Weight, mass and gravity

The weight of an object is the force on it due to the gravitational pull of gravity at that point. Since it is a force, weight is measured in Newtons (not kilograms).

Gravity is different on different planets, so the weight of an object on different planets (or moons) is different from its weight on Earth.

The mass of an object is the amount of matter that makes up the object and is measured in kilograms. The mass of an object remains the same no matter where the object is in the universe.

Gravitational field strength

The gravitational field strength ( g) of a planet is the weight per unit mass of an object on that planet. It has the units, newtons per kilogram, N kg^{-1}.

Examples

  • Earth g = 9.8\, N kg^{-1}
  • Mars g = 3.7\, N kg^{-1}
  • Moon g = 1.6\, N kg^{-1}

Calculating weight

The weight of an object can be calculated on different planets so long as we know that object's mass and the gravitational field strength of the planet. We can calculate weight using the following formula.

W = mg

Where W = weight and is measured in Newtons (N)

m = mass and is measured in kilograms kg

g = gravitational field strength and is measured in newtons per kilogram (N kg^{-1})

Question

An astronaut of mass 75kg travels to the moon. Calculate the weight of the astronaut on the moon if the gravitational field strength of the moon is 1.6 N kg^{-1}

To calculate the astronaut’s weight on the moon you need to take the following steps:

Weight = mass \times gravitational\,field\,strength

= 75 \times 1.6

= 120\,Newtons\,(120N)