What is gravitation?
Gravitation is the attractive interaction between objects that have mass. Every object with mass produces a gravitational influence, although that influence becomes especially noticeable when at least one of the objects is very massive.
Newton's description of gravity explains many everyday and astronomical phenomena. Later, Einstein's general theory of relativity provided a deeper description in terms of spacetime.
Newton's law of universal gravitation
Newton proposed that every pair of masses attracts each other. The strength of this gravitational force depends on the masses and decreases with the square of the distance between their centres.
F = Gm₁m₂ / r²
G is the universal gravitational constant, m₁ and m₂ are the two masses, and r is the distance between their centres.
Gravitational field
A gravitational field describes the gravitational influence surrounding a mass. Instead of thinking only about a force between two objects, we can describe the region around a mass as a field.
g = F / m
Gravitational field strength is the force experienced per unit mass.
Near the surface of Earth, the magnitude of the gravitational field is approximately 9.8 m/s², although the exact value varies slightly with location and altitude.
Mass and weight
Mass and weight describe different physical quantities. Mass measures an object's inertia and does not depend on the local gravitational field. Weight is the gravitational force acting on that mass.
W = mg
Here, g represents the local gravitational field strength.
Gravitational potential energy
An object's position within a gravitational field can be associated with gravitational potential energy. Near Earth's surface, the familiar expression depends on mass, gravitational field strength, and height.
U = mgh
The zero level for potential energy is chosen according to the physical situation.
For large distances from a spherical mass, the gravitational potential energy is more generally written relative to a reference at infinity.
U = −GMm / r
This expression assumes a spherically symmetric central mass M and a smaller mass m at distance r.
Orbital motion
An orbit occurs when an object continuously falls toward a massive body while also moving sideways. Its trajectory can therefore curve around the central body instead of reaching its surface.
Circular orbits provide a useful simplified model. In such an orbit, gravitational force supplies the centripetal force required to keep the object moving in a circle.
v = √(GM / r)
For a circular orbit around a spherical central mass M.
Escape velocity
Escape velocity is the minimum initial speed required for an object to escape the gravitational influence of a body when atmospheric resistance and other complications are ignored.
vₑ = √(2GM / r)
The expression applies to an object escaping from distance r from the centre of a spherical mass M.
Kepler's laws
Before Newton developed his theory of gravitation, Johannes Kepler identified important patterns in planetary motion from astronomical observations.
Quick example
An object has a mass of 5 kg near Earth's surface. Taking g ≈ 9.8 m/s², what is its weight?
Using:
W = mg
W = 5 × 9.8