Why can't a three/more body problem be reduced to a one-body problem?

  • Context: Graduate 
  • Thread starter Thread starter neelakash
  • Start date Start date
  • Tags Tags
    Central force Force
Click For Summary
SUMMARY

The three-body problem cannot be simplified to a one-body problem due to the absence of an equivalent reduced mass that can encapsulate the interactions among three or more bodies. While the two-body problem can be analyzed using a single equivalent mass, the complexity of the gravitational interactions in a three-body scenario necessitates the use of multiple independent vectors. Specifically, two independent vectors plus the center of mass coordinate are required to fully describe the system, making reduction to a one-body problem infeasible.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with the two-body problem in physics
  • Knowledge of coordinate transformations in multi-body systems
  • Basic grasp of gravitational interactions and center of mass concepts
NEXT STEPS
  • Research the mathematical formulation of the three-body problem
  • Study coordinate transformations in multi-body dynamics
  • Explore numerical methods for solving the three-body problem
  • Investigate the implications of chaotic behavior in three-body systems
USEFUL FOR

Students and professionals in physics, mathematicians specializing in dynamical systems, and researchers focused on celestial mechanics will benefit from this discussion.

neelakash
Messages
491
Reaction score
1
We know a two body problem may be analysed as an equivalent one body problem.Why a three/more body problem cannot be reduced to a one-body problem?

I think in that case we do not find an equivalent reduced mass...
Anyone can say something?
 
Physics news on Phys.org
Try to come up with a coordinate transformation that does any good. Relative coordinates don't work, you need three to specify everything. This is no better than the starting position. Just give it a shot and you'll see.
 
For three bodies, you can reduce the independent vectors to two plus the coordinate of the overall center of mass.
 

Similar threads

  • · Replies 30 ·
2
Replies
30
Views
3K
  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 26 ·
Replies
26
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 29 ·
Replies
29
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
2
Views
3K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 15 ·
Replies
15
Views
2K