The classical theory of gravition was developed by Sir Isaac Newton in the 17th century; however, Albert Einstein showed in the early 20th century that the Newtonian theory of gravity is just an approximation. Einstein’s general theory of relativity, replaces Newtonian theory and describes gravity as a distortion of spacetime.
Quantum mechanics has yet to be successfully combined with general relativity and a quantum theory of gravity is considered to be a “holy grail” of theoretical physics.
In 1687, Isaac Newton published his Philosophiæ Naturalis Principia Mathematica often known simply as Principia. In this work, Newton described his theory of universal gravitation, that any two bodies in the universe attract each other by a force that is proportional to the mass of the two bodies and inversely proportional to the square of the distance between them. This law is often referred to as the inverse square law.
The Inverse Square Law
In mathematical term, the force between two objects is given by the equation:
F = GmM / r2
Where F is the strength of the force, m and M are the masses of the two bodies, r is the distance between them and G is a constant known as the gravitational constant.
G has a value of around 6.673×10−11 N m2 kg−2
(N.B in algebra the times symbol x is usually omitted, but the above equation could also be written F = G x m x M / r<sup>2</sup>)
The equation for the acceleration due to the gravitational pull of a large body is given by substituting the equation from Netwon’s second law of motion, Force equals mass times acceleration or F = ma, into the equation for the inverse square law – where m is the mass of the smaller object and a represents the acceleration.
ma = GmM / r2
Since m is on both sides of the equation, it cancels out leaving:
a = GM / r2
This shows mathematically that all objects will experience the same acceleration (a) in the gravitational field of a more massive body (M), as the mass of the smaller body (m) has cancelled out and does not appear in this equation.
Setting M as the mass of the Earth (approximately 5.972 × 1024 kg, and r as the Earth’s mean radius (approximately 6371.0 km or 6,371,000 metres) gives a value for the acceleration due to gravity at the Earth’s surface. This acceleration is usually donated as g rather than a, so:
g = 6.673×10−11 N m2 kg−2 x 5.972×1024 kg / 6,371,0002 = 9.81 m s−2
This means that all objects will experience an acceleration near the surface of the Earth of approximately 9.81 metres per second every second.
Newton’s theory of gravitation can be considered to be an approximation of the description of gravity given by Einstein’s general theory of relativity, where gravity is considered to be due to the distortion of space-time. (See general relativity.)
Quantum Theories of Gravity
In the theory of quantum mechanics, gravity is considered to be a mediated by a particle known as the graviton (see fundamental forces). No theory yet exists, however, that can successfully combine this concept of gravity with the general theory or relativity.