A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Gravitational Force Between Point Masses — mark scheme explained
The short answer
Gravity is a fundamental force of nature that acts between all masses in the universe. It is an attractive force, meaning it always pulls objects together rather than pushing them apart. The strength of this gravitational force can be calculated using Newton's law of universal gravitation.
The question
Calculate the gravitational force between a planet with mass 6 × 10 24 kg and its moon with mass 7 × 10 22 kg, separated by 3.8 × 10 8 meters.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculations, marks are typically awarded for identifying the correct formula (1 mark), substituting the correct values (1-2 marks), and performing the calculation correctly (1-2 marks). For estimates, marks may be given for reasonable assumptions and the final value.
What the command words demand
- Calculate
- Perform a numerical calculation using the given data and formula.
- Estimate
- Provide an approximate value based on reasonable assumptions.
- Explain
- Give a detailed account of how or why something happens.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 3 minutes to solve a typical gravitational force calculation question. This includes reading the question, identifying the formula, substituting values, and performing the calculation.
- Identify the given values: m 1 = 6 × 10 24 kg, m 2 = 7 × 10 22 kg, r = 3.8 × 10 8 m.0 marks
- Use the gravitational force formula: F = G × (m 1 × m 2 ) / r 2 .1 mark
- Substitute the values into the formula: F = 6.674 × 10 -11 × (6 × 10 24 × 7 × 10 22 ) / (3.8 × 10 8 ) 2 .2 marks
- Calculate the numerator: 6 × 10 24 × 7 × 10 22 = 4.2 × 10 47 kg 2 .1 mark
- Calculate the denominator: (3.8 × 10 8 ) 2 = 1.444 × 10 17 m 2 .1 mark
- Divide the numerator by the denominator: 4.2 × 10 47 / 1.444 × 10 17 ≈ 2.91 × 10 30 .0 marks
- Multiply by G: F = 6.674 × 10 -11 × 2.91 × 10 30 ≈ 1.94 × 10 20 N.1 mark
Final answer: 1.94 × 10 20 N
Work through every step correctly and you earn all 6 marks.
Another worked example
Calculate the gravitational force between a satellite with mass 500 kg and Earth (mass 5.97 × 10 24 kg) at an altitude of 400 km.
- Identify the given values: m 1 = 5.97 × 10 24 kg, m 2 = 500 kg, r = radius of Earth + altitude = 6,371 km + 400 km = 6,771 km = 6.771 × 10 6 m.1 mark
- Use the gravitational force formula: F = G × (m 1 × m 2 ) / r 2 .1 mark
- Substitute the values into the formula: F = 6.674 × 10 -11 × (5.97 × 10 24 × 500) / (6.771 × 10 6 ) 2 .1 mark
- Calculate the numerator: 5.97 × 10 24 × 500 = 2.985 × 10 27 kg 2 .1 mark
- Calculate the denominator: (6.771 × 10 6 ) 2 ≈ 4.584 × 10 13 m 2 .1 mark
- Divide the numerator by the denominator: 2.985 × 10 27 / 4.584 × 10 13 ≈ 6.51 × 10 13 .0 marks
- Multiply by G: F = 6.674 × 10 -11 × 6.51 × 10 13 ≈ 4,350 N.1 mark
Final answer: 4,350 N
Work through every step correctly and you earn all 6 marks.
Common mistakes
Using the wrong value for G (gravitational constant).
Why it happens: Students may use an incorrect or approximate value for G, leading to significant errors in their calculations.
Fix: Always use the standard value of G = 6.674 × 10 -11 N·m 2 /kg 2 .
Forgetting to square the distance (r) in the denominator.
Why it happens: Students may forget that the distance between the masses must be squared, leading to incorrect results.
Fix: Ensure that you always square the distance (r 2 ) when using the gravitational force formula.
Using the wrong units for mass or distance.
Why it happens: Students may use incorrect units, such as grams instead of kilograms or centimeters instead of meters, leading to errors in their calculations.
Fix: Always convert masses to kilograms and distances to meters before using the formula.
Confusing gravitational force with other forces (e.g., electrostatic force).
Why it happens: Students may mix up the formulas for different types of forces, leading to incorrect calculations.
Fix: Ensure you are using the correct formula for gravitational force: F = G × (m 1 × m 2 ) / r 2 .
Not converting altitude to distance from the center of the Earth.
Why it happens: Students may use the altitude directly instead of adding it to the radius of the Earth, leading to incorrect results.
Fix: Always add the altitude to the radius of the Earth to get the correct distance (r) between the masses.
Rounding too early in calculations.
Why it happens: Students may round intermediate results, leading to significant errors in their final answer.
Fix: Perform all calculations with full precision and only round the final answer to the required number of significant figures.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Gravitational Force | Use Newton's law of gravitation to find the force between a planet and its moon. | 6 |
| Calculate Gravitational Force | Find the gravitational attraction between a satellite and Earth using Newton's law of gravitation. | 6 |
| Calculate Gravitational Force | Use Newton's law of gravitation to find the force between two masses at a given separation | 5 |
| Calculate Gravitational Force | Use Newton's law of gravitation to find the force between two masses separated by a distance. | 5 |
| Total across these question types | 22 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.