Improved Gravity Ellipses - page 1
The original equation I used to describe gravitational force to create a gravity field around the Earth (for example) was:
y^2 = sin x + cos x
which produces a good ellipse as in figure "Sun Gravity Field 1".
In figure "Gravitational Ellipses 2"
we find that we cannot use the equations:
y^2 = (cos (x))^2 - (sin (180 - x))^2
and
y^2 = (sin (x))^2 - (cos (180 - x))^2
or
y^2 = (sin x)^2 + (cos x)^2
because they generate circles and not ellipses as we want to conform
to the observed gravitational fields and an elliptical geometry.
In figure "Gravitational Ellipses 2"
we find that we can use modified equations to generate ellipses.
Perhaps this is telling us that the fabric of space resists gravitational
flux until it is large enough to incline the real plane into complex space.
This inclination need not be great but eventaully the system as a whole
balances with a square root of 2 by a square root of 3 ellipse.
However I do want to use sine squared terms. I have discovered that if we change and improve this equation to:
y^2 = (sin (x))^2 - (cos (x))^2 = B
See figure "Gravitational Ellipses 3"
we need a negative sign for the second term to get an ellipse
implying that we actually have a complex ellipse:
y^2 = (sin (x))^2 + (i cos (x))^2 = B
