Effective Potential and Gravity

astronomy simulation

Instructions: The slider will change the values. Notice how the overlap of the energy curve (in blue) and the $U_\textrm{eff}$ indicate the shape of the orbit.
Explanation: The concept of an effective potential is very useful for understanding the shape of orbits in a central force problem. Here we have plotted the effective potential curve $$U_\text{eff}(r) = \frac{L^2}{2mr^2} - \frac{GmM}{r} $$ overlain on a simulated orbit. You can change the parameters such as the speed and direction of the orbiter, and notice how both the plot and the shape of the orbit change. Also shown is the total energy of the orbiter. Due to conservation of energy, this value will remain constant during the motion.

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effective potential

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