Question

What force acts on the earth perpendicular to the force of the sun which causes the tangential accelerations characteristic of an ellipse?

Answer 1

There is no such force.

Explanation:

According the Newton's laws a body moves in a straight line unless acted on by an external force. In order for a body to be in a circular or elliptical orbit a centripetal force is required which is perpendicular to the tangent at the orbit. Newton stated that the centripetal force is equal to the gravitational force exerted by the Sun. The formula for this is:
`(GMm)/r^2=(mv^2)/r`
Where `G` is the gravitational constant, `M` is the mass of the Sun, `m` is the mass of the Earth and `r` is the distance between the Sun and the Earth.

In reality neither of these forces exist. There is no force of gravity and there is no centripetal force acting on the Earth to keep it in orbit. According to Einstein's General Theory of Relativity, the mass of the Sun bends the fabric of 4 dimensional spacetime. The Earth is actually travelling along a geodesic which is the extension of a straight line in 4 dimensional spacetime. The elliptical orbit which we observe is in fact a projection of the 4 dimensional geodesic onto our familiar 3 dimensional space.