problem16

Author

Vishal Paudel

Published

April 12, 2025

  1. For two unequal particles with mass \(m_1\) and \(m_2\) what is the period of circular motion if the distance between the particles is \(d\) and the only force is the force between them is from classical inverse-square Newtonian gravity, \(F = Gm_1m_2/r^2\)?
  2. Pick numbers for \(G\), \(m_1\), \(m_2\) and \(r\) and, using appropriate initial conditions, test your analytical result with a numerical simulation. Make any plots needed to make the agreement of your numerical and analytical results convincing.
  3. For three equal particles, \(m_1 = m_2 = m_3 = 1\) and \(G = 10\) what is the angular speed for circular motion on a circle with diameter of \(d = 3\)?
  4. Check your result for three particles with a numerical simulation, as you did for 2 particles, above.

../../media/problem16/problem16-fbd.png
Figure 1: Problem Diagram

1 For two unequal particles with mass \(m_1\) and \(m_2\) what is the period of circular motion if the distance between the particles is \(d\) and the only force is the force between them is from classical inverse-square Newtonian gravity, \(F = Gm_1m_2/r^2\)?

2 Pick numbers for \(G\), \(m_1\), \(m_2\) and \(r\) and, using appropriate initial conditions, test your analytical result with a numerical simulation. Make any plots needed to make the agreement of your numerical and analytical results convincing.

3 For three equal particles, \(m_1 = m_2 = m_3 = 1\) and \(G = 10\) what is the angular speed for circular motion on a circle with diameter of \(d = 3\)?

4 Check your result for three particles with a numerical simulation, as you did for 2 particles, above.

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