`implies` Newton.s universal law of gravitation :
`implies` "Every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
`implies` This force is on the line joining the bodies.
`implies` This force is known as gravitational attractive force, gravitational force or gravitation force.
`:. |vecF_(12)|=|vecF_(21)|=(Gm_1m_2)/r^2`
where `m_1 m_2` masses of both the bodies.
r = distance between the bodies.
G = universal gravitational constant.
Obtaining the vector form of gravitational force :
`implies` According to the figure `m_1 and m_2` are two placed in Cartesian system `vecr_1 and vecr_2` are the position vectors of masses `m_1 and m_2`
`:. ` The resultant vector `vecr_(12) = vecr_(2) -vecr_(1)`
(From figure)
`:. ` Unit vector `hatr_(12)=(vec(r_(12)))/(|vec(r_(12))|)=(vec(r_2)-vec(r_1))/r`
where `|vec(r_(12))|=r`
`implies` The gravitation force on mass `m_1` by mass `m_2`
`vecF_(21) = (Gm_1m_2)/r^2xxhatr_(12)`
`implies` The gravitation force on mass `m_2` by mass `m_1`
`vecF_(21) = (Gm_1m_2)/r^2xxhatr_(21)=-(Gm_1m_2)/r^2hatr_(12) `
`implies` Both forces `vecF_(12) and vecF_(21)` and are shown in figure. Gravitational forces are internal force due to mutual interactions hence gravitation force on mass `m_2` by mass `m_1` is equal and opposite.
`:. vecF_(12)=-vecF_(21)`
`:. |vecF_(12)|=|-vecF_(21)|=vecF`
