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The dark energy due to expansion is.Repulsive gravity model for dark energy https://arxiv.org/abs/1003.1379
So let me say again there is no repulsive force from the sun keeping the planets in orbit. If you would read the orbital mechanics links I supplied, you would see that.
Google this phrase: "tunnel through earth simple harmonic motion". You'll get hundreds of examples.
This gives for G and E --> gravitational potential energy - the kinetic energy = 0Isn't it bivectors?
Thanks for the detail.
In case you've forgotten, there is no repulsive force from the sun keeping the planets in orbit. If you would read the orbital mechanics links I supplied, you would see that.
Now I know that the potential barrier due to the deformation of the space-time grid which plays a role. In fact, the object which orbits by inertia slides along this potential energy barrier. For the same reason that a geostationary object remains at a distance is due to the potential barrier produced by the defonrmation of the space-time grid.
I use this distortion and represent potential edges in energy (mass conversion).Quite simply. It is obvious and straightforward.
The calculations are the same, and do not change.
I am simply saying that by deforming the space-time curvature, create a border which retains the massive object in its envelope expressed in energy of gravitational potential.
Please show how your statement: deforming the space-time curvature, create a border which retains the massive object in its envelope expressed in energy of gravitational potential reduces to the equations for the orbital velocity and orbital radius.
Now you need to bring in your statement about a 'border', an 'envelope' and spacetime curvature to give the equations for the distance and velocity of an orbiting body.
With the effective potential? (also known as effective potential energy) combines multiple, perhaps opposing, effects into a single potential. In its basic form, it is the sum of the 'opposing' centrifugal potential energy with the potential energy of a dynamical system. It may be used to determine the orbits of planets (both Newtonian and relativistic) and to perform semi-classical atomic calculations, and often allows problems to be reduced to fewer dimensions.
... but you still have not shown how your statement can reduce to the equations for the velocity and the radius of an orbiting body.