Explain the principle of superposition for gravitational force.

(N/A) The principle of superposition states that the net gravitational force on a particle is the vector sum of the individual gravitational forces exerted on it by all other particles.
If a particle of mass $m_1$ is surrounded by particles of masses $m_2, m_3, ..., m_n$ at distances $r_{12}, r_{13}, ..., r_{1n}$ respectively,the total force $\vec{F}_1$ on $m_1$ is:
$\vec{F}_1 = \vec{F}_{12} + \vec{F}_{13} + ... + \vec{F}_{1n} = \sum_{i=2}^{n} \vec{F}_{1i}$
Where the force due to any mass $m_i$ is given by:
$\vec{F}_{1i} = G \frac{m_1 m_i}{|\vec{r}_{1i}|^2} \hat{r}_{1i}$
Here,$\hat{r}_{1i}$ is the unit vector pointing from $m_1$ towards $m_i$. The total force is the vector sum of these individual forces as shown in the diagram.