Question

prove that no central force can enable a particle to move in a straight line​

Answer 1

This is an interesting relation that, we will see, is related to properties 2 and 3 above. However, one use for

it should be apparent. If you know the r component of the motion it allows you to compute the θ component

by integration. This is another example of how constants of the motion allow us to “integrate” the equations

of motion. It also explain why constants of the motion are often referred to as integrals of the motion.

Now, let us return to property 3 above and derive the Law of Areas.