Is there any simple relation (approximate or otherwise) between the angular momentum/rotation rate of stars vs their mass and radius?
I ask because of this thread:
Grav "stumbled" upon a formula for orbital precession of Mercury and other planets that agrees closely with GR. He postulated that the orbital precession (in fractions of a revolution per revolution, "orbits per orbit" roughly) was given by v/c*R/d, where R is the radius of the sun, and 'd' is the rough radius of an orbit. Now, guess what? For the sun that comes out to be very close to GR's (approximate, dropping higher order terms that are negligible for solar system orbits) formula for the same as
3*r_s/L, where r_s is the Schwarzchild radius, and L is the "semilatus rectum", which for near circular orbits will be about 'd' as well.
Taking the ratio of grav's coefficient vs 3*r_s, one gets this:
c/6G * vR/M
Now, vR is roughly proportional to the specific angular momentum (to "zeroth order", not paying attention to variations in density, differential rotation and all that good stuff), so Grav's ratio is propotional to ratio of specific angular momentum to mass, or angular momentum per mass squared.
For the sun, that times c/6g is ~ 1. I would like to know why this ratio is so close to 1 for the sun. Pure coincidence or is there some physics at work here?