A planet, mass m, moves around its sun. The radial motion can be described using an effective potenital: $$ U_{eff}(r) = \frac{l^2}{2mr^2} - \frac{GMm}{r} $$
For a given value of the total energy, E, the trajectory can be a closed orbit, an open orbit or 'no solution'.
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In the animation, values for G, M, m, l are chosen such that the minimum of the effective potential has a value of -2.
The left graph shows the 'solution' of the r(t), the blue dot.
The red dot shows the value of the effective potential.
The right grap shows \( dr/dt \) en \( d\phi /dt\). Note that the latter shows that the velocity of the planet is never zero, even if \( dr/dr = 0 \). Do you understand why we new upfront that \( d\phi / dt \neq 0\)?
Choose am energy value via the slider and start the motion.
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