University · Ages 18+First-year university · Physics olympiadsAdvanced

 

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Setups other learners found interesting in Three Body Problem. Try one, then tweak it.

Three Body Problem

Three masses attract each other through Newtonian gravity. Unlike the two-body problem, this system has no general closed-form solution: the motion is chaotic, and tiny changes in the starting positions or velocities lead to completely different futures. The simulation integrates the equations numerically with small sub-steps to stay accurate through close approaches.

Key formulas

  • F⃗ij=− G mimj∣r⃗ij∣2 r^ij\vec{F}_{ij} = -\,G\,\dfrac{m_i m_j}{|\vec{r}_{ij}|^{2}}\,\hat{r}_{ij}

    Gravitational force between two bodies

    Open the formula card
  • F⃗i=∑j≠iF⃗ij\vec{F}_i = \sum_{j \ne i} \vec{F}_{ij}

    Net gravitational force

    F⃗i\vec{F}_i
    Net force on body iN
    F⃗ij\vec{F}_{ij}
    Force on body i from body jN
    Open the formula card

What you can change

  • Starting configuration
  • Body mass
  • Gravitational constant
  • Body size
  • Randomness

Key concepts

  • Newton's law of universal gravitation
  • Superposition of forces from multiple bodies
  • Sensitivity to initial conditions (deterministic chaos)
  • Numerical integration and conservation checks