# Central Force Activities

Install Ejs and then right-click on a launch node (green arrow) to copy the Free Fall model from this package into the Ejs workspace to do the following activities.

### Circular motion

Objects in uniform circular motion accelerate toward the center with an acceleration of magnitude |a| = v2/r where v is the speed of the object. Assume that this centripetal acceleration is produce by an inverse square law central force. Compute the velocity needed to produce circular motion with r =2, 4, and 8. Test your answers by entering them into the Central Force program's input fields. Verify that the Central Force model satisfies Kepler's third law.

### Angular Momentum and Energy

Add a custom method to the model to compute the total energy and test various ODE solvers to see how well energy is conserved. Perform your test for both circular and eccentric (elliptical) orbits. Repeat for total angular momentum.

### Polar Coordinates (Advanced)

Model the inverse square law using polar coordinates by deriving (or looking up) the differential equations for r and θ and using these equations to evolve the system. As was done in the Pendulum model, you must convert r and θ polar coordinates to x and y Cartesian coordinates to set the position of the orbiting particle.