
1.3 Precession of the Perihelion of Mercury
explanation was considered to be a great triumph for the theory. The orbits of the planets beyond Mercury too
undergo precession due to the gravitational force of the other planets, but the general relativistic effect is too
small to be observed, because of the greater distance from the Sun of the planets beyond Mercury.
There are other systems in which the precession of the periastron is much greater than for Mercury. One
of these is the binary pulsar PSR B1913+16 which was discovered Joseph Taylor and Russell Hulse in 1974.
It consists of a binary systems of two neutron stars which are in an elliptical orbit around each other. One of
the neutron stars is a radio pulsar, the radio observations of which allow the orbital parameters to be measured
accurately. The neutron stars are very compact but massive, with a radius ˜10 km, and mass ˜1.4 times the
mass of the Sun. The periastron for the orbit (which is the closest distance of between the two neutron stars)
is ˜7,70,00 km, which is very much smaller than the perihelion distance Mercury, which is 46 million km. We
can therefore expect that the precession of the periastron for the binary neutron system is very large compared
to its value of mercury, and indeed it is found to be ˜4.2 degrees per year, which is ˜8600 times the perihelion
precession for Mercury.
There is an important consequence of the discovery of the binary pulsar. In 1916, a year after the publication
of the general theory of relativity, Einstein predicted the existence of gravitational waves. The compact, massive
binary neutron star system is an ideal engine for the production of these waves. Emission of the gravitational
waves leads to loss of energy from the system, which therefore shrinks in size with time, and the period of
rotation decreases at a certain rate. The observed pattern of decrease of the period very closely matches the
prediction of general relativity, thus establishing the reality of gravitational waves. The direct detection of the
waves by the LIGO detectors of course had to wait until 2015. For their discovery of the binary pulsar, Hulse
and Taylor were awarded the Nobel Prize in physics in 1993.
Another interesting example of periastron is provided by a supermassive object which is located at the
centre of our Galaxy, the Milky Way. It has been known for a long time that the centre of our galaxy is coincident
with a very compact radio source known as Sagittarius A* (Sgr A*). Since this source shows very little motion
over the years, it was suspected that it has very large mass. If that is true, then the presence of the mass should
be influencing the motion of stars in its vicinity. Over a period spanning almost two decades, two groups of
astronomers, one led by Andrea Ghez at the University of California in Los Angeles, and the other by Reinhardt
Genzel of the Max Planck Institute for Extraterrestrial Physics in Munich, made precision measurements of the
position of stars around Sagittarius A*. The orbit that they determined for a particular star labelled S2 is shown
in Figure 4.
The observations established that the orbit of S2 is a near perfect ellipse, with Sgr A* located at one focus
of the ellipse, as per Kepler’s law, with orbital period of 16.05 yr. Using Newtonian mechanics, the mass of
Sgr A* was determined to be 4.3 million Solar masses. The periastron distance is about 180 million km. The
very close distance of approach to the large mass means that the object should be very compact, and it can be
argued that the object is a supermassive black hole. A careful look at the upper portion of the ellipse in Figure
4 shows that even though a whole orbit has been completed, the ellipse does not close on itself. The small
deviation is significantly larger that the measurement errors. It was believed for some time that the deviation is
caused by a small motion of the compact object, which would perturb the elliptical orbit leading to the observed
deviation. But later measurements with improved measurements have shown that the deviation can be ascribed
to a general relativistic periastron precession of the orbit of S2, at the rate of 12.1 arcminutes per orbit, which
amounts to 0.0125 degrees per year. This is much large than the perihelion precession of Mercury, but smaller
than precession for the binary pulsar. An artist’s impression of the precession is shown in Figure 5. For their
work, Andrea Ghez and Reinhardt Genzel were awarded were awarded the Noble Prize in physics in 2020. They
shared half the prize, while the other half was awarded to Roger Penrose for his theoretical work on black holes.
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