Quick questions on Newton's law of universal gravitation explained: HSC Physics Module 5

Every pair of point masses attracts each other with a force directed along the line joining them:

Force is inversely proportional to the square of the distance. Doubling $r$ reduces the force to one quarter. Halving $r$ quadruples the force. This rapid fall-off explains why Earth's gravity dominates near the surface but becomes negligible far from the planet.

The gravitational field strength $g$ at a point is the gravitational force per unit mass on a test mass placed there:

For an object of mass $m$ in free fall in a gravitational field $g$, the acceleration is $a = g$ (regardless of $m$, because $F = mg$ and $a = F/m$). All objects fall with the same acceleration in a given gravitational field, in the absence of air resistance.

$r$ in the formula is always measured from the centre of the source body. For a satellite at altitude $h$ above Earth: $r = R_E + h$.

The denominator is $r^2$, not $r$. Halving the distance multiplies the force by four, not two.

$G$ is a universal constant ($6.67 \times 10^{-11}$). $g$ depends on the source mass and your distance from it.

This is only true at Earth's surface. At higher altitudes or on other planets, recalculate using $g = G M / r^2$.

Gravity extends to infinity, just very weakly. The "edge" of Earth's gravity is fictional.