# GR Approximation for PSR 1913+16

1. Jun 26, 2007

### shalayka

I came across a fairly simple General Relativity related formula the
other day that calculates the precession rate for the binary star PSR
B1913+16.

I have seen some pretty complicated methods for PSR 1913+16 before,
but not this one, so I thought I would bring it up to anyone else that
it might be new for.

The following mass, apoapsis and periapsis values were gathered from:
http://www.johnstonsarchive.net/relativity/binpulsar.html

Average mass m = 1.414*1.98892e30 = 281233288e22 kg
Apoapsis distance a = 1576800e3 m
Periapsis distance p = 373300e3 m
Average radius r = (a + p) / 2 = 975050e3 m
Eccentricity e = 1 - p/r = 0.617148
Average velocity v = sqrt(Gm/r) = 438713 m/s

GR precession in orbits per orbit n = 3*G*m/(r*c^2) / (1 - e^2) = 1.03767e-005
Average circumference C = 2*pi*r = 6126419834 m
Average combined orbit time t = 2 * C/v = 27929.1 s

Precession in degrees per year:
del = n*360*(365/(t/(24*60*60)))
del = 4.21806

If you have any citations for this method, I would greatly appreciate any information that you could pass my way. Thank you.

- Shawn

Last edited: Jun 26, 2007