Maximum acceleration of the body in elliptic orbit.

[amiras]

There was this question in the book, at which place on the elliptic orbit the body has maximum acceleration.

Since acceleration is proportional to force, a = GM/r^2, this should happen when the distance r is minimum, this is when the planet is at perihelion. But the contradiction is that at perihelion the body (or satellite) has its maximum speed, that means that it no longer accelerates to increase speed.

To explain this I would guess that at this point acceleration changes direction and begin slowing the satellite down. Is that really what happens?

 

[nasu]

A significant component of the acceleration is normal to the path. At the perihelion this is the only component. The tangential component of the acceleration is zero at the perihelion and yes, this component changes direction as the body goes through the perihelion.

 

[Blibbler]

Maybe it would be helpful to think not in terms of speed but in terms of velocity.

Acceleration is a change in velocity and so can be just a change in speed or also a change in direction or any mixture of the two.

 

[sophiecentaur]

The simplest way to look at this is to remember that Force equals Mass times Acceleration.

The Force is highest when at its lowest point of orbit (nearest to the centre of the Earth) and so the acceleration must also be greatest at that point.