G2 Version 1.1.1
Ó P.G.Bass March 2004

Following the presentation of a new theory of gravitation in [1], this short paper discusses three further aspects concerning kinetics within the gravitational Space-Time Domain D₁. They are (i) the spatial-temporal distribution of the internally generated accelerative force, (ii) the relationship between gravitational and inertial mass, and (iii) kinetic energy.

G2 Version 1.1.1
Ó P.G.Bass March 2004

In the Relativistic Space-Time Domain D₀, Pseudo-Euclidean Space-Time, it was shown in [2] that an artificially applied accelerative force can be resolved into two spatial and two temporal forces, all of which produce a reaction in the accelerated mass. Similarly, it was shown that the kinetic energy induced in the accelerated matter resulted in the increase of mass from that at rest to that at the achieved spatial velocity, and this was referred to as energy mass. Finally, it was shown that the two spatial reaction terms resulting from the applied force, combine to produce a further apparent increase in mass of the accelerated matter, and this was equated to inertial mass. All of these concepts are examined here within the gravitational Relativistic Space-Time Domain D₁. The examination is conducted for motion which is (i) purely gravitational, and, (ii) where the gravitational motion is augmented by an artificially applied force.

Note that a term will only be defined in this paper if it has not previously been so in either [1] or [2] with which familiarity is assumed.

G2 Version 1.1.1
Ó P.G.Bass March 2004

Similar to the case of forced motion in D₀, the reaction forces induced in a gravitationally accelerated mass in D₁ can be seen from [1] Eq.(3.2), to consist of four components. The analysis of these terms can be simplified, without any loss of generality, by considering simple rectilinear motion only, and the rectilinear version of [1] Eq.(3.2) can be obtained by putting w to zero, to obtain

(2.1)

where represents the internally generated accelerative force of gravitation and all other terms are as defined in [1].

Clearly, (2.1) contains four reaction terms, two spatial and two temporal and, in the same manner as in [2] Fig. (3.1), these reaction forces can be expressed in relation to the Existence Velocity Vector of the gravitating mass as shown in Fig. 2.1 below

where in Fig. 2.1, represents the component of along the Existence Velocity Vector of the gravitating mass and the component transverse to it.

From (2.1) and Fig. (2.1) it is clear that

(2.2)

and therefore relates the energy mass to the time rate of change of the Existence Velocity Vector.

Similarly

(2.3)

and thus relates the Existence Velocity Vector to the time rate of change of energy mass.

From (2.2) and (2.3), following the same process as in [2], the balanced force vector diagram for gravitational rectilinear motion can be established as in Fig. 2.2 below

Accordingly, as in [2], the four reaction terms can be defined as follows:-

1. The spatial term is the reaction force of the energy mass to spatial acceleration.
2. The temporal term is the reaction force of the energy mass to temporal deceleration.
3. The temporal term is a reaction force generated by the combination of energy mass rate and temporal velocity and acts in opposition to the term in (ii).
4. The spatial term is a reaction force generated by the combination of energy mass rate and the spatial velocity and acts as an additional reaction to spatial acceleration.

The above results are very similar to those obtained in [2] for the analysis of forced motion in D₀. However, there is one very significant difference. This is the manner in which the motion is driven. In D₀ it is due to the application of an external force to produce an acceleration proportional to the applied force and the inertial mass of the accelerated body. In D₁ the motion is driven by the action of the Acceleration Potential of D₁ on the gravitating mass, to produce an internally generated accelerative force proportional to the energy mass of the gravitating body. This difference has important implications concerning the mass and energy of the gravitating mass which are analysed in depth in the following Section.

It is also noted that, as in D₀, the temporal terms are equal in magnitude but opposite in sign and therefore cancel. This is confirmed by additional analysis in the next Section.

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