Feynman's Lecture on Motion of Planets: Explained

[WiFO215]

In Feynman's lecture on the motion of the planets [page 2] he says

Suppose we take a certain fractional part of an orbit, some fixed angle, a small angle and a particle has a certain velocity. And the change in velocity during an interval if time - a fixed time - which is the force, is evidently proportional to to the velocity of in the orbit times the time that it takes to go acoss this fraction of the orbit. I mean, divided by the time. So the velocity changes proportional to the velocity. And the time over which that change has taken place is proportional to the time it takes to go around the orbit. Therefore the centripetal acceleration, or change per second of velocit towards the center, is proportional to the velocity of the orbit divided by the time it takes to go around.


I don't understand. Can someone explain?

 

[lippyka]

Feynman is saying that the change in velocity (acceleration) of a particle in an orbit is proportional to the velocity of the particle and inversely proportional to the time it takes to go around the orbit. In other words, the centripetal acceleration (change in velocity per second towards the center of the orbit) is proportional to the velocity of the orbit divided by the time it takes to go around. This means that if the velocity increases, or the time decreases, the acceleration will increase.