Gravitational Field due to a Point Mass (Edexcel International A Level Physics)

The Earth's gravitational field strength at its surface is 9.81 N kg^–1. 

Calculate the Earth's gravitational field strength 1 million km away from its surface. 

Use the following data:

• Mass of Earth = 6.0 × 10²⁴ kg

• Radius of Earth = 6400 km

Answer:

Step 1: Write the known quantities

• Mass of Earth = 6.0 × 10²⁴ kg

• Radius of Earth = 6400 km = 6400 × 10³ m

• Newton's Universal Gravitation Constant G = 6.67 × 10^-11 N m² kg^–2 

• Distance from the Earth's surface = 1 million km = (1 × 10⁶) × 10³ m = 1 × 10⁹ m

Step 2: Write the equation for gravitational field strength

• The gravitational field strength g at some distance r due to a mass M is given by the equation:

g = 

Step 3: Determine the distance r from the centre of mass M

• The Earth is causing the gravitational field in the question

• 1 million km from the Earth's surface means the distance from Earth's centre of mass r = (6400 × 10³) + (1 × 10⁹) = 1.0064 × 10⁹ m

Step 4: Substitute values and calculate the gravitational field strength

• Therefore, the gravitational field strength is given by:

g = = 4.0 × 10^–4 N kg^–1

When using the equation for gravitational field strength, remember that the mass M is the mass causing the gravitational field. The mass m is the object that experiences the gravitational field of M : hence, you may see m referred to as a 'test mass'. 

It should make sense, therefore, that g is defined as the 'force experienced per unit mass' in a gravitational field. The force experienced is by the 'test mass', in the field, m.