Newton's Law of Gravitation
Newton's Law of Gravitation states that there is a force of attraction between any two objects in the universe.
$$
F = \frac{Gm_{1}m_{2}}{r^2}
$$
where:
- $F$ is the gravitational force, in $N$.
- $G$ is the Universal Constant of Gravitation, value $6.67\times 10^{-11}\,m^3\,kg^{-1}\,s^{-2}$.
- $m_{1}$ and $m_{2}$ are the masses of the two objects, in $kg$.
- $r$ is the distance between the two objects, in $m$.
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🗒️ The size of the gravitational force is:
- Proportional to the product of the masses of the two objects.
- Inversely proportional to the square of the distance between them.
</aside>
Gravitational Field Strength
<aside>
📕 The gravitational force acting on unit mass.
</aside>
The acceleration due to gravity, $g$, is found from Newton's second law of motion:
$$
F = ma
$$
$$
\therefore W = mg
$$
We can substitute for $F$ in this equation:
$$
mg = \frac{GMm}{r^2}
$$
$$
\therefore g = \frac{GM}{{r}^2}
$$
where:
- $g$ is the gravitational field strength, in $N\,kg^{-1}$.
- $G$ is the Universal Constant of Gravitation, value $6.67\times 10^{-11}\,m^3\,kg^{-1}\,s^{-2}$.
- $M$ is the mass of the body, in $kg$.
- $r$ is the distance from the centre of the body, in $m$.