Expert: Ed - 8/19/2008

Question
This is the most amazing thing.
I have an English translation of Einstein's original paper c1916 on General Relativity. I also have an original copy of his Princeton lectures of 1921 (reprinted 1974) 'The Meaning of Relativity'.

I have seen various interpretations of THE FORMULA for the precession of planet Mercury but I cannot see any better than Einstein's own.

Einstein says, both in his original paper and his 1921 lectures, that the equation for the precession of Mercury is (p = precession)


p =     24 pi^3 *a^2     /   T^2 * c^2 * (1 - e^2)

where

a = semimajor axis in centimeters
e = numerical excentricity
c = 3 * 10^10 (ie. centimeters per second)
T = period of revolution in seconds.

The result of this computation is supposed to be 43 seconds of arc per century.
The problem is that, try as I might (using excell), I CANNOT get the maths to work out.

I wonder -


Can you make sense of and explain to me the meaning of the following statement in Einstein's 1921 lectures (and his 1916 paper):

"The most important result we get from this is a secular rotation of the elliptic orbit of the planet [Mercury] in the same sense as the revolution of the planet, amounting in radians per revolution to

p = bla, bla as above.

This expression furnishes the explanation for the motion of the perihelion of the planet Mercury."

I wonder -

Could you help me by doing the maths involved in the EQUATION above in order that I can see where I have made mistakes?

Thank you for your help.

Jim Watson  

Answer
James,
It sounds like you're really interested in this, and this is why I originally started answering questions on allExperts.  (To help people like you, and to meet people like you on the internet).  

Unfortunately, right now my math skills are much too rusty for me to be able to help you within the time limit given by AllExperts.  I'm sorry.  

I think you should ask Philip Stahl.  He definitely has the mathematical background to quickly help you understand this stuff.
http://www.allexperts.com/ep/1360-23079/Astronomy/Philip-Stahl.htm

best,
--Ed