SPRING THEORY

MY NEW THEORY THAT COMBINES GRAVITY AND ELECTROMAGNETISM..I CALL IT SPRING THEORY
HERE IT IS:

SPRING THEORY
A window into a new propulsion system
This will create lift using the earth gravitational field

The ∇×F of 𝐺𝑚1𝑚2𝑟2

In this discourse, I am trying to integrate the curl vector with the equation for gravitational force F in the equation: 𝐹 = 𝐺𝑚1𝑚2𝑟2: (use an equation editor so that your equations, like the one I’ve redone, are correct and readable) in an attempt to show that gravity and electromagnetic field can be integrated in a single equation to produce a more visual representation of what I actually occurring in between any two objects.
Do you know what IS actually going on between two objects? If not, then why would you think combining curl with the general gravitational equation would provide a model for what is going on? I suggest a couple of sentences below that gravity acts in a curl wave fashion.
I call it spring theory. Since, the curl is essentially a spring moving clockwise or counter clockwise Theoretically speaking most of the time in nature gravity is being produced by an mass M(1) is attracting M(2): In spring theory the gravity acts in a curl wave resembling a spring twisting as it goes:this is what is creating an attraction only countered by the centrifugal force of the opposing objects. The two objects are attracted since the the curl motion of gravity is the mirrored between M2 and M2.
Maybe what you’ve said above (and in the following paragraph) makes sense to a physicist, but as I’ve said, I’m not a physicist. I’d need a lot more evidence/explanation/rationale before I could judge whether it made any sense at all.
Thus, the curl of F is twisting motion between the two respective bodies.
But if the curl of opposing sides is going in the same direction, there is a repulsing effect or anti-gravitational effect. So that, a device can be built to create an electromagnetic wave that is going in the same direction as the wave being produced by the earth at that given side, creating lift. Thus, this allows for a possibility of understanding how anti- gravitational devices might be constructed using a field that is essentially going in the same direction as the opposing force F at point A.
TO BEGIN:
PHYSICAL INTERPRETATIONS OF CURL AND DIVERGENCE
(Your points 1 and 2 below are just a retelling of the standard interpretations of curl and divergence, although it is very hard to read as typed. We don’t need a calculus lesson; what we really want to know is what the curl and divergence have to do with gravity. You haven’t really explained this. Forget the TO BEGIN part of this and explain the statements you’ve made above.)
1. Physical Interpretation of the Curl
Let F(x, y, z) = (P(x, y, z),Q(x, y, z),R(x, y, z)) be a vector field. We can think of F as representing the velocity field of some fluid in space. We want to give a physical meaning to the curl ∇ × F of this vector field at a point. Choose Coordinates so that our point of interest is the origin. Consider a small circle ° of radius h centered at the origin, in the x-y plane, oriented counterclockwise. We can parameterize this curve as:
° : r(t) = (h cos(t), h sin(t), 0) 0 ≤ t ≤ 2¼ (I’m assuming you mean 2π, not 2.25)
The line integral of the vector field F over this path ° measures the circulation of the vector field along this path, or the tendency of the field to follow the path. A positive circulation means that as we traverse the path °, we tend to move in the direction of the vector field F, while a negative circulation means we tend to move in the opposite direction of F. Since we assume the circle to be very small, and F is assumed to be differentiable, we will take the first order (linear) approximation of the vector field near the origin 0 = (0, 0, 0):
P(x, y, z) = P(0) + Px(0)x + Py(0)y + Pz(0)z
Q(x, y, z) = Q(0) + Qx(0)x + Qy(0)y + Qz(0)z
R(x, y, z) = R(0) + Rx(0)x + Ry(0)y + Rz(0)z
Since we are computing a line integral of F over the curve °, we substitute
x = h cos(t), y = h sin(t), and z = 0 in the above to obtain:
P(r(t)) = P(0) + Px(0)h cos(t) + Py(0)h sin(t)
Q(r(t)) = Q(0) + Qx(0)h cos(t) + Qy(0)h sin(t)
R(r(t)) = R(0) + Rx(0)h cos(t) + Ry(0)h sin(t)
Note that if we were taking quadratic or higher order approximations the extra terms would all have at least an ℎ2 factor in them. The velocity vector field of the curve ° is
(1.1) r′(t) = (−h sin(t), h cos(t), 0)
So the integrand in the line integral becomes (after some rearranging):
F(r(t)) ・ r′(t) = h (Q(0) cos(t) − P(0) sin(t))
+ h2 ¡Qx(0) cos2(t) − Py(0) sin2(t) + (Qy(0) − Px(0)) sin(t) cos(t)¢
+ h3 (・ ・ ・ )
1
This is very hard to read and what is the ¢ symbol supposed to be?
2 PHYSICAL INTERPRETATIONS OF CURL AND DIVERGENCE
The term (・ ・ ・ ) represents all the leftover parts from a higher order approximation.
Now we integrate this from 0 to 2pi in t, and use the fact that: (in the following I guess you mean for Z to be ∫ -- you should definitely use an equation editor to get this all correct.)
Z 2pi
0
sin(t)dt = Z 2pi
0
cos(t)dt = Z 2pi