Yep, it's simple. And that's not Helio Centric model.
That is the HC model, if you take that model and rotate it around Earth.
It is the same model, just viewed from a different reference frame.
The note to consider:
The sun chatching up the moving forward moon will not give such a traveling umbra whose velocity is like the letter "U", i.e. the umbra goes deceleration and then goes acceleration.
Why?
Do you have any basis at all for that claim?
To begin with, what velocity are you measuring?
The velocity of the umbra on the surface of Earth?
If so, that is exactly what you would expect.
It has nothing to do with the moon changing speed, but everything to do with Earth being round.
This roundness of Earth has 2 effects. One is that the distance to the moon changes, and the further you are from the moon, the faster the umbra moves.
But the more important point is the change in direction of the surface.
If you have a shadow moving at an angle to a surface, at some speed
v, then the speed of the shadow along that surface
vs we can get this image of how it all looks:
This means the variables will be related as:
cos(
a) =
v/
vsThus
vs =
v/cos(
a)
So as the umbra passes over Earth, its surface speed will change dramatically.
It starts off at an angle of basically 90 degrees. This means cos(
a) is basically 0 and thus
vs is basically infinite.
Then as it goes roughly 1/4 of the way around the surface, it is at 45 degrees, thus cos(
a) is 1/sqrt(2) and thus
vs is sqrt(2)
v, which is much less than infinite.
But it keeps getting lower. When it is 50% of the way across it is at 0 degrees cos(
a) is 1 and thus
vs is
v, slower than before.
Now as it moves further the angle goes negative, but cos is still positive.
When it is 3/4 of the way along the surface it is at -45 degrees, thus cos(
a) is 1/sqrt(2) and thus
vs is sqrt(2).
Then just before leaving the surface, it is at basically -90 degrees. This means cos(
a) is basically 0 and thus
vs is basically infinite.
If you plot this as a function of how it varies as you move along the surface, you get this:
(X axis is a percentage of the way along the surface, y axis is the factor by which
v is multiplied.)
Is that enough of a U shape for you?
If instead you want it expressed as a function of time, assuming a constant velocity of the shadow, you have a plot of 1/cos(asin(x/50-1))
(axis as above, but now x is a measure of the time to cross, not the distance along the surface).
This was already explained to you, with numbers provided for you to show that the results match what is observed.
Stop just spouting nonsense and start actually justifying your nonsense, including making reference to what has already been provided which already shows you are wrong.