Gravity

Gravity

David Barwacz

7778 Thornapple Bayou SE, Grand Rapids, MI 49512

http://members.triton.net/daveb

Using the concepts discussed in the preceding papers ( http://members.triton.net/daveb ), I will now derive a formula for gravity. The formula will reduce to Newton’s for objects in close proximity and to the MOND formula for objects relative to the center of the galaxy. If the reader is unfamiliar with MOND, a quick internet search would be helpful. MOND theory basically alters the gravitational field from one over r squared to one over r when the field strength is very small. It has been enormously successful in predicting the motion of stars relative to the center of galaxies without the assumption of dark matter. It is an empirical formula with no basis in physics.

Assume we have two large objects and that their times both read 0 at the same time, which is the start of the observation, in an observer’s reference space. We will assume that our cyclic system is very large, (the Milky Way galaxy for example) and our objects are the earth and moon.

Under these constraints we can conclude that the space time radiuses and both scale, when scaled to a reference space, to essentially the same value which we shall call.

We write the following equations for both.

Object 1 Object 2

eq. 4.0 eq. 4.1

eq. 4.2 eq. 4.3

Where we use the Universal Invariant discussed previously (http://members.triton.net/daveb ). Now we take the square root of each equation using the Dirac matrices.

eq. 4.4 eq 4.5

eq 4.6 eq. 4.7

P and S are vectors in general, but we can simplify them to one dimension. Since we only have two objects we make one axis lie on the line connecting the objects. We assume that these two objects are at rest relative to our observer at time 0, so we need only concern ourselves with one component of P which also will lie on the same axis. S is simply the distance between the objects in their respected spaces.

Now we multiply equation 4.4 by equation 4.7. If we assume that the total energy for both objects remains constant over the length of any measurement, then this is no different then saying 2 x 2 = 4.

The result of the multiplication is:

These objects are massive objects and remains small over the time of our observation. From our previous discussion, this could literally be millions of years. is essentially

We will eliminate the term as it is very small compared to .

This leaves .

We can evaluate the change in P to get:

Now from equation 4.7

We can now “vaporize” the matrices by squaring and then taking the square root to get:

but

This leaves us with: where we are using

Now we convert everything to our common reference frame (see previous paper) using the following relations. Remember that simply becomes by the restrictions we set.

. The reference energy for space and time are distinguished since they may be different.

and

Substituting yields

dividing by and substituting Newton’s definition of Force, F=ma

We get where G= k and r =

K is a constant. is the space time distance from the origin of the rotating system.

In the above discussion I arbitrarily used but I could have used and got the opposite force.

Using the opposite sign would yield anti-gravity.

Quantum mechanics is just a result of the same cyclic nature of space/time and a description of a quantum object must include these anti-gravity states.

For all objects in close proximity ( a distance that could be astronomical relative to the radius of a galaxy), is essentially constant and we see that the gravity equation reduces to Newton’s formula.

When describing the motion of a star relative to the center of mass of a galaxy, r is the spatial radius, and is the space/time distance.

Assume that is equal to r. It certainly won’t be less than r.

Then the gravitational formula becomes:

which is functionally equivalent to the MOND formula.

We can get a value for k, by considering our own solar system.

G= k.

G is just our local gravitational constant in cgs units

If we assume is the distance to the center of the galaxy (8500 pc) or ,

Then

The MOND gravitational field equation can be written:

where a is the field strength, is the MOND constant (determined empirically) G is the local gravitational constant, is the mass of the galaxy and r is the distance to the center.

Converting my gravitational formula to a field equation yields:

Equating to MOND:

Simplifying yields:

We know G, we estimated k and (the visible mass of the galaxy) is about

We calculate that:

is an elusive value because of the number of unknowns, however all the literature estimates it to be on the order of , just as we calculated.

Summary

Although there may very well be a form or forms of dark matter, the existence of dark matter isn’t necessary to explain the motion of stars in a galaxy. There definately isn’t a need for 90 % of the matter in a galaxy to be dark.

The value of the local gravitational constant decreases with decreasing distance to the center of the galaxy, approaching zero at the center. One would expect then a region of “emptiness” at the center, there is nothing to hold matter there.

The nuclear furnace inside stars is driven by the force of gravity. If gravity is less near the center of the galaxy, it would be reasonable to expect stars to burn cooler (given the same mass) near the center. Most stars do in fact burn cool near the center. The present explanation is that they are old stars having essentially burned out. With this theory they could very well be young stars burning slower.