Gravity, Gravitational Acceleration

Gravitational force

Gravity comes from the Latin word gravitas, which means "weight". It is a fundamental and universal interaction between any two entities with mass or energy.

Sir Isaac Newton first formulated and quantified gravity as gravitational force, so that the effect of gravity on kinematics of objects could be measured and predicted. An object with larger mass is able to attract other objects more strongly. Also, when an object is closer to other objects, it can attract more strongly. Mathematically, we can write

$$F_g=G\frac{m_1m_2}{r^2}$$

where $F_g$ is the gravitational force, $m_1, m_2$ are the masses of two objects, $r$ is the distance between those two objects, and $G\approx 6.6743\times 10^{-11} m^3/(kg\cdot s^2)$ is called the gravitational constant, which is assumed to be unchanging anywhere anytime.

Gravity is the weakest fundamental reaction, roughly $10^{38}$ times weaker than the strong nuclear force, $10^{36}$ weaker than the electromagnetic force, and $10^{29}$ times weaker than the weak nuclear force.

Gravity as curvature of spacetime

In general relativity, Albert Einstein redefined gravity not as a force, but as the bending of spacetime. An object with larger mass is able to curve spacetime more. The bending is less for locations farther from the object.

Gravitational acceleration

If we consider the acceleration caused by the gravitational force, we can combine Newton's second law with the gravitational force:

$$F_g=G\frac{m_1m_2}{r^2}=m_1a\Rightarrow a=\frac{Gm_2}{r^2}$$

We usually specialize the gravitational acceleration on the surface of a huge body as $g=\frac{GM}{R^2}$, where $M$ is the mass of the body, such as the mass of Earth, and $R$ is the radius of the body, such as the radius of Earth.