Gravity and Gravitational Force

Gravity is an attractive force between all objects with mass. Near Earth's surface, gravity pulls objects downward with a gravitational field strength of approximately 10 N/kg. Weight is the gravitational force on an object and is calculated using W = mg. Weight and mass are different quantities.

What is Gravity?

Gravity is an attractive force between any two objects with mass. The more mass the objects have, and the closer they are, the stronger the gravitational force between them.

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

Gravitational Field Strength (g)

The gravitational field strength ( $g$ ) is the gravitational force per unit mass:

$g = \frac{F}{m}$

On Earth's surface: $g \approx 10$ N/kg (or 10 m/s²)

This means every kilogram of mass experiences a downward pull of 10 N.

Location	g (approx.)
Earth surface	10 N/kg
Moon surface	1.6 N/kg
Mars surface	3.7 N/kg

Weight vs. Mass

Property	Mass	Weight
What is it?	Amount of matter	Gravitational force
Symbol	$m$	$W$
Unit	kg	N (Newtons)
Changes with location?	NO	YES

$W = mg$

Calculating Weight

An astronaut has a mass of 70 kg. Calculate their weight on Earth and on the Moon.

On Earth: $W = 70 \times 10 = 700$ N On Moon: $W = 70 \times 1.6 = 112$ N

Their mass stays at 70 kg in both locations.

Free Fall

When an object falls with only gravity acting (no air resistance), it is in free fall. Every second, its speed increases by $g = 10$ m/s.

Note

In free fall on Earth, all objects accelerate at the same rate (10 m/s²), regardless of their mass. A feather and a hammer dropped simultaneously in a vacuum hit the ground at the same time.

Real world: satellite orbits

The International Space Station orbits Earth at about 400 km altitude. At that height, $g \approx 8.7$ N/kg — still nearly 90 % of Earth's surface gravity. Gravity provides the centripetal force that continuously curves the ISS's path into a circle. The ISS is not weightless because gravity is absent; it is in free fall — falling toward Earth but moving so fast sideways that it keeps missing the surface. Astronauts feel weightless because everything inside the station falls together.

Real world: weighing yourself on Mars

A person with a mass of 70 kg would weigh $W = 70 \times 10 = 700$ N on Earth. On Mars ( $g = 3.7$ N/kg), they would weigh $W = 70 \times 3.7 = 259$ N — about 37 % of their Earth weight. Their mass stays 70 kg. Mars explorers can carry heavier payloads and jump further, but their muscles and bones adapted to Earth gravity would weaken over time.

Real world: ocean tides

The Moon's gravity is weaker than Earth's ( $g_{\text{Moon}} = 1.6$ N/kg at its surface), but its gravitational pull varies across the diameter of Earth. The side of Earth closest to the Moon experiences slightly stronger pull than the far side. This differential pull stretches Earth's oceans into an elongated shape, creating two high tides per day as Earth rotates. Tidal power stations on coastlines harness this predictable twice-daily rise and fall to generate electricity.

Tip

Where do you see gravity at work? Falling objects, orbiting satellites, ocean tides, the atmosphere being held around Earth, rain falling, rivers flowing downhill, and the way a ball arcs through the air — all are driven by gravitational attraction.

Practice Problems

Calculate the weight of a 5 kg bag on Earth. (g = 10 N/kg)

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W = mg = 5 × 10 = 50 N

An object weighs 120 N on Earth. What is its mass?

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m = W/g = 120/10 = 12 kg

An astronaut weighs 600 N on Earth and 100 N on the Moon. Does their mass change?

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No. Mass stays the same (60 kg). Only weight changes because the gravitational field strength is different on the Moon (1.6 N/kg vs 10 N/kg on Earth).