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A-Level Physics · guided topic map

Gravitation for Cambridge International AS & A Level Physics

Gravitation for A-Level Physics, organized into 1 syllabus topic and 3 mapped concept guides.

Syllabus topics
1
Mapped concept guides
3
Educational level
Cambridge International AS & A Level

Syllabus to lesson

Choose the exact concept

Work in order or jump to the concept named in your specification, course outline, or assignment.

13

Gravitational fields

A Level extension

3 guides
  1. 01Gravitational fields and the inverse-square lawMapped lesson
  2. 02Circular orbits and centripetal accelerationMapped lesson
  3. 03Gravitational potential and potential energyMapped lesson

Diagrams

Gravitation as A-Level Physics draws it

The figures from the A-Level Physics practice papers that sit on these syllabus points — the apparatus, circuits and graphs an exam question actually puts in front of you.

01Fig. 7.1Motion in a circle · Gravitational fieldsA Level
A satellite in a circular orbit of radius r about the centre of the EarthEarthrsatellitenot to scale

Figure comment

Fig. 7.1The Earth is drawn as a circle, labelled, with a dot marking its centre. A second, larger circle drawn concentric with it is the satellite's circular orbit. The satellite itself is a small block sitting on that larger circle, above and to the right of the Earth, and a dashed straight line runs from the dot at the centre of the Earth out to the satellite, labelled r. The figure is marked not to scale.

Read the comment once, then trace every arrow, label, axis or component in the drawing before opening the questions.

12 Motion in a circle13 Gravitational fieldsOpen A Level question · A Level extension Q7
Guided questions 5 parts

Reading cue. The dashed line labelled r runs from the dot at the Earth's centre to the satellite, so it is the orbit radius, not the height above the surface, and it is not to scale.

  1. aState State what provides the centripetal force on the satellite in Fig. 7.1, and state its direction on the figure.

    recall2 marks

    Check answer 2 marks
    1. the gravitational attraction of the Earth on the satellite
    2. directed along the dashed line towards the dot at the centre of the Earth

  2. bCalculate The orbit radius r is 4.2 × 10⁷ m and the radius of the Earth is 6.4 × 10⁶ m. Calculate the height of the satellite above the Earth's surface.

    routine2 marks

    Check answer 2 marks
    1. height = r − radius of the Earth = 4.2 × 10⁷ − 6.4 × 10⁶
    2. = 3.6 × 10⁷ m

  3. cDetermine The satellite has a mass of 1.5 × 10³ kg, and for the Earth GM = 3.99 × 10¹⁴ m³ s⁻². Determine the gravitational field strength of the Earth at this orbit radius and the force the Earth exerts on the satellite.

    demanding3 marks

    Check answer 3 marks
    1. g = GM/r² = 3.99 × 10¹⁴ / (4.2 × 10⁷)²
    2. g = 0.23 N kg⁻¹
    3. F = mg = 1.5 × 10³ × 0.226 = 3.4 × 10² N

  4. dDeduce A second satellite is placed in a circular orbit of radius 2.1 × 10⁷ m about the same centre, with GM = 3.99 × 10¹⁴ m³ s⁻² as before. Deduce its period, and deduce whether it can remain above one point on the equator.

    top of the paper4 marks

    Check answer 4 marks
    1. GMm/r² = 4π²mr/T², so T = 2π√(r³/GM)
    2. T = 2π√((2.1 × 10⁷)³ / 3.99 × 10¹⁴) = 3.0 × 10⁴ s
    3. = 8.4 hours, so it circles the Earth almost three times each day
    4. its period is not 24 hours, so it cannot stay above a single point on the equator

Transfer challenge

A moon of Jupiter moves in a circular orbit of radius 4.22 × 10⁸ m with a period of 1.53 × 10⁵ s. Determine the mass of Jupiter.

Check answer 3 marks
  1. GMm/r² = 4π²mr/T²
  2. M = 4π²r³/(GT²)
  3. M = 4π² × (4.22 × 10⁸)³ / (6.67 × 10⁻¹¹ × (1.53 × 10⁵)²) = 1.9 × 10²⁷ kg