Advanced Newtonian Gravity

The equations for advanced Newtonian gravity are discussed in the article by A Worsley entitled, “An advanced dynamic adaptation of Newtonian equations of gravity. The adaptation of Newtonian dynamics.” (Physics Essays 21, 3 (2008) pg. 222-227)

Worsley starts the article by briefly discussing the history of general relativity (GTR) and it's successes and failures, namely it's tendency to breakdown mathematically when dealing with black holes. In addition, Worsely points out, the equations become increasingly complex: a definite downside.

What is interesting is the approach that Worsley uses to arrive at his advanced dynamic adaptation of Newtonian gravity. He postulates that by reversing Einstein's process of arriving at GTR, he can reformulate the equations for gravity into a force. This method provides many advantages listed by the author. First, the method is much easier to use with far less complicated computations, it obviates the infinitely dense black hole singularity predicted by full GTR, and restores the principle of simultaneity. Worsley even goes as far as to say that the new equations of adapted Newtonian gravity can be used to shed light on the “dark matter” of the universe.

Basically, Worsley takes the curvature of space-time equations for GTR and modifies them mathematically by defining the equations in terms of geodesics. He then translates these new curvature equations back into the equations for an advanced Newtonian force of gravity. Although the actual derivations of Worsley's equations are not included in the paper, his resulting equations are.

To prove that the new equations are valid, the paper works several examples... namely the general relativistic estimate for the perihelion advance of Mercury. The results show that the advanced Newtonian equations can give results that agree almost perfectly with GTR and observed data. The author then uses his equations in higher mass density objects (like binary pulsars & black holes) with great success; the equations do not collapse.

In full GTR equations, the Schwartzchild radius seem to be the limit of the calculations... but by using the advanced Newtonian force of gravity equations, Worsley is able to estimate the forces exerted by the Schwarzschild radius and inside the black hole. Additionally, the Schwarzschild radius can now be used to define the radius for the escape velocity of light. This is important, because modern physics tells us that the speed of space-time is allowed to exceed the speed of light! (I didn't know this.. prior to the paper!)

In the end, Worsley states that advanced Newtonian gravity achieves a far greater accuracy than Newton's laws of gravity because of the use of the higher order terms. Since the equations prove valid (that is, they agree with calculations from GTR on low and medium density bodies), the author claims that they must also be valid for higher mass density objects like black holes... and by using these calculations for the force of gravity, even at the Schwarzschild radius, we can make calculations of the missing dark matter of the universe.