Thus it is just a way of expressing the resultant force tending to push an object away from a string or a gravitational force. It appears that there are two different but similar cases. In the case of a string, the object spinning around a center point wants to go in a straight line. The string prevents this and you end up with a vector problem in which the string has actual centripetal force acting from the center point. This is just simple mechanical engineering 101. Now let us look at the Earth spinning around the sun. For simplicity we can say that the ellipse is basically a circle although the equations are the similar.
I didn’t find the right solution from the Internet.
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