Obstruction Theory

 



To Contents
Next Part
Back to Actual Speed

3 The Obstruction Theory and the Additional Gravitational Acceleration

 The acceleration experienced by an object is directly related to the gradient of time dilation experienced near its mass. Specifically, the acceleration is proportional to the gradient of time dilation.

If, as the Obstruction Theory prescribes, we consider a mass as an obstruction that prevents us from seeing the universe beyond, we must determine the magnitude of that obstruction. This turns out to be equal to the solid angle subtended by the black spot surrounding the mass, as seen from the observer.

Ø            The black spot is the area within the Einstein ring surrounding a mass. For the Einstein ring, the magnitude is  meters.

The solid angle is then  sr.
Here r is the distance at which the mass is located, ψ is the angle at which the radius of the Einstein ring is observed and R0 is the radius of the black hole to which the mass can be compressed   meters.
This solid angle, compared to the total solid angle subtended by the universe, can be equated to the time dilation (TDL) at that location, as    sec/sec.

Provided  ,

this becomes

   sec/sec.

This is Einstein's well-known expression for the time dilation near a mass.

From this, we find the gravitational acceleration via the derivative with respect to r, that is, the gradient, and then multiplied by c2 gives

   m/sec2.

 But if we assume the exact solid angle, the acceleration becomes:

m/s2.

With      meters , we obtain a new gravity formula:


   m/s2.

Ø            This is Newton's improved formula according the Onstruction Theory.

 For distances within the solar system but sufficiently far outside the sun, we may approximate the formula as  m/s2.

This is a crucial result of the obstruction theory because, for the first time in centuries, Newton's formula from 1686 has been improved. It shows that gravitational acceleration is always slightly greater than calculated with Newton's formula.

Ø            The question is to what extent this updated formula can contribute to understanding the anomalous accelerations that the Pioneers and Comet Oumuamua have been measured to undergo.

If we work out the formula, we find    m/s2.

The first term   we recognize as Newton's law of gravity.

The second term  is the additional gravitational acceleration.

We see that the additional acceleration decreases with the cube of the distance.

 In Newton's law of gravity, the decrease in acceleration is quadratic. Any contribution to acceleration that is measured to be quadratic will therefore be attributed to mass if there is no other explanation.

Such an alternative explanation applies, for example, to the counteracting acceleration and deceleration the Pioneers experienced as they approached and departed from the sun due to the comet's "outgassing" caused by the sun's radiant pressure.

 However, one term that decreases with the power of three stands out. This deviation has never been noticed before because its value is on the borderline of measurable: approximately  1x10–10 m/s2   at Earth's distance. This is 1/100 of a billionth of the gravitational acceleration at Earth's surface.

We will investigate whether this explains the deviations in the orbital motions of the Pioneers (§6) and Oumuamua (§7–8).

Back

To next Part