What Happens if Masses are Negative in Newtonian Potential?

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SUMMARY

The discussion centers on the implications of negative masses in the Newtonian potential formula V=-G*m*M/r. It explores four specific cases: 1) both masses negative (m<0, M<0); 2) one mass positive and larger (m>0, M<0, m>|M|); 3) one mass positive and smaller (m>0, M<0, m<|M|); and 4) one mass positive and equal in magnitude but opposite in sign (m>0, M=-m). The participants emphasize the need for an analytical approach to solve these cases, drawing parallels to electrostatic potential V=-kqq'/r, where both charges can also be positive or negative.

PREREQUISITES
  • Understanding of Newtonian mechanics and gravitational potential.
  • Familiarity with the concept of central force motion.
  • Basic knowledge of electrostatic potential and its mathematical representation.
  • Ability to perform analytical problem-solving in physics.
NEXT STEPS
  • Research the implications of negative mass in theoretical physics.
  • Study the mathematical derivation of gravitational potential energy in various scenarios.
  • Explore the analogy between gravitational and electrostatic forces in detail.
  • Learn about central force motion and its applications in classical mechanics.
USEFUL FOR

This discussion is beneficial for physics students, educators, and researchers interested in advanced mechanics, particularly those exploring non-standard scenarios involving negative masses and their effects on potential energy.

jack7992
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Homework Statement



Imagine that you have two particles with masses m and M, interacting with the standard Newtonian potential V=-G*m*M/r . When both masses are positive, you have a textbook example of central force motion. What happens if masses are negative? Discuss the cases 1) m<0, M<0; 2) m>0, M<0, m>|M|; 3) m>0, M<0, m<|M|; and 4) m>0, M=-m respectively.

Homework Equations


The Attempt at a Solution



I was planning on just doing more of a analytic approach versus a computational, but my professor want's me to solve it explicitly, and I'm not to sure how to do that. Any hints for just one of the cases would be great!
 
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So, note that the Electro-static potential is V=-kqq'/r

Here q and q' can be either positive or negative. So...try to see some analogy with that maybe? k->G, q->M, q'->m.
 

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