The gravitational field and weight

From the gravitational field to weight

A celestial body of mass M and radius R creates a gravitational field around itself. At the surface of this celestial body, the intensity of this field, denoted by g, is given by: g = G * M / R^2

This field g is expressed in N/kg (or, equivalently, in m/s²). The weight P of an object of mass m placed in this field is therefore: P = m * g

Weight is a force directed towards the centre of the celestial body; whilst the mass m is an intrinsic property of the object that never changes.

Weight depending on the celestial body

Celestial body	g (N/kg)	Weight of a 70 kg mass
Earth	9.8	686 N
Moon	1.6	112 N
Mars	3.7	259 N
Jupiter	24.8	1736 N

g also varies with altitude

The further away you are from the centre of the celestial body (using R + altitude instead of R), the lower g becomes, as g is inversely proportional to the square of the distance from the centre. This is why g is slightly weaker at the top of a mountain than at sea level, and much weaker in orbit.

Common pitfalls

• Mass and weight are not synonymous: mass (in kg) is constant throughout the universe, whilst weight (in N) depends on location.
• In everyday language, we say ‘weigh 70 kg’, which is a misnomer: we should say ‘have a mass of 70 kg’.
• Remember to use R + altitude (and not just R) when the object is not exactly on the surface of the celestial body.