Precession angle per orbit of perhelion precession mercury

1. Jul 28, 2008

fakrudeen

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 wrong?
What is the intution for above approximation? Shouldn't the total angle be less than $$2\pi$$ + $$\Delta$$$$\Phi$$
because planet takes short cut [analagous to hypotenuse length being less than sum of other two sides]

2. Aug 1, 2008

fakrudeen

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
$$\omega$$= $$\omega$$0 + $$\omega$$1

now in one period T, $$\omega$$0 contributes 2$$\Pi$$ because it is the motion in ecliptic and $$\omega$$1's contribution is precession per orbit by definition which adds up to angle contributed by real motion.