CHAPTER 5 | GRAVITY 93
distance compared with the planet’s diameter of 4850 km that it
could never have been detected had it not been cumulative. Each
orbit, Mercury gains 29 km, and in a century it gains over
12,000 km—more than twice its own diameter. Th is tiny eff ect,
called the advance of perihelion of Mercury’s orbit, accumulated
into a serious discrepancy in the Newtonian description of the
universe.
Th e advance of perihelion of Mercury’s orbit was one of the
fi rst problems to which Einstein applied the principles of general
relativity. First he calculated how much the sun’s mass curves
space-time in the region of Mercury’s orbit, and then he calcu-
lated how Mercury moves through the space-time. Th e theory
predicted that the curved space-time should cause Mercury’s
orbit to advance by 43.03 seconds of arc per century, well within
the observational accuracy of the excess (Figure 5-14b).
When his theory matched observations, Einstein was so
excited he could not return to work for three days. He would beand acceleration are related, a conclusion now known as the
equivalence principle:
Equivalence principle: Observers cannot distinguish
locally between inertial forces due to acceleration and
uniform gravitational forces due to the presence of a
massive body.
Th is should not surprise you. Earlier in this chapter you read
that Newton concluded that the mass that resists acceleration is
the same as the mass that exerts gravitational forces. He even
performed an elegant experiment with pendulums to test the
equivalence of the mass related to motion and the mass related
to gravity.
Th e importance of the general theory of relativity lies in its
description of gravity. Einstein concluded that gravity, inertia,
and acceleration are all associated with the way space is related to
time in what is now referred to as space-time. Th is relation is
often referred to as curvature, and a one-line description of gen-
eral relativity explains a gravitational fi eld as a curved region of
space-time:
Gravity according to general relativity: Mass tells
space-time how to curve, and the curvature of space-
time (gravity) tells mass how to accelerate.So, you feel gravity because Earth’s mass causes a curvature of
space-time. Th e mass of your body responds to that curvature by
accelerating toward Earth’s center, and that presses you down-
ward in your chair. According to general relativity, all masses
cause curvature, and the larger the mass, the more severe the
curvature. Th at’s gravity.
Confi rmation of the Curvature
of Space-Time
Einstein’s general theory of relativity has been confi rmed by a
number of experiments, but two are worth mentioning here
because they were among the fi rst tests of the theory. One involves
Mercury’s orbit, and the other involves eclipses of the sun.
Johannes Kepler understood that the orbit of Mercury is
elliptical, but it wasn’t until 1859 that astronomers discovered
that the long axis of its orbit sweeps around the sun in a motion
that is an example of precession (■ Figure 5-14). Th e total
observed precession is a little over 1.5° per century. Th is preces-
sion is produced by the gravitation of Venus, Earth, and the
other planets and by the precession of Earth’s axis. However,
when astronomers take all known eff ects into account and use
Newton’s description of gravity to account for the gravitational
infl uence of all of the planets, they are left with a small excess.
Mercury’s orbit is advancing 43 seconds of arc per century faster
than Newton’s laws predict.
Th is is a tiny eff ect. Each time Mercury returns to perihe-
lion, its closest point to the sun, it is about 29 km (18 mi) past
the position predicted by Newton’s laws. Th is is such a small
Advance
of perihelionSunOrbit of
MercurySun5600.73 seconds
of arc/centuryba■ Figure 5-14
(a) Mercury’s orbit precesses 43.11 arc seconds per century faster than
predicted by Newton’s laws. (b) Even when you ignore the infl uences of the
other planets, Mercury’s orbit is not a perfect ellipse. Curved space-time
near the sun distorts the orbit from an ellipse into a rosette. The advance of
Mercury’s perihelion is exaggerated about a million times in this fi gure.