Gravitational fields
The same pull, near and far
- An apple falls; the Moon circles the Earth. Both feel the same pull.
- A gravitational field is any region where a mass feels a gravitational force.
- We measure its strength with one simple idea.
Field strength
- Gravitational field strength is the force per unit mass: $g = \dfrac{F}{m}$.
- It is a vector, pointing toward the source mass.
Practice
Gravitational field strength is the force per unit:
$g = \dfrac{F}{m}$ — the gravitational force on each kilogram of a small test mass.
A familiar number
- The unit is $\dfrac{\text{N}}{\text{kg}}$ — exactly the same as $\dfrac{\text{m}}{\text{s}^2}$.
- So $g$ is just the acceleration of free fall in the field.
Practice
A $2.0\ \text{kg}$ mass feels a gravitational force of $20\ \text{N}$. What is $g$ there?
$g = \dfrac{F}{m} = \dfrac{20}{2.0} = 10\ \dfrac{\text{N}}{\text{kg}}$.
Practice
The unit N/kg is the same as m/s².
Yes — $g$ is also the acceleration of free fall, so its units are equivalent.
Field lines
- Around a point mass or sphere: lines are radial, pointing inward.
- Near a surface (small region): lines are parallel — a uniform field. Closer lines = stronger field.
Practice
Around a sphere (seen from outside), the gravitational field lines are:
Gravity always attracts, so the lines point inward toward the centre, like a point mass.
Practice
Field lines drawn closer together represent a ____ field.
Line spacing shows strength — closer lines mean a stronger field.
You've got it
Key idea
- gravitational field strength $g = \dfrac{F}{m}$ (a vector toward the mass)
- $\dfrac{\text{N}}{\text{kg}} = \dfrac{\text{m}}{\text{s}^2}$ — $g$ is the free-fall acceleration
- field lines: radial for a sphere, uniform near a surface; closer = stronger