Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities
φ/
c2 and
(v/c)2 are both much less than one, where
φ is the
gravitational potential,
v is the velocity of the objects being studied, and
c is the
speed of light.
[32] For example, Newtonian gravity provides an accurate description of the Earth/Sun system, since
where
rorbit is the radius of the Earth's orbit around the Sun.
In situations where either dimensionless parameter is large, then
general relativity must be used to describe the system. General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.
Newton's Theory of Gravitation requires that the gravitational force be transmitted instantaneously. Given the classical assumptions of the nature of space and time before the development of General Relativity, a significant propagation delay in gravity leads to unstable planetary and stellar orbits.
Newton's Theory does not fully explain the
precession of the
perihelion of the
orbits of the planets, especially of
planet Mercury, which was detected long after the life of Newton.
[33] There is a 43
arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th Century.
The predicted angular deflection of light rays by gravity that is calculated by using Newton's Theory is only one-half of the deflection that is actually observed by astronomers. Calculations using
General Relativity are in much closer agreement with the astronomical observations.