When applying Newton’s laws near Earth, you often assume gravity is constant to simplify force and motion equations. This approximation is valid only when position changes are small compared with the relevant gravitational distance scale.

What “gravity is constant” means (and what it doesn’t)

Treating gravity as constant means the gravitational force magnitude on an object and the gravitational field strength at its location do not change appreciably during the motion being analysed.

• Direction: near Earth’s surface, gravity is taken to point straight down (toward Earth’s centre).

• Magnitude: the gravitational field strength is taken as a constant value, typically $g \approx 9.8\ \text{m/s}^2$ (often rounded to $10\ \text{m/s}^2$ when appropriate).

This is an approximation, not a new law; the true gravitational force depends on separation distance.

Distance dependence of gravity

The reason the approximation can work is that gravity varies with distance by an inverse-square relationship, so small fractional changes in distance produce small fractional changes in force.

This diagram shows two masses separated by a center-to-center distance $r$, with the gravitational forces drawn along the line connecting their centers of mass. It reinforces the meaning of $r$ in $F_g = \dfrac{Gm_1m_2}{r^2}$ and visually connects Newton’s third-law force pair to the geometry of the interaction. Source

For near-Earth motion, one of the masses is Earth, and the object’s distance from Earth’s centre is $r=R_E+h$, where $h$ is altitude above the surface.

The “small change in distance” condition

A practical way to state the syllabus idea (“distance changes very little”) is as a small fractional change in $r$:

• If the motion changes the object’s distance from Earth’s centre by a small amount $\Delta r$ compared with $r$ itself, then $F_g$ and $g$ change very little.

• Near the surface, $r \approx R_E$ is very large, so everyday heights and vertical displacements often satisfy $\Delta r \ll R_E$.

Because $F_g \propto 1/r^2$, the fractional change behaves approximately like:

• $\dfrac{\Delta F_g}{F_g} \approx 2\dfrac{\Delta r}{r}$ for small $\Delta r/r$.

So even a noticeable height change in a lab can correspond to a tiny percentage change in $r$, making the change in gravity negligible for AP Physics 1 modelling.

Consequences for modelling forces and motion

When gravity can be treated as constant, you can use a uniform gravitational field model, which simplifies dynamics:

In this model:

• The gravitational force on an object is treated as constant: $F_g \approx mg$ with constant $g$.

• Acceleration due to gravity is treated as constant, so kinematics with constant acceleration can be used in the vertical direction when other forces are accounted for.

• In multi-step Newton’s second law problems, you do not need to update $g$ as the object moves slightly (e.g., over a ramp height, short drop, or elevator travel).

When the constant-gravity approximation can fail

You should question the approximation when the object’s distance from the attracting body changes enough that the inverse-square variation matters.

Indicators that $g$ may not be treated as constant:

• The motion involves large changes in altitude compared with the planet’s radius.

• The scenario involves space-scale distances where $r$ changes substantially.

• The problem statement provides (or asks for) changing $r$ explicitly, suggesting you should use the inverse-square dependence rather than a constant $g$.

In AP Physics 1 Algebra, the key skill is recognising when “distance changes very little” is a valid assumption so that gravity can be modelled as constant without significantly affecting predicted motion.