Quote:
Originally Posted by rtomes
It is worth noting here that as far as accelerations go (which may
or may not be important) the formula is I*M/D^2 while for the resulting
displacements the formula is I*M*P^2/D^2 where M=Mass, P=Period and
D=Distance and I=inclination to the sun. But (as Kepler showed) P^2 is
proportional to D^3 and so the result may be expressed as I*M*D.
For the four major planets, all the I's are within 10% of 6 degrees, and
so the result is approximately proportional to M*D which is the same
formula used by COM adherents! However, only the component of COM
which is at right angles to the line of the nodes is important, the
component in the direction of the nodes is not (all the nodes of the
major planets orbits are within 10 degrees of longitude 245 of the
sun's equator).
Note: The COM (Centre of Mass) hypothesis states that the motion of
the sun about the COM of the solar system somehow has an effect on
the sun. There has been no meaningful mechanism proposed for it to
work. The other alternative previously proposed has been tidal forces,
but although there is a mechanism, the effects are too small.
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"I M / D
2" as acceleration has a unit of "radians kg / m
2" strange unit for an acceleration which usually is "m / s
2
I think it is time you show some real equations, not some handwaving arguments and made up stuff I M / D
2 naturally has something to do with a gravitational force G M m / r
2 but how and what about the inclination remains a mystery. If the rotation around the sun averages out, then why does the N-S motion not average out, because the motion of the planet can be split up into an ellips in the equatorial plane and an ellips in the perpendicular plane.
There are several papers discussing the effects on the sun of the planets and the motion around the barycenter or COM, just take a look at de Jager and Versteegh and at Shirley.