Short on time? This page is the recap. For diagrams, graphs and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- Any two masses attract. The force acts along the line joining their centres of mass and can be drawn from each centre of mass.
- The two forces are a third-law pair: equal and opposite, whatever the masses.
- A field gives the force per kilogram at each point. Gravitational field strength g is in N/kg, which equals m/s².
- Weight is the gravitational force from a planet or moon on a nearby small object: mg.
- g is effectively constant when the object’s distance from the centre changes by only a tiny fraction (anything near the ground).
- Apparent weight is the normal force. It differs from mg whenever the system accelerates. A system appears weightless when gravity is the only force on it (free fall), or when no forces act.
- Equivalence principle: in an accelerating frame, you cannot tell apparent weight from real gravity.
- Inertial mass (resists changes in motion) and gravitational mass (feels gravity) are equal by experiment, so all objects fall with the same acceleration.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| F_g = G m₁m₂ / r² | G = 6.67 × 10⁻¹¹ N·m²/kg², r in m | force between two masses |
| g = F_g / m = GM / r² | N/kg = m/s² | field strength at distance r from mass M |
| weight = mg | g = 9.8 N/kg at Earth’s surface | gravitational force near a planet |
| F_N = m(g + a_y), +y up | a_y signed | apparent weight in a lift |
| F_g ∝ 1/r² | factor-of-change: 2r → ¼ force |
Assumptions behind the numbers
- Planets and spheres act as if all their mass is at their centre (for points outside them).
- Near Earth’s surface, g = 9.8 N/kg (10 N/kg where stated).
- The ground is an inertial frame; a lift that accelerates is not.
Mistakes to avoid
- Using surface-to-surface distance. Use centre to centre, so add the planet’s radius to a height.
- Forgetting to square r. Halving r gives four times the force.
- Saying the larger body pulls harder. The forces are equal; the smaller body accelerates more.
- Linking scale readings to velocity. Only the acceleration matters.
- “No gravity in orbit.” g is still large; there is just no normal force.
- Mixing mass and weight. kg is not N.
Quick self-check
- The distance between two objects is tripled. By what factor does the gravitational force change? (It becomes one ninth.)
- A 70 kg astronaut stands on the Moon, where g = 1.6 N/kg. What is her weight there? (about 110 N)
- Take +y up. A 50 kg person stands on a scale in a lift accelerating downward at 2.0 m/s². What does the scale read? (390 N)
Next: practice questions.