# 7.1.2 Gravitational Field Strength

### Gravitational Force

• There is a universal force of attraction between all matter with mass
• This force is known as the ‘force due to gravity’ or the weight
• The Earth’s gravitational field is responsible for the weight of all objects on Earth
• A gravitational field is defined as:

A region of space where a mass experiences a force due to the gravitational attraction of another mass

• The direction of the gravitational field is always towards the centre of the mass
• Gravitational forces cannot be repulsive
• Gravity has an infinite range, meaning it affects all objects in the universe
• There is a greater gravitational force around objects with a large mass (such as planets)
• There is a smaller gravitational force around objects with a small mass (almost negligible for atoms) The Earth’s gravitational field produces an attractive force

### Gravitational Field Strength

• The strength of this gravitational field g at a point is the force F per unit mass m of an object at that point: • Where:
• g = gravitational field strength (N kg-1)
• F = force due to gravity, or weight (N)
• m = mass (kg)

• This equation shows that:
• The larger the mass of an object, the greater its pull on another object
• On planets with a large value of g, the gravitational force per unit mass is greater than on planets with a smaller value of g
• An object’s mass remains the same at all points in space
• However, on planets such as Jupiter, the weight of an object will be a lot greater than on a less massive planet, such as Earth
• This means the gravitational force would be so high that humans, for example, would not be unable to fully stand up
• Factors that affect the gravitational field strength at the surface of a planet are:
• The radius (or diameter) of the planet
• The mass (or density) of the planet

#### Worked Example

Calculate the mass of an object with weight 10 N on Earth. #### Exam Tip

There is a big difference between g and G (sometimes referred to as ‘little g’ and ‘big G’ respectively), g is the gravitational field strength and G is Newton’s gravitational constant. Make sure not to use these interchangeably!

Remember the equation density ρ = mass m ÷ volume V, which may come in handy with some calculations

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