iSoul In the beginning is reality

Law of levitation

This was derived for circular orbits here. In this post it is derived directly from Newtonian gravitation.

The law of gravitation states that the gravitational force is proportional to the product of the masses divided by the square of the semi-major axis, As, of the orbit:

F = G mM / As².

Because of Newton’s second law, the gravitational acceleration is

a = Gm / As².

The object is to transpose this into time-space by expressing it in terms of prestination and vass. The first step is to use Kepler’s third law, which is an estimate that states:

T² ∝ As³, or

T4/3As²,

where T is the sidereal period. This may be expressed in terms of the radial time, i.e., the corresponding time to traverse the semi-major axis, At = t, estimated as a proportion of the period:

At = tT,

so that

t4/3As².

This allows the gravitational acceleration to be expressed in terms of radial time:

amt–4/3.

The next step is to integrate, with a = dv/dt:

∫ dv = ∫ C1 mt–4/3 dt = –3 C1 mt–1/3 + C2 = v.

Then integrate again, with v = dr/dt:

r = ∫ dr = ∫ –3 C1 mt–1/3 + C2 dt = –(9/2) C1 mt2/3 + C2t + C3,

where the radial distance r = As. For the purposes of stating a law, set C2 = C3 = 0, and then solve for t:

t = –(2/9mC1)3/2 r3/2 = –C4 ℓr3/2,

where ℓ is the vass. Then take the derivative:

dt/dr = –(3/2) C4 ℓr1/2 = u,

where u is the celerity. Take the derivative again to get:

du/dr = –(3/4) C4 ℓ/r1/2 = b,

where b is the prestination of levitation, since the sign is the opposite of gravitation. This leads to

Γ = H ℓN/r1/2,

for vasses ℓ and L, the levitational constant H, and the levitational surge Γ.

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