Abstract
In this paper, we used Howusu’s planetary equation. The general equation of motion is derived for particle of non-zero rest mass in a gravitational field based upon Riemannian geometry and the golden metric tensor which is thereby opens the way for further studies or to pave the way for applications such as planetary theory.
Highlights
In the recently published book entitled “The metric tensor for gravitational fields and the mathematical principles of Riemannian theoretical physics”, the general equation of motion in the gravitational field based upon Riemannian geometry is given by [1, 2]
We obtained general linear acceleration vector based upon the Riemannian geometry and the golden metric tensor in Spherical polar coordinates proposed by Howusu by replacing the well-known Newton’s geodesic equation of motion given as [1, 2]
We obtained general gravitational intensity vector based upon the Riemannian geometry and the golden metric tensor in Spherical polar coordinates proposed by Howusu by replacing the well-known Newton’s gravitational which was built upon the Euclidean gradient operator [1, 2]
Summary
In the recently published book entitled “The metric tensor for gravitational fields and the mathematical principles of Riemannian theoretical physics”, the general equation of motion in the gravitational field based upon Riemannian geometry is given by [1, 2]
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