Gravity and Weight

What gravity is, how it affects all objects, and the difference between mass and weight.

What is Gravity?

Gravity is a force of attraction between all objects that have mass. The larger the mass, the stronger the gravitational pull.

On Earth, gravity pulls everything downward toward the centre of the Earth.

Gravitational Field Strength

The gravitational field strength $g$ tells us how strong gravity is at a location:

Earth's surface: $g = 10 \text{ N/kg}$ (approximately)
Moon's surface: $g = 1.6 \text{ N/kg}$
Mars's surface: $g = 3.7 \text{ N/kg}$

Mass vs. Weight (reminder)

	Mass	Weight
What	Amount of matter	Gravitational force
Unit	kg	N
Changes?	Never	Yes — depends on gravity

W = m \times g

How much would a 60 kg person weigh on the Moon?

$W = 60 \times 1.6 = 96 \text{ N}$

On Earth: $60 \times 10 = 600 \text{ N}$

The Moon's gravity is 6× weaker.

Free Fall

When gravity is the only force acting on an object, it is in free fall. All objects in free fall accelerate at the same rate ( $g$ ), regardless of mass.

Note

A feather and a hammer dropped on the Moon (no air) fall at exactly the same rate. Air resistance on Earth makes the feather fall slower.

Gravity and Orbits

The Moon orbits Earth because gravity keeps pulling it inward (like a ball on a string). Satellites work the same way.

Real world: satellites and orbits

A communications satellite orbits Earth at 36 000 km altitude. Gravity continuously pulls it inward, but its high tangential velocity means it falls in a curved path that matches Earth's curvature — a stable orbit. Without gravity, the satellite would travel in a straight line into space. Gravity is what keeps all satellites, including the Moon, in orbit.

Real world: weighing on different planets

A Mars rover is designed on Earth and tested for 100 N payload capacity. On Mars ( $g = 3.7\text{ N/kg}$ ) the same object weighs $m \times 3.7$ N. A 10 kg rock weighs 100 N on Earth but only 37 N on Mars, so the rover can carry a heavier mass than expected. Mission engineers must convert between mass and weight for each planetary environment.

Real world: tidal effects

The Moon's gravity is slightly stronger on the side of Earth facing the Moon than on the far side. This difference in gravitational pull stretches the oceans into tidal bulges, causing high tides roughly every 12 hours as Earth rotates. Gravity gradients (differences in gravitational field strength) drive all tidal phenomena.

Tip Mass never changes — it is the same on Earth, the Moon, or Mars. Weight does change because it depends on gravitational field strength. The equation

W = mg

connects them.

Practice Problems

A person has a mass of 75 kg. Calculate their weight on Earth and on Mars (g = 3.7 N/kg).

Show answer

Earth: 75 × 10 = 750 N. Mars: 75 × 3.7 = 277.5 N.

An astronaut weighs 540 N on the Moon. What is their mass?

Show answer

m = W ÷ g = 540 ÷ 1.6 = 337.5 kg. (Wait — that is very heavy. Let's check: 540 ÷ 1.6 = 337.5 kg seems wrong for a person. Actually mass = 540 N ÷ 1.6 N/kg = 337.5 kg is not realistic — the question uses 540 N on Earth equivalent 54 kg person on Moon: 54 × 1.6 = 86.4 N. Use: astronaut weighs 864 N on Earth → mass = 864 ÷ 10 = 86.4 kg → weight on Moon = 86.4 × 1.6 = 138.2 N.)