Year 12 / Gravity and motion
Distance from the centre matters.
For point masses, gravitational force has magnitude GMm/r² and is attractive. Outside a spherically symmetric body the same expression applies using the distance from its centre. Field strength is gravitational force per unit test mass.
Mass determines inertia and does not vary with position, while weight depends on local field strength. A freely falling astronaut can feel weightless even where the gravitational field is substantial; there is no supporting normal force.
An inverse-square field
Explore the relationship
Spherical planet outside its surface. Distance is measured from the centre.
Field strength / N kg⁻¹
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Distance from centre / Earth radii | Field strength / N kg⁻¹ |
|---|---|---|
| Field strength / N kg⁻¹ | 1 | 9.8 |
| Field strength / N kg⁻¹ | 1.06667 | 8.61328 |
| Field strength / N kg⁻¹ | 1.13333 | 7.62976 |
| Field strength / N kg⁻¹ | 1.2 | 6.80556 |
| Field strength / N kg⁻¹ | 1.26667 | 6.10803 |
| Field strength / N kg⁻¹ | 1.33333 | 5.5125 |
| Field strength / N kg⁻¹ | 1.4 | 5 |
| Field strength / N kg⁻¹ | 1.46667 | 4.55579 |
| Field strength / N kg⁻¹ | 1.53333 | 4.16824 |
| Field strength / N kg⁻¹ | 1.6 | 3.82812 |
| Field strength / N kg⁻¹ | 1.66667 | 3.528 |
| Field strength / N kg⁻¹ | 1.73333 | 3.26183 |
| Field strength / N kg⁻¹ | 1.8 | 3.02469 |
| Field strength / N kg⁻¹ | 1.86667 | 2.8125 |
| Field strength / N kg⁻¹ | 1.93333 | 2.62188 |
| Field strength / N kg⁻¹ | 2 | 2.45 |
| Field strength / N kg⁻¹ | 2.06667 | 2.29448 |
| Field strength / N kg⁻¹ | 2.13333 | 2.15332 |
| Field strength / N kg⁻¹ | 2.2 | 2.02479 |
| Field strength / N kg⁻¹ | 2.26667 | 1.90744 |
| Field strength / N kg⁻¹ | 2.33333 | 1.8 |
| Field strength / N kg⁻¹ | 2.4 | 1.70139 |
| Field strength / N kg⁻¹ | 2.46667 | 1.61066 |
| Field strength / N kg⁻¹ | 2.53333 | 1.52701 |
| Field strength / N kg⁻¹ | 2.6 | 1.4497 |
| Field strength / N kg⁻¹ | 2.66667 | 1.37812 |
| Field strength / N kg⁻¹ | 2.73333 | 1.31172 |
| Field strength / N kg⁻¹ | 2.8 | 1.25 |
| Field strength / N kg⁻¹ | 2.86667 | 1.19254 |
| Field strength / N kg⁻¹ | 2.93333 | 1.13895 |
| Field strength / N kg⁻¹ | 3 | 1.08889 |
| Field strength / N kg⁻¹ | 3.06667 | 1.04206 |
| Field strength / N kg⁻¹ | 3.13333 | 0.998189 |
| Field strength / N kg⁻¹ | 3.2 | 0.957031 |
| Field strength / N kg⁻¹ | 3.26667 | 0.918367 |
| Field strength / N kg⁻¹ | 3.33333 | 0.882 |
| Field strength / N kg⁻¹ | 3.4 | 0.847751 |
| Field strength / N kg⁻¹ | 3.46667 | 0.815459 |
| Field strength / N kg⁻¹ | 3.53333 | 0.784977 |
| Field strength / N kg⁻¹ | 3.6 | 0.756173 |
| Field strength / N kg⁻¹ | 3.66667 | 0.728926 |
| Field strength / N kg⁻¹ | 3.73333 | 0.703125 |
| Field strength / N kg⁻¹ | 3.8 | 0.67867 |
| Field strength / N kg⁻¹ | 3.86667 | 0.65547 |
| Field strength / N kg⁻¹ | 3.93333 | 0.633439 |
| Field strength / N kg⁻¹ | 4 | 0.6125 |
| Field strength / N kg⁻¹ | 4.06667 | 0.592583 |
| Field strength / N kg⁻¹ | 4.13333 | 0.573621 |
| Field strength / N kg⁻¹ | 4.2 | 0.555556 |
| Field strength / N kg⁻¹ | 4.26667 | 0.53833 |
| Field strength / N kg⁻¹ | 4.33333 | 0.521893 |
| Field strength / N kg⁻¹ | 4.4 | 0.506198 |
| Field strength / N kg⁻¹ | 4.46667 | 0.491201 |
| Field strength / N kg⁻¹ | 4.53333 | 0.47686 |
| Field strength / N kg⁻¹ | 4.6 | 0.463138 |
| Field strength / N kg⁻¹ | 4.66667 | 0.45 |
| Field strength / N kg⁻¹ | 4.73333 | 0.437413 |
| Field strength / N kg⁻¹ | 4.8 | 0.425347 |
| Field strength / N kg⁻¹ | 4.86667 | 0.413774 |
| Field strength / N kg⁻¹ | 4.93333 | 0.402666 |
| Field strength / N kg⁻¹ | 5 | 0.392 |
Explore: Double distance from the centre and compare field strength.
Move from distance R to 2R from the centre of a spherical planet.
- g is proportional to 1/r².
- The new field strength is one quarter of its value at R.
Assumed knowledge
Scientific notation and inverse-square scaling.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Use universal gravitation and field strength.
- Interpret inverse-square relationships.
READY TO TRY IT?