understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass

Definition

A gravitational field is an example of a field of force. It tells us how much force a mass would feel at any point in space.

Mathematically, it is defined as the force per unit mass:

\$\,\displaystyle \vec{g} = \frac{\vec{F}}{m}\,\$

where \$\vec{F}\$ is the gravitational force on a test mass \$m\$.

Analogy & Example

Think of the Earth as a giant magnet that pulls everything toward its centre. The gravitational field is like invisible “force lines” that show how strong the pull is at any point.

• 🌍 Earth’s surface – the field is strongest here, about \$9.81\,\text{m/s}^2\$.
• 🛰️ At 10 km altitude – slightly weaker, \$9.78\,\text{m/s}^2\$.
• 🚀 At 100 km (edge of space) – still strong, \$9.71\,\text{m/s}^2\$.

Example: A 10 kg object on Earth feels a force \$F = m\,g = 10\,\text{kg} \times 9.81\,\text{m/s}^2 = 98.1\,\text{N}\$.

Key Formula

For a point mass (like a planet) the field at a distance \$r\$ from its centre is:

\$\,\displaystyle \vec{g} = -\frac{GM}{r^2}\,\hat{r}\,\$

where:

• \$G\$ – gravitational constant \$6.674\times10^{-11}\,\text{Nm}^2/\text{kg}^2\$
• \$M\$ – mass of the attracting body
• \$r\$ – distance from the centre of mass
• \$\hat{r}\$ – unit vector pointing radially outward

Exam Tips

1. Always state the definition of the gravitational field before using it.
2. Remember the negative sign in the formula – the field points toward the mass.
3. Use the formula \$g = \frac{GM}{r^2}\$ when calculating the field at a specific distance.
4. Check units: \$g\$ should be in \$\text{m/s}^2\$.
5. When given weight \$W\$, you can find \$g\$ by \$g = \frac{W}{m}\$.