Its a known fact that Gravity is a force that attracts all matter towards the earth's center. The gravimeter is a well known instrument that measures earth's gravity.

The Gravity formula used casually for earth is given by,
g = $\frac{GM}{R^2}$.

Where G is gravitational constant (6.67 $\times$ 10-11 Nm2/Kg2), M is the earth mass, R is the earth radius.

The universal law of gravitation is also a gravity formula given as,
F = $\frac{G m_1 m_2}{r^2}$.

Where F is force existing due to gravity, G is gravitational constant (6.67 $\times$ 10-11 Nm2/Kg2), m1 and m2 are the masses separated by distance r.

There is another gravity formula for any spheroid given as,
g$\phi$ = 9780318.5(1 + 0.0052788995 sin2 $\phi$ + 0.00002362 sin4 $\phi$)g.u.

Where g$\psi$ is predicted value of gravity at latitude $\psi$. The Gravity formula is used to compute the latitude correction in gravity reduction.

The Gravity in expressed in meter per second square (ms-2).

Let's see some examples on Gravity:

Question 1: Calculate the gravitational force between two bodies of masses 3kg and 5kg separated by distance 0.2 m.
Solution:

Given: Mass of first body m1 = 3 kg, Mass of second body m2 = 5 kg, Gravitational constant G = 6.67 $\times$ 10-11 Nm2/Kg2, distance r = 0.2 m

The gravity formula given as,
F = $\frac{G m_1 m_2}{r^2}$

F = $\frac{6.67 \times 10^{-11} Nm^2/Kg^2 \times 3 kg \times 5 kg}{0.2^2 m^2}$

F = 2.5 $\times$ 10-8 N.

Question 2: Find the gravity of earth if mass of earth is 5.972 $\times$ 1024 kg and radius of earth is 6,371 km.(Gravitational constant G = 6.67 $\times$ 10-11 Nm2/Kg2)
Solution:

Given: Gravitational constant G = 6.67 $\times$ 10-11 Nm2/Kg2, mass of earth m = 5.972 $\times$ 1024 kg and radius of earth R = 6,371 km

The Gravity formula is given by,
g = $\frac{GM}{R^2}$

g = $\frac{6.67 \times 10-11 Nm^2/Kg^2 \times 5.972 \times 10^24 kg}{(6371 \times 10^3)^2 km^2}$

g = 9.8 m/s2.