orbital_precession

last edited on December 07, 2010 01:48 AM by admin

Typeset

# Additional constants and formulas for Mercury [4]
m = 3.31e23 # mass (kg)
p = 42.98 # observed precession of orbit (arcsec per century)
print (42.98 * 0.241/100), 'arc-seconds precession per orbit'
print n(pi/180)/3600, 'radians per arc-second'

print 'delta phi (radians per orbit):'
dphi1 = 6*pi*G*M / (c*c*A*(1 - e*e))
print n(dphi1), 'from reference [3]'
dphi2 = (42.98 * 0.241/100)*(pi/180)/3600
print n(dphi2), 'from observations'

v = A * (2*pi/T); print 'v:', n(v), 'average velocity (m/sec)'
h = A * v; print 'h:', n(h), 'orbital constant L/m'
print 'a:', n(a), 'orbital constant GM/h^2'
print 'b:', n(b), 'perturbation constant'
print '(1 - a^2*b):', n(1 -a^2*b)

Precession of Mercury

The effects of general relativity cause the orbit of Mecury to precess about the sun 43 arc seconds per century (0.5 microradians for each orbital period). This tiny effect has been most accurately measured with radar, but as early as 1859, Urbain Le Verrier, without even a pocket calculator, had an accurate estimate (38 arc seconds). [1]

[1] http://en.wikipedia.org/wiki/Tests_of_general_relativity  1.1 Perihelion precession of Mercury
[2] http://demonstrations.wolfram.com/MercurysPerihelionPrecession for the equations used in this simulation.
[3] http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity  3.5 Precession of elliptical orbits - nice animation, derivation of equations.
[4] http://en.wikipedia.org/wiki/Mercury orbital characteristics of Mercury

http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity

evaluate

0.103581800000000 arc-seconds precession per orbit
4.84813681109536e-6 radians per arc-second
delta phi (radians per orbit):
5.01192755292382e-7 from reference [3]
5.02178737539517e-7 from observations
v: 47866.8427264971 average velocity (m/sec)
h: 2.77149019386418e15 orbital constant L/m
a: 1.72803373944232e-11 orbital constant GM/h^2
b: 7.68115789468533e19 perturbation constant
(1 - a^2*b): 0.977063289766260

0.103581800000000 arc-seconds precession per orbit
4.84813681109536e-6 radians per arc-second
delta phi (radians per orbit):
5.01192755292382e-7 from reference [3]
5.02178737539517e-7 from observations
v: 47866.8427264971 average velocity (m/sec)
h: 2.77149019386418e15 orbital constant L/m
a: 1.72803373944232e-11 orbital constant GM/h^2
b: 7.68115789468533e19 perturbation constant
(1 - a^2*b): 0.977063289766260