Acceleration due to gravity

Beginner

Near Earth's surface all objects fall with the same acceleration.

Key relationg ≈ 9.8 m/s²

Near Earth's surface g ≈ 9.8 m/s² downward, varying slightly with latitude and altitude (9.78 at the equator, 9.83 at the poles). It is the same for all objects in free fall. On the Moon g ≈ 1.6 and on Jupiter ≈ 24.8 m/s².

Worked example

On the Moon you could jump about six times higher with the same effort.

Common mistake

g is an acceleration, not a force; the weight is mg.

In more detail

The acceleration due to gravity, g, is about 9.8 m/s² at Earth's surface. It varies with height, latitude and local rock density.

How to solve it

Write g = GM/R² for a spherical body, using its mass M and radius R.
Insert the mass and radius in SI units, using scientific notation for both.
Compute the result and compare it with the 9.8 m/s² value for Earth.
For a height h above the surface, replace R with R + h, or use g = g0(R/(R + h))².

Worked examples

Example 1: The Moon has mass 7.35 × 10²² kg and radius 1.74 × 10⁶ m. What is its surface gravity?

g = (6.67 × 10⁻¹¹)(7.35 × 10²²) / (1.74 × 10⁶)² = 4.90 × 10¹² / 3.03 × 10¹² = 1.62 m/s², about one-sixth of Earth's value.

Example 2: What is g at 1000 km above Earth's surface? Use R = 6371 km and g0 = 9.8 m/s².

g = g0 (R/(R + h))² = 9.8 × (6371/7371)² = 9.8 × 0.747 = 7.32 m/s².

Checking your answer

Gravity should be weaker on smaller or less massive bodies, and weaker farther from the centre. Both examples follow that pattern.

Real-world uses

Pendulum clocks and gravimeters measure g to map underground structures.
Engineers use the local value of g when designing lifts and cranes.
Engineers use g to design structures such as lifts and cable cars, where gravity drives the loads on cables and supports.

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Frequently asked questions

Is g the same everywhere on Earth?

No. It is slightly larger at the poles than at the equator, and it decreases with altitude.

Is 9.8 m/s² exact?

It is a standard value, rounded for convenience. Precise measurements give slightly different values.

Why does g vary across Earth?

It is slightly larger at the poles than at the equator, and it decreases with altitude and depends on local rock density.