Gravitational Field Strength

This lesson covers: 

  1. Defining gravitational field strength (g) and its calculation.
  2. Understanding that g is a vector quantity pointing towards the mass center.
  3. Explaining the relationship between g and r in a radial field.
  4. Applying the equation to calculate g and estimate a planet's mass.
  5. Suggesting helpful diagrams.

Gravitational field strength (g)

Gravitational field strength, denoted as 'g', is the force per unit mass experienced by a small test mass placed at a specific point. The formula for calculating g is:


g = mF​


Where:

  • g = gravitational field strength (N kg-1)
  • F = gravitational force (N)
  • m = test mass (kg)


On Earth, g typically has a value of approximately 9.81 N kg-1, also referred to as the "acceleration due to gravity."

Gravitational field strength in a radial field

In radial gravitational fields, like those around spherical objects or point masses, g varies with the distance (r) from the mass. The equation is:


g = r2G M​


Where:

  • g = gravitational field strength (N kg-1)
  • G = gravitational constant (6.67 x 10-11 N m2 kg-2)
  • M = mass of object (kg)
  • r = distance from the object's centre of mass (m)


This formula shows that g decreases as the distance r from the mass centre increases, following an inverse square law.

Worked example - Calculating the gravitational field strength of Earth.

Calculate the gravitational field strength of Earth given that the mass of Earth is 5.97 x 1024 kg.

The radius of Earth is 6.37 x 106 m.


Step 1: Formula

g = r2G M​


Step 2: Substitution and correct evaluation

g = 6.37×1066.67×10−11×5.97×1024​ = 9.81 N kg−1

Worked example - Estimating the mass of Mars

Calculate the mass of mars given that the gravitational field strength at the surface is 3.7 N kg-1.

The radius of Mars is 3.4 x 106 m.


Step 1: Rearranged formula

M = Gg r2​


Step 2: Substitution and correct evaluation

M=6.67×10−113.7×(3.4×106)2​=6.41×1023 kg