Figure 2
The following figure shows the amount of influence the movement of the
gravitational field of each celestial body exerts on the origin. The table
shows the calculation formulae for this example. On the right, the compositions
of υ1, υ2 and υ3
are shown in expanded form.
Figure 3
The strength of exertion from the gravitational field generated by mass
point m3 (at a distance of 7r1 from the origin) on the origin would be, from
Newton’s law of universal gravitation, 1/(7r1)2
compared with that of m1.
If the mass of m3 is four times that of m1, then the influence that speed V3 exerts on the origin would be V3 × 4 m1/(7r1)2. This value is υ3.
Now consider how this compares, as a
ratio, to the gravitational movement of m1.
First, the effect that the speed of m1
has on the origin is similarly calculated as υ1 = V1 × m1 / r12.
If the earlier speed V3 is five times that of V1 (V1 is the speed of m1),
then υ3 can be expressed as follows:
υ3 = 5V1 × 4m1 / (7r1)2.
|