Main Concept

All objects are attracted to each other by a gravitational force of magnitude

$F\=\frac{G\cdot m\cdot M}{r^2}$,

where G is the universal constant of Gravitation, m and M are the masses of the two objects, and r is the distance between them. Using Newton's 2nd law, $F\=m\cdot a$, the corresponding acceleration towards a nearby body of mass $M$  is

$a\=\frac{G\cdot M}{r^2}$.

The total acceleration a body experiences when there are many other gravitational bodies in the vicinity, of masses $M_i$ and at distances $r_i$ , is therefore given by the sum of the individual accelerations towards each other body:

$\mathrm{Total} \mathrm{acceleration} \=\sum _i {\mathit{a}}_i\=\sum _i\frac{G\cdot M_i\cdot {\mathit{r}}_i}{r_i^3}$,

where we have now used vector notation because the displacements may be in different directions.

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