1.0 Newton's law of gravitation

1.1 Characteristics of gravitational force
1.2 Universal gravitational constant
1.3 Principle of superposition of gravitation
1.4 Gravity
1.5 Acceleration due to gravity
1.6 Relation between $g$ and $G$

It states that every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

Mathematically it is given by, $$F \propto {m_1}{m_2}$$ and $$F \propto \frac{1}{{{r^2}}}$$ So, $$F \propto \frac{{{m_1}{m_2}}}{{{r^2}}}$$

Thus the magnitude of the gravitational force $F$ between two particles of masses $m_1$ and $m_2$ placed at a distance $r$ is,

$$F = \frac{{G{m_1}{m_2}}}{{{r^2}}}$$

where $G$ is a universal constant known as gravitational constant.

Also, $$G = 6.67 \times {10^{ - 11}}N{m^2}/k{g^2}$$

Newton's law of gravitation in vector form is, $$\overrightarrow F = - \frac{{G{m_1}{m_2}}}{{{r^2}}}\widehat r$$ or $$\overrightarrow F = - \frac{{G{m_1}{m_2}}}{{{r^3}}}\overrightarrow r $$

Also, $${\overrightarrow F _{AB}} = - {\overrightarrow F _{BA}}$$

But, $$\left| {{{\overrightarrow F }_{AB}}} \right| = \left| { - {{\overrightarrow F }_{BA}}} \right|$$

Note: Negative sign shows that the force is attractive.