Gravity and weight

All objects with mass have a gravitational field around them. A gravitational field is where a mass experiences a force.

All matter has a gravitational field that attracts other objects. The more mass an object has, the greater its gravitational field will be. For example, the Earth has a greater gravitational field than the Moon because it has a much greater mass than the Moon. The Moon is attracted to the Earth because it is within the Earth’s gravitational field.

Gravitational fields

The formula that links mass and gravitational field strength is:

gravity force = mass × gravitational field strength (g)

This is when:

  • gravity force is measured in newtons (N)
  • mass is measured in kilograms (kg)
  • gravitational field strength (g) is measured in newtons per kilogram (N/kg)
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The Earth’s gravitational field strength (g) is 10 N/kg. This means that for each kg of mass, an object will experience 10 N of force.

What is weight?

Weight refers to the gravity force of planets and other bodies in the Universe, and the effect that this has on objects. It is important to remember that weight is not the same as mass - the weight of an object and its mass are directly proportional. This means that for a given gravitational field strength, the greater the mass of the object, the greater its weight.

Weight is a non-contact force because gravity exerts its force through a field. An object does not need to be touching the Earth to have a weight. The weight of an object can be measured using a calibrated spring-balance, often called a Newton meter. Weight is also referred to as ‘gravity force’.

gravity force = mass × gravitational field strength (g)

This is when:

  • gravity force (weight) is measured in newtons (N)
  • mass is measured in kilograms (kg)
  • gravitational field strength (g) is measured in newtons per kilogram (N/kg)

The equation can be rearranged to make mass the subject:

mass = \frac{gravity~force}{gravitational~field~strength}

Example

Calculate the gravity force (weight) of a skydiver with a mass 70 kg falling towards the Earth?

(Remember that gravitational field strength = 10 N/kg on Earth).

weight = mass × gravitational field strength

weight = 70 × 10

weight = 700 N

Question

A team of astrophysicists sends a probe to Jupiter. The gravitational field strength of Jupiter is 27 N/kg, and the probe is 1200 kg. Calculate the gravity force (weight) of the probe on Jupiter.

weight = mass × gravitational field strength

weight = 1,200 × 27

weight = 32,400 N (or 32.4 kN)

Acceleration due to gravity

The constant g can also be referred to as the acceleration due to gravity. An object falling towards the surface of a large body would have this acceleration. It is the largest acceleration that the falling object would experience in free fall.

resultant force = mass × acceleration due to gravity

This is when:

  • resultant force is measured in newtons (N)
  • mass is measured in kilograms (kg)
  • acceleration due to gravity is measured in (m/s2)
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Acceleration due to gravity is 9.81 m/s2 on Earth but it is acceptable to use 10 m/s2 for calculations.