Please enable JavaScript.

Coggle requires JavaScript to display documents.

10 Fields (Gravitational Field (Gravitational Potential (\(V…

- - - - Force pushes charges together and stores ":heavy_plus_sign:" EPE
    - - Force brings charges closer together and stores " :heavy_minus_sign: " EPE
- - - - \(\frac{mv^2}{r}=\frac{GMm}{r^2}\)
        
        \(v=\sqrt{\frac{GM}{r}}\)
  - - - From orbital velocity
        \(v^2=\frac{GM}{r}\)
        
        KINETIC ENERGY
        \(\frac{1}{2}mv^2=\frac{GMm}{2r}\)
      - \(E_T=\frac{GMm}{2r}-\frac{GMm}{r}\)
        
        \(E_T=-\frac{GMm}{2r}\)
- - - - \(E_T=\frac{1}{2}mv^2-\frac{GMm}{r}=0\)
        
        \(\frac{1}{2}mv^2=\frac{GMm}{r}\)
        
        \(v=\sqrt{\frac{2GM}{R}}\)
    - - \(E_T=\frac{1}{2}mv^2-\frac{GMm}{r}=-\frac{GMm}{d}\)
        
        \(v\) is a fraction of \(v_{esc}\)
        
        \(a^2\frac{GMm}{r}-\frac{GMm}{r}=-\frac{GMm}{d}\)
        
        Maximum Distance
        
        :one: Solve for d
        
        :two: If asking for distance from surface,
        SUBTRACT PLANET RADIUS
        
        \(v=av_{esc};0≤a≤1\)
        
        If \(\frac{1}{2}mv_{esc}^2=\frac{GMm}{r}\)
        
        \(\frac{1}{2}m(av_{esc})^2=a^2\frac{GMm}{r}\)
        
        d: max distance achieved