The gravitational force due to earth is called gravity.
Newton's Law of Gravitation: In this universe all things attract each other. The force of attraction acting between two bodes of masses m1 and m2 separated by a distance r is directly proportional to product of their masses and inversely proportional to square of the separation between them.
$$ F = \frac{Gm_1m_2}{r^2} $$
Here, G is proportionality constant is called Gravitation constant.
G = × 6.67 x 10-11 Nm2 × kg-2
Relation between g (Acceleration due to gravity) and G (gravitation constant)
$$ g = \frac{GM}{r^2} $$
The value of g near the surface of the earth is taken as 9.8 ms-2.
Motion of object under gravity
When a body is falling down, then a is replaced by g.
When a body is thrown up then a is replaced by -g.
Buoyancy
Whenever a body is immersed in a fluid, an upward force is exerted by the fluid on the body, called force of buoyancy or buoyant force. This is also known as upthrust.
Archimedes Principle
When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to weight of the fluid displaced by it.