I was trying to approximate perihelion precession as helix and its arc length.
It turns out the approximation used is simple angular velocity addition
if angular velocity about ecliptic is w0 and angular velocity of precession is w1,
then their vector sum is the real angular velocity...
Yes - "matter tells spacetime how to curve, which in turn tells the matter how to move" looks like a round about way saying "matter tells matter how to move" - I can understand where you are coming from.
But I think spacetime curvature is as real as spacetime itself. How physical is...
Many derivations of mercury precession angle per orbit \Delta\Phi, equate this to extra angle per orbit \delta in excess of 2\pi
that is \delta = \Delta\Phi
But I am getting this relation
\sqrt{4\pi\delta}= \Delta\Phi
from arc length of helix and circular orbit.
What am I doing...
thank you. It was very useful - I searched for this translation after reading about it in lorentz's wikipedia page. which says poincare discussed synchronising clocks using light here [before Einstein]
[I assume you are talking to me] I understand that. I was saying about the 'opposite direction'.
BTW, I answered the question why moon always shows the same face, which is due to periods being roughly same and opposite from the view of the observer in earth.
[which btw, is due to moon...
I think it has some measure of truth. How do you measure time if nothing moves or oscillates? you define second as some huge number of oscillations of cesium. But if it doesn't oscillate, there is no time - it effectively freezed as well.
But I don't know if temperature decreases, each cesium...
I meant if orbital motion is to your left [as seen from Earth lying face up looking at the moon], moon should rotate to right. To an Earth observer aren't they in opposite directions?
unlike 24 hours and 365 days for earth, for moon periods of spin and orbit are roughly the same and are in opposite directions. [think of a ball rolling on the floor and at the same time rotating in opposite direction]
If you don't use conjugate but simple symmetry it will produce a contradiction with the axiom X . X >= 0
assume X.Y = Y. X
X.X >=0
=> c1 X . c1 X >= 0 [where c1 is a complex number with an imaginary part]
=> c1 (c1 X . X) > = 0 by linearity
=> c1 (X . c1 X) > = 0 by symmetry...