Elliptical orbits of planets

Question

As we know, the velocity of the planet changes as it orbits around the sun, both in its magnitude and direction. The centripetal acceleration causes the change in the direction of velocity but I want to know what is the tangential force that acts on the planet to change the velocity by its $magnitude$.

The answer normally as to why the speed changes is:

If the force that the Sun exerts on the planet increases (as the planet moves closer), then the acceleration of the planet must increase, resulting in a higher orbital speed, and vice versa.

But this force is not along the body but towards the sun. So such a force should only change its direction.

Answer 1

The gravitational force does do work on a satellite in elliptical orbit because there is a component of the force in the direction the satellite moves.

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One easy way to verify this is conservation of angular moment which states that v×r = constant so as the distance varies so does the velocity

Note that as the satellite is moving away from the Sun, the gravitational force is doing negative work on the satellite, so GPE is being stored (KE converting to GPE). As the satellite moves toward the Sun, the gravitational force does positive work, and the satellite speeds up (GPE converting to KE). The total work done by gravity in a complete orbit is zero.

Answer 2

It is the force of gravity towards the sun what causes the change in magnitude because the orbit is an ellipse.

In a perfect circular motion, the force towards the center does not have any component in the direction of the velocity vector. Thus, the magnitude of velocity cannot change and remains constant.

However, in an ellipse, the force is directed to one of the focal points and has two components: one that is perpendicular to the trajectory and changes the direction of movement, and another one tangent to the trajectory and parallel to the velocity vector that changes the magnitude.