• The gravitational field strength at a point describes how much gravitational force is experienced by a test mass at that point
• The strength of a gravitational field caused by a point mass can be derived using Newton’s Law of Universal Gravitation
  • For calculations involving gravitational forces, a spherical mass can be treated as a?point mass?at the centre of the sphere

   

• Newton’s Law of Universal Gravitation states that the magnitude of the attractive gravitational force?F?between two masses?M?and?m?with separation?r?is equal to:

• The gravitational field strength at a point is defined as the force?F?per unit mass?m

• Substituting the force?F?with the gravitational force?FG?leads to:

• Cancelling mass?m, the equation becomes:

• Where:
  • g?= gravitational field strength due to a point mass?M?(N kg–1)
  • G?=?Newton’s Gravitational Constant?(N m2?kg–2)
  • M?= mass of the body producing the gravitational field (kg)
  • r?= distance from the centre of mass?M? to a chosen point in the field (m)

   

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:

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: