`implies` The net gravitational force on a particle is the vector sum of the individual gravitational forces on the particle.
`implies` Gravitational force on point mass `m_1` due to point mass `m_2`
`vecF_(12)=G(m_1m_2)/(|vecr_(12)|).hatr^2" "` or
`vecF_(12)=(-Gm_(1)m_(2))/(|vecr_(21)|)^2.hatr_(21) " "...(1)`
`hatr_(12)` is a unit vector from `m_(1) " to " m_2`
`hatr_(21)` is a unit vector from `m_(2) " to " m_1`
`implies` Gravitational force of mass `m_1` due to mass `m_3`
`vecF_(13)=(Gm_1m_3)/(|vecr_(13)|).hatr_(13)=(-Gm_(1)m_(2))/(|vecr_(31)|^2)hatr_(31)" "...(2)`
`implies` Gravitational force of mass `m_1` due to mass `m_4`
`vecF_(14)=(Gm_1m_4)/(|vecr_(14)|).hatr_(14)=(-Gm_(1)m_(4))/(|vecr_(41)|^2)hatr_(41)" "...(3)`
`implies` The total force on `m_1`
`vecF_(1)=(Gm_1m_2)/(|vecr_(12)|).hatr_(12)+G(m_(1)m_(2))/(|vecr_(13)|^2)hatr_(31)+(Gm_(1)m_(4))/(|vecr_(14)|^2)" "...(4)`
`vecF_(1)=-((Gm_1m_2)/(|vecr_(21)|).hatr_(21)+G(m_(3)m_(1))/(|vecr_(31)|^2)hatr_(31)+(Gm_(4)m_(1))/(|vecr_(41)|^2)hatr_(41))" "..(5)`
Note : The gravitational field intensity is the force on a unit mass at a point in the field.
