbits, arguing that if they are elliptical, the bodies would not be orbiting around each other.
  • One participant clarifies that the two bodies would orbit around a common center of mass, proposing a circular path for simplicity and discussing the forces involved without gravity.
  • Another participant emphasizes that all orbits are elliptical, stating that both bodies follow elliptical paths around their common center of mass, regardless of mass differences.
  • Several participants share links to a simulation tool that may assist in visualizing the concepts discussed.

Areas of Agreement / Disagreement

There is disagreement regarding the nature of the orbits, with some participants asserting they are elliptical while others challenge this claim. The discussion remains unresolved as participants present differing views on the orbital dynamics.

Contextual Notes

Participants express varying assumptions about the conditions of the orbits, including the influence of gravity and the potential for collision. The discussion does not resolve these assumptions or the implications of different orbital shapes.

ionowattodo
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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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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.
 
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.
 
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.
 
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.
 
Last edited by a moderator:
the bodies will revolve around the common center of gravity.
 
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:
 
Last edited by a moderator:
  • #10
cool! :smile: I like it!
 

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