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First teaching 2020

Last exams 2024

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Gravitational Field Strength (CIE A Level Physics)

Revision Note

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Katie M

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Katie M

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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
    • The gravitational field strength unit is N kg-1

Gravitational Field Strength Formula:

  • 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

What is the Gravitational Field Strength on Earth?

  • 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

The mean density of the moon is ⅗ times the mean density of the Earth. The gravitational field strength is ⅙ on the Moon than that on Earth.Determine the ratio of the Moon’s radius rM and the Earth’s radius rE.

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

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Katie M

Author: Katie M

Expertise: Physics

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.