Gravitational Force

Gravitational force is the force that exit between two bodies with masses, gravity is the measure of the force on a body in relation to the earth surface, according to Newton’s second law of motion, force is given by mass X acceleration , f = ma,  but under gravitational force a = g, which is acceleration due to gravity or acceleration of a free all.

f=ma

but a= g

thus, f= mg

where g has the value of 9.8ms^-2

the force on a body of mass m and acceleration due to gravity g is called its weight.

weight is therefore equal to mass X g

thus w = m X g,

the gravitational force is the force between the earth and the sun, it is the force that keeps the earth and other planet to revolve around the sun in their orbit in the solar system, therefore it is called universal gravitational force. but this  force is balanced by the centripetal force that keeps  the solar system.

gravitational force f_g = GM₁M₂/r²   and the centripetal force f_c =mv²/r

mv² = GM₁M₂/r

thus  r = GM/v²

thus v = [GM/r]^1/2 where v is the velocity of a body m moving around the earth surface

G =mv²r/M1M2

G is the gravitational constant , = 6.7X 10^-11Nm^-2kg^-2

 also comparing the g and G

F_g = GM1M2/r²

w = mg

we get

GM1M2/r² = mg

Thus g = GM/r²