Gravitational Field Strength (DP IB Physics: HL): Revision Note

Gravitational Field Strength

• 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 test mass experiences a force due to the gravitational attraction of another mass

• The direction of the gravitational field always acts toward the centre of the mass which produces the field

  • This is because gravitational forces are always attractive

• 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. The force of gravity is always attractive

• The gravitational field strength at a point is defined as:

The force per unit mass experienced by a test mass at that point

• This can be written in equation form as:

$g=\frac{F}{m}$

• Where:

  • g = gravitational field strength (N kg⁻¹)

  • F = force due to gravity, or weight (N)

  • m = mass of test mass in the field (kg)

• This equation shows that:

  • 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 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 able to fully stand up

A person’s weight on Jupiter would be so large that a human would be unable to fully stand up

• Factors that affect the gravitational field strength at the surface of a planet are:

  • the radius r (or diameter) of the planet

  • the mass M (or density) of the planet

• This can be shown by equating the equation F = mg with Newton's law of gravitation:

$F=\frac{GMm}{r^2}$

• Substituting the force F with the gravitational force mg leads to:

$mg=\frac{GMm}{r^2}$

• Cancelling the mass of the test mass m leads to the equation:

$g=\frac{GM}{r^2}$

• Where:

  • G = Newton's Gravitational Constant

  • M = mass of the body causing the field (kg)

  • r = distance from the mass where you are calculating the field strength (m)

• This equation shows that: 

  • The gravitational field strength g depends only on the mass of the body M which produces the field

• Hence, objects with any mass m in that field will experience the same gravitational field strength

  • The gravitational field strength g is inversely proportional to the square of the radial distance, r²