Central force as a conic: How to show it?

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SUMMARY

The discussion focuses on demonstrating that a particle under a central force, defined as F = -k/r² (where k > 0), follows a conic path. The connection to Kepler's second law is established, and the relationship between the force and the conic equation r = (pe)/(1 + ecosB) is explored. Participants emphasize the importance of following specific steps outlined in the referenced thread to derive the conic trajectory from the given force equation.

PREREQUISITES
  • Understanding of central force dynamics
  • Familiarity with Kepler's laws of planetary motion
  • Knowledge of conic sections and their equations
  • Basic calculus for analyzing motion under forces
NEXT STEPS
  • Study the derivation of Kepler's laws from central force equations
  • Learn about the properties of conic sections in physics
  • Explore the mathematical techniques for solving differential equations related to motion
  • Investigate the implications of central forces in orbital mechanics
USEFUL FOR

Students of physics, mathematicians interested in celestial mechanics, and anyone studying orbital dynamics will benefit from this discussion.

kthouz
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If F denotes the central force and is given as the inverse of the square distance
F=-k/r^2. where k>0. How can i show that F the path of the partilce under that force is a conic?
What i can see is that it is the second law of Kepler. And when i try to compare F with the former equation of conics r= (pe)/(1+ecosB). I can find p!
Just i need your help
 
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