CIE A Level Physics (9702) 2019-2021

Revision Notes

15.1.4 Gravitational Field Strength

Deriving Gravitational Field Strength (g)

  • The gravitational field strength at a point describes how strong or weak a gravitational field is at that point
  • The gravitational field strength due to a point mass can be derived from combining the equations for Newton’s law of gravitation and gravitational field strength
    • 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 gravitation states that the attractive force F between two masses M and m with separation r is equal to:

Deriving Gravitational Field Strength (g) equation 1

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

Deriving Gravitational Field Strength (g) equation 2

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

Deriving Gravitational Field Strength (g) equation 3

  • Cancelling mass m, the equation becomes:

Deriving Gravitational Field Strength (g) equation 4

  • Where:
    • g = gravitational field strength (N kg-1)
    • G = Newton’s Gravitational Constant
    • M = mass of the body producing the gravitational field (kg)
    • r = distance from the mass where you are calculating the field strength (m)

Calculating g

  • Gravitational field strength, g, is a vector quantity
  • The direction of g is always towards the centre of the body creating the gravitational field
    • This is the same direction as the gravitational field lines
  • On the Earth’s surface, g has a constant value of 9.81 N kg-1
  • However outside the Earth’s surface, g is not constant
    • g decreases as r increases by a factor of 1/r2
    • This is an inverse square law relationship with distance
  • When g is plotted against the distance from the centre of a planet, r has two parts:
    • When r < R, the radius of the planet, g is directly proportional to r
    • When r > R, g is inversely proportional to r2 (this is an ‘L’ shaped curve and shows that g decreases rapidly with increasing distance r)

g v R graph on Earth (1), downloadable AS & A Level Physics revision notes

g v R graph on Earth (2), downloadable AS & A Level Physics revision notes

Graph showing how gravitational field strength varies at greater distance from the Earth’s surface

  • Sometimes, g is referred to as the ‘acceleration due to gravity’ with units of m s-2
  • Any object that falls freely in a uniform gravitational field on Earth has an acceleration of 9.81 m s-2

Worked example: Gravitational field strength
Calculating_g_Worked_example_-_Gravitational_Field_Strength_Question, downloadable AS & A Level Physics revision notes

Step 1:            Write down the known quantities

Calculating g Worked Example equation 1

Calculating g Worked Example equation 2

gM = gravitational field strength on the Moon, ρM = mean density of the Moon

gE = gravitational field strength on the Earth, ρE = mean density of the Earth

Step 2:            The volumes of the Earth and Moon are equal to the volume of a sphere

Calculating g Worked Example equation 3

Step 3:            Write the density equation and rearrange for mass M

Calculating g Worked Example equation 4

M = ρV

Step 4:            Write the gravitational field strength equation

Deriving Gravitational Field Strength (g) equation 4

Step 5:            Substitute M in terms of ρ and V

Calculating g Worked Example equation 5a

Step 6:            Substitute the volume of a sphere equation for V, and simplify

Calculating g Worked Example equation 6a

Step 7:            Find the ratio of the gravitational field strengths

Calculating g Worked Example equation 7a

Step 8:            Rearrange and calculate the ratio of the Moon’s radius rM and the Earth’s radius rE

Calculating g Worked Example equation 8a

Calculating g Worked Example equation 9a

Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
Close

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now
Go to Top