iSoul In the beginning is reality

Centers of motion

Bodies in space-time orbit by gravitation around their barycenter, the center of mass. The word barycenter is from the Greek βαρύς, heavy + κέντρον, center. The barycenter is one of the foci of the elliptical orbit of each body.

For the two-body case let m and M be the two masses, and let r and R be vectors to m and M respectively. Then the center of mass or barycenter is

(mr + MR) / (m + M).

Define the reduced mass μ = mM/(m + M). Then the orbit is as if the orbiting body has reduced mass μ and there is a stationary central body with mass equal to the total mass (m + M). That is, the two bodies mutually orbit the center of mass.


Let’s reconsider the orbit in relation to the vasses, the mass inverses, orbiting by levitation. For the two-body case let  and L be the two vasses, and let r and R be vectors from an origin to and L respectively. Then the center of vass is

(ℓr + LR)/( + L) = (Mr + mR) / (m + M).

Define the reduced vass Λ = ℓL/( + L). Then the orbit is as if the orbiting body has reduced vass λ and there is a stationary central body with vass equal to the total vass ( + L). That is, the two bodies mutually orbit the center of vass.

The result for vass is the same except that the roles of the bodies are reversed. One could call the center of vass the elaphracenter after ελαφρά, light (weight) + κέντρον, center.

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