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2.4.2 Gravitational Acceleration

It has been shown that the inverse square law of gravity is proportional to the gradient of displacement. However, it does not show why the constant of proportionality is such that gradient of displacement is the origin of gravitational acceleration.

It is a basic tenet of this new theory that the ideal energy continuum is a hyper-sphere with an expanding vector radius, \(R\), and that this expansion is exponential according to \(R=R_o e^{Ht}\), so that the expansion velocity is the time differential of this expression, \(HR\), which is also the current speed of light, \(c\). Exponential expansion means that expansion velocity also increases which is expansion acceleration.

\begin{align} Radius\ of\ the\ ideal\ universe\ is\ R(t)=&\ R_o e^{Ht} \nonumber \\ Expansion\ velocity\ = \frac{\partial R(t)}{\partial t} = H R_o e^{Ht} =&\ H R(t) = c\ speed\ of\ light \nonumber \\ Expansion\ Acceleration\ = \frac{\partial^2 R(t)}{\partial t^2} = H^2R(t) =&\ H c \nonumber \end{align}

Expansion acceleration applies to each point in the continuum including gravitational systems and their gradient structure. In order to maintain the shape of the displacement region, each point must expand with the same velocity and acceleration and in the direction of expansion. Since the gradient of displacement is at an angle to the direction of expansion, a component of acceleration is directed at the tangent of this angle in the direction of radius. This component of acceleration is simply \(Hc \times A/r^2\), and acts in a centripetal direction.

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