Collision of Unequal Mass Particles in a Gravitational Field

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Discussion Overview

The discussion revolves around the collision of two unequal mass particles in a gravitational field, exploring whether they collide at their center of mass (CM) under different conditions, including the presence of an external uniform gravitational field. The scope includes theoretical considerations and conceptual clarifications regarding the nature of the collision and the definition of center of mass.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question whether the particles will always collide at their center of mass, particularly when considering them as point particles versus rigid bodies.
  • One participant emphasizes that the center of mass of an n-body system remains unchanged regardless of the individual movements of the particles.
  • Another participant discusses the forces acting on the particles, suggesting that if the forces are aligned along the line connecting the two particles, they will move towards each other and eventually collide.
  • There is a consideration of how a uniform gravitational field affects the motion of the particles, with one participant proposing that the gravitational field's direction and components could influence the collision dynamics.
  • One participant asserts that if the bodies are treated as point particles, the geometry implies they must collide at the center of mass, although the position of the center of mass may vary depending on the mass distribution.

Areas of Agreement / Disagreement

Participants express differing views on the definition of "collide at CM" and whether this holds true under various conditions. The discussion remains unresolved, with multiple competing perspectives on the implications of gravitational fields and the nature of the particles involved.

Contextual Notes

Participants note limitations regarding the definitions of center of mass and the assumptions made about the particles' sizes and rigidity, which may affect the conclusions drawn about their collision behavior.

gianeshwar
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Dear friends!
If there are two particles of unequal masses in a system on which there are no external forces.When let free they collide under the influence of gravitation.
Should they always collide at CM.
If the system were under an external force of uniform gravitational field will the collision occur at CM only.
Thanks!
 
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Draw a picture of the two particles and mark by dots the locations of their centres of mass. Draw a line between the two dots. Then draw two vector arrows, showing the direction of the gravitational force on each of the two particles.

Then you need to clearly specify what you mean by 'collide at CM'. For almost all particles, the CM is inside the particle, so it is impossible for the CMs of the two particles to touch one another. Which definition you choose will affect the answer to the second part of the question.
 
Thanks andrewkirk! Yes I understand their centre of mass cannot touch due to their sizes as they are assumed rigid bodies.
If I assue them to be point particles then what happens?
 
If there are no other things around, the center of mass of an n-body system does not change, whatever the individual objects do.
 
With two point particles and no other bodies, the forces on the two bodies are along the line that connects the two particles, so they move towards one another. Is there any reason for either of them to deviate from that line? If not, they will eventually collide.

If there's a uniform gravitational field, imagine it in an x-y plane, first where the two points have the same y coordinates and the grav field points in the positive y direction. Then you can consider the vertical and horizontal components of velocity separately, because the axes are orthogonal and do not change direction. The horizontal components are the same as in the first case. So if in the first case the two particles collide at time T, what happens in the second, assuming the only difference between the two cases is the gravitational field?

More generally, the grav field may not be orthogonal to the line between the two particles. In that case, it imparts an additional horizontal acceleration to both particles, as well as the vertical accelerations. But since that horizontal acceleration is the same for both, it doesn't affect when they collide.
 
Last edited:
gianeshwar said:
Should they always collide at CM.
The geometry of the situation means that has to be correct if the bodies are points. When they are together, they are at the CM. Where else could the CM be? It has to be between them and can't be outside the system. If one body is much bigger than the other then they won't get close enough and the CM can be below the surface of one of them.
 
Thanks mathman,andrewskirk and sophicentaur!
 

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