How Do You Use Newton's Universal Law of Gravitation (F = Gm1m2/r²)?

Newton's universal law of gravitation calculates the attractive gravitational force between two masses. Substitute both masses in kilograms and their centre-to-centre separation in metres into $F=\frac{Gm_1m_2}{r^2}$.

This is part of D.1 Gravitational fields and applies to both SL and HL.

How to Apply the Equation

In the equation:

• $F$ is the gravitational force in newtons ($\text{N}$).
• $G=6.67\times10^{-11}\ \text{N m}^2\text{ kg}^{-2}$, from the IB Physics data booklet.

The equation applies directly to point masses. Spherically symmetric bodies, such as planets, can also be treated as point masses when they do not overlap, with their mass considered to be concentrated at the centre.

Before substituting, convert every quantity to SI units. If radii, altitude, or a surface gap are provided, calculate $r$ first. For two spheres of radii $R_1$ and $R_2$ separated by a surface gap $d$, .

For example, two spherical objects have masses $m_1=1000\ \text{kg}$ and $m_2=2000\ \text{kg}$, with their centres separated by :

$$F=\frac{(6.67\times10^{-11})(1000)(2000)}{(2.0)^2}$$ $$F=3.34\times10^{-5}\ \text{N}$$

Each object experiences this same force magnitude, directed towards the other object. The forces form a Newton's third-law pair: they are equal in magnitude and opposite in direction.

The inverse-square relationship predicts changes without repeating the full calculation:

This comparison assumes the masses remain constant. It shows that the relationship is nonlinear.

A common misconception is to use the distance between the surfaces. Always use the centre-to-centre distance. Also square only $r$, not the masses or the entire denominator.

Exam Technique

For a Calculate question, show the equation, substitution, and final value. Use SI units, identify the direction if requested, and use $G=6.67\times10^{-11}\ \text{N m}^2\text{ kg}^{-2}$ from the data booklet.