[sjastro]

Originally Posted by Jarvamundo

Yup, this is what's covered.... and why it's best familiarize yourself with all of the celestial mechanics papers.

Or yes get the book, it's easier this way since Miles has ordered the thesis in a more digestible manner. I wish i'd done this earlier.

I could back n fro here on IIS, but it'll just be pointless. The ideas need to be layed out from first principles, i do not have time to do this, and Miles has already done so.

Tickle your interest: http://milesmathis.com/ellip.html

I'll loan you my book when i'm done with it, or yeah i think it's 9 bucks for the e-copy.

All experiments and observations have confirmed that Kepler's equations are correct and that the shape of the orbit is indeed an ellipse, as he told us.

Since Mathis agrees Kepler's equations are correct and that Kepler uses pi=3.1416.... then clearly pi <> 4 as Mathis suggests for a "kinematic" event.

Now for the refutation of Mathis' ideas on orbital ellipses.

Mathis needs to introduce an E/M repulsive force in order to get an elliptical orbit to "work" is more a reflection in gaps in his own knowledge and understanding of the dynamics of an elliptical orbit than any issues with Newtionian physics.
The reality is that Newtonian theory for orbits is simple and straighforward and doesn't require a repulsive force.
This will be made abundantly clear.

Because there is no mechanism to impart tangential velocity by a gravitational field. Both Newton and Einstein agreed on this. Einstein’s tensor calculus shows unambiguously that there is no force at a perpendicular to the field, and Einstein stated it in plain words. How could there be? The force field is generated from the center of the field, and there is no possible way to generate a perpendicular force from the center of a spherical or elliptical gravitational field.

This is only partially true. The gravitational field doesn't act perpendicular on an object. Where as gravity is an external force, a force acting along the tangent doesn't have to be external as Mathis suggests.
For example the occupants in a car will experience a centrifugal force when the car goes around a bend. The centrifugal force is a reaction force to the inward acting centripetal force. The centripetal force is not external but is created as a result of the non straight line motion of the car.
In an elliptical orbit a tangent force exists due to the angular velocity being variable. If the angular velocity became constant, the tangent force vanishes and the orbit becomes circular.

If we take the two most important differentials, those at perihelion and aphelion, and compare them, we find something astonishing. The tangential velocities due to innate motion are equal, meaning that the velocity tangent to the ellipse is the same in both places. But the accelerations are vastly different, due to the gravitational field. And yet the ellipse shows the same curvature at both places. The ellipse is a symmetrical shape, just like the circle.

This is not correct. The tangential velocity of a planet at perihelion is greater than that at aphelion.

Tangential velocity = Radius X Angular velocity.

If the angular velocity was constant, the tangential velocity at perhelion would in fact be less than the tangential velocity at aphelion as the radius has a minimum value at perihelion. What happens is that the angular velocity increases at a faster rate as perihelion is approached.

The relationship between angular velocity and radius is given by the equation (Radius)^2 X Angular velocity = Constant.

If you half the radius, the angular velocity will increase 4-fold.
The tangential velocity reaches a maximum value at perihelion.

To make the ellipse work, you have to vary not only the orbital velocity, but also the tangential velocity. To get the correct shape and curvature to the orbit, you have to vary the object's innate motion. But the object's innate motion cannot vary. The object is not self-propelled. It cannot cause forces upon itself, for the convenience of theorists or diagrams. Celestial bodies have one innate motion, and only one, and it cannot vary.

Mathis describes orbital velocity as the vector sum of tangential velocity and centripetal acceleration. This is total nonsense as you cannot add velocity and acceleration as their dimensional units are different.

The tangential acceleration is mathematically derived as a consequence of a non constant angular velocity. The tangential force follows from this.

This eliminates the need of introducing external contrived factors such as a repulsive E/M force.

Regards

Steven