On the Precession of Mercury’s
something of a tour de force astronomers have determined that, if Mercury were
the only planet in the solar system, then the perihelion of its orbit would
precess .43 arc seconds per Earth year. That is a very subtle “whisper”
effect. (One arc second equals 1/3600 of a degree.) In this article we discuss
how Newtonian Universal Gravitation and Gravitomagnetic theories may combine to
produce such a precession.
begin by noting that, since the Sun can be viewed to spin in the xy-plane with w pointing in the positive
z-direction, then according to gravitomagnetic theory a dipolar O
field is engendered, said field pointing in the negative
z-direction at points in the far equatorial plane. Since Mercury orbits the Sun
with the same sense as w, it must
experience a real gravitomagnetic force away
from the Sun, in addition to the omnipresent gravitational force toward the Sun.
The net force of attraction is slightly
less than it would be if the Sun were not spinning.
the Sun’s mass is steadily (but very gradually) losing mass every second owing
to its emission of radiation and a solar “wind” of subatomic particles. If M
is the Sun’s mass, then dM/dt is
very small (compared to the total mass, M), but its effect should also be a
subtle, decreasing attraction toward
the gravitomagnetic and dM/dt forces should very subtly lessen the Newtonian
version of the attractive force on Mercury. This gradual decrease in the net
attraction should subtly affect the Newtonian theoretically perfect elliptic
orbit of Mercury.
the precession of the planet’s perihelion one of the ramifications of such a
perturbing effect? It is worth considering. The net effect would not be quite as
straightforward as discussed above. Mercury’s orbital plane does not precisely
coincide with the Sun’s equatorial plane. Furthermore the Sun is not a solid
sphere with a single spin rate of w.
Nonetheless, further consideration by astronomers of the combined effects of (a)
gravitomagnetism, and (b) a nonzero dM/dt may result in a Mercurial perihelion
precession of .43 arcseconds per annum … an effect analytically predicted by
Einstein’s General Relativity theory.