Quick questions on Newton's law of universal gravitation and gravitational fields (QCE Physics Unit 3)

Every pair of point masses (or spherically symmetric masses) attracts each other with a force directed along the line joining their centres:

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

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

For a freely falling object of mass $m$ in a gravitational field $g$, the acceleration is $a = g$ (independent of $m$, because $F = m g$ and $a = F / m$). All objects fall with the same acceleration in a given gravitational field, in the absence of air resistance. This is why $g$ appears in projectile-motion equations as the constant downward acceleration.

The field of a point or spherical mass is radial, pointing toward the source mass, and uniform in magnitude on any sphere centred on the source. The field-line picture has lines pointing inward at every point on a sphere, getting denser closer to the mass.

Expect a table of $g$ at various altitudes and a question asking you to extract $M$ of the planet, or a single-line problem asking you to compute $g$ at a given altitude and discuss the apparent weight of an astronaut. Markers focus on candidates who substitute altitude $h$ for $r$ instead of $R_E + h$.

A common IA2 measures local $g$ by timing a simple pendulum at different lengths and linearising $T^2$ against $L$ (slope $= 4 \pi^2 / g$). The Unit 3 universal-gravitation theory provides the framework in the justification section: the value of $g$ extracted should agree with $G M_E / R_E^2$ at the school's altitude.

$r$ in the formulas 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 ($6.67 \times 10^{-11}$ N m$^2$/kg$^2$). $g$ depends on the source mass and your distance from it, and is a field strength in N/kg (or an acceleration in m/s$^2$).

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

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

Apparent weightlessness in orbit is caused by free fall, not by the absence of gravity. The astronaut in low Earth orbit still feels nearly the surface gravitational field.