Gravitation of moving objects

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SUMMARY

The discussion centers on calculating the effective force between two moving objects with masses m1 and m2, separated by a distance r, while both are traveling at relativistic velocity v in a flat, static spacetime. The key takeaway is that one can apply Special Relativity principles and utilize Lorentz transformations to derive the force in the rest frame. This approach simplifies the analysis, likening the force to that exerted by a spring or similar mechanism.

PREREQUISITES
  • Understanding of Special Relativity principles
  • Familiarity with Lorentz transformations
  • Basic knowledge of force and mass concepts
  • Concept of flat, static spacetime
NEXT STEPS
  • Study the implications of Lorentz transformations on force calculations
  • Explore the relationship between relativistic velocity and force
  • Investigate the concept of effective force in different frames of reference
  • Learn about the application of spring force analogies in relativistic contexts
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Physicists, students of theoretical physics, and anyone interested in the applications of Special Relativity in force dynamics.

johank
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Assuming a flat, static spacetime, what would the effective force between two objects, with mass m1 and m2 respectively, separated by a distance r from one another, both moving in the same direction with relativistic velocity v, be ?
 
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johank said:
Assuming a flat, static spacetime, what would the effective force between two objects, with mass m1 and m2 respectively, separated by a distance r from one another, both moving in the same direction with relativistic velocity v, be ?

For that simple case you can just use Special Relativity and use a Lorentz transformation from the force in the rest frame. It's just the same as if the force were due to a spring or similar.
 

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