AQA A Level Physics

Topic Questions

7.2 Gravitational Potential

1a2 marks

State the definition for the gravitational potential at a point.

1b2 marks

Explain why gravitational potential is always negative.

1c3 marks

A satellite orbiting the moon, M, is moved from orbit A to orbit B, as shown in Figure 1.  

Figure 1

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The gravitational potential due to the moon of each of these orbits is: 

      Orbit A: –2.10 MJ kg–1

      Orbit B:  –1.65 MJ kg–1  

Calculate the gravitational potential difference as the satellite moves from orbit A to orbit B.

1d2 marks

The satellite has a mass of 950 kg. 

Calculate the work done in moving the satellite from orbit A to orbit B.

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2a4 marks

The gravitational potential at a particular point is given by the equation: 

         V = –fraction numerator G M over denominator r end fraction 

Explain what each symbol in the equation represents.

2b1 mark

Explain what is meant by a gravitational equipotential line.

2c4 marks
(i)
On Figure 1 below, draw 4 equipotential lines for equal changes in potential around the Earth.

Figure 1

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(ii)
On Figure 2 below, draw 4 equipotential lines for equal changes in potential above the Earth’s surface.

Figure 2

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2d1 mark

State the work done when moving an object along an equipotential line or surface.

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3a2 marks

Figure 1 shows how the gravitational potential varies with distance in the region above the surface of Pluto. Pluto has a radius of 1.2 ×  106 m. 

Figure 1

7-2-s-q--q3a-easy-aqa-a-level-physics

Use Figure 1 to determine the gravitational potential on the surface of Pluto.

3b3 marks

Use the information in part (a) to calculate the mass of Pluto.

3c6 marks

2.6 × 108 J of work is required to launch a satellite of mass 1 000 kg from the surface of Pluto into an orbit around the planet. 

Calculate: 

(i)         The gravitational potential difference of the satellite when it reaches its orbit. 

(ii)        The gravitational potential of the satellite in an orbit.

3d2 marks

Use Figure 1 to determine the distance from the centre of Pluto to the orbit of the satellite.

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4a2 marks

State whether gravitational potential is a scalar or vector quantity. 

Give a reason for your answer.

4b3 marks

The Earth has a radius of 6.37 × 106 m and a mass of 5.97 × 1024 kg. 

Calculate the gravitational potential on the Earth’s surface. 

State an appropriate unit for your answer.

4c1 mark

A satellite moves from a point where the gravitational potential due to the moon is –30 MJ kg–1 to another point where the gravitational potential due to the moon is –50 MJ kg–1. 

State whether the satellite has moved closer to or further from the moon.

4d4 marks

The satellite has a mass of 120 kg. 

When the satellite is moves from a gravitational potential of –30 MJ kg–1 to another point where the gravitational potential is –50 MJ kg–1 calculate: 

            (i)         the gravitational potential difference 

            (ii)        the change in gravitational potential energy of the satellite.

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5a2 marks

Calculate the gravitational potential at a point 4.23 × 107 m from the centre of the Earth.

5b2 marks

The gravitational potential on the surface of the Earth is –6.25 × 107 J kg–1

Calculate the gravitational potential difference between the surface of the earth and a point 4.23 × 107 m from the centre of the Earth.

5c2 marks

Calculate the work done in taking a 5.0 kg mass from the surface of the Earth to a point 4.23 × 107 m from the centre of the Earth.

5d5 marks
(i)
State the magnitude of the gravitational potential at a point where the Earth’s gravitational effect is negligible
(ii)
Calculate the gravitational potential difference between the Earth’s surface and point where the Earth’s gravitational effect is negligible
(iii)
Calculate the work done in taking the 5.0 kg mass from the surface of the Earth to a point where the Earth’s gravitational effect is negligible.

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1a3 marks

The International Space Station (ISS) orbits the Earth at a height of 400 km above the Earth’s surface. The Soyuz spacecraft is used to transport astronauts to the ISS. At lift-off, the spacecraft, with all its contents and fuel, has a mass of 308 000 kg .

Calculate the work done in taking the Soyuz spacecraft from the Earth’s surface to the ISS. 

Assume that the mass of the Soyuz spacecraft remains constant.

1b2 marks

In reality it takes less work than your answer to part (a) to get the Soyuz rocket from the surface of the Earth to the ISS. 

Discuss a possible reason for the difference in values of work done.

1c2 marks

Calculate the work done in taking the Soyuz spacecraft from the Earth’s surface to a point where the Earth’s gravitational effect is negligible.

1d2 marks

Explain why there is no work done by the ISS when it maintains a constant orbit around the Earth.

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2a4 marks

A space shuttle of mass 2 × 106 kg is travelling from the Earth to the moon.  It accelerates uniformly from launch at 5.25 m s–2.It has enough propellant to provide thrust for the first 124 seconds. 

Calculate the work done by the rocket during the first 124 seconds after launch. Assume the mass of the space shuttle does not change during launch.

2b2 marks

The Moon has a diameter approximately 27% that of the Earth, and a mass of 1.2% that of the Earth. 

Calculate the gravitational potential at the surface of the moon in terms of the gravitational potential on the surface of the Earth.

2c3 marks

Figure 1 below shows the gravitational field strength lines between the Earth and the moon.  Point P is the neutral point between the Earth and the moon where there is no resultant gravitational field.

Figure 1

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On Figure 1 sketch the equipotential lines between the Earth and the moon.  

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3a2 marks

The graph in Figure 1 shows how the amount of work done on a spacecraft relates to the gravitational potential above the Moon’s surface during a launch from the surface of the Moon.   

Figure 1

7-2-s-q--q3a-hard-aqa-a-level-physics

Use Figure 1 to calculate the mass of the spacecraft.

3b4 marks

Using the graph in Figure 1, calculate the work done on the spacecraft to raise it to a point where the gravitational potential is half of the value at the surface of the Moon. 

3c2 marks

Calculate the height of the spacecraft above the surface of the Moon when it is raised it to a point where the gravitational potential is half of the value at the surface of the Moon, as in part (b). 

   The Moon has a mass of 7.37 × 1022 kg

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4a2 marks

A binary planet system consists of two stars, A and B, as shown in Figure 1A has a mass of mass 4.0 × 1030 kg and B has a mass of 8.0 × 1030 kg.  The centre of the stars is separated by a distance of 2 × 1011 m.

Figure 1

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Calculate the gravitational potential at the midpoint between the stars.

4b4 marks

The amount of energy required to send a space probe of mass 1800 kg from the surface of star A to the midpoint between stars A and B is 4.2 × 1011 J.

Calculate the gravitational field strength on the surface of star A.

4c4 marks

Star A is drifting away from star B

Calculate how far star A will have drifted if its gravitational potential energy decreases by 10% of its initial value.

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5a2 marks

Mars is 1.885 times smaller than the Earth. Table 1 shows how the gravitational potential varies for three points above the surface of Mars.

                           Table 1 

Distance from centre of Mars
/ × 106 m

Gravitational potential
/ × 106 J kg–1

3.38

–12.5

6.08

–6.96

11.6

–3.65

 

Use the data to determine the gravitational field strength on the surface of Mars.

5b4 marks

The Mars Global Surveyor is a robotic space probe with a mass of 1030 kg.  In 1996 it took 1.29 × 109 J of energy to launch the probe from the surface of Mars into an orbit where it maintains a constant height above the surface. 

Calculate the height of the Mars Global Surveyor above the surface of Mars 

5c2 marks

The Mars Global Surveyor has a fuel reserve of 1.5 × 106J to allow it to be moved to different orbital heights.

Determine whether this fuel reserve would be sufficient for the Mars Global Surveyor to escape its orbit calculated in (b) to a point where it is no longer influenced by the gravitational attraction of Mars.

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1a2 marks

Calculate the gravitational potential of a satellite at a point 2500 km above the Earth’s surface.

1b2 marks

What is the effect, if any, on the values of the gravitational potential energy, E subscript p and the gravitational potential, V, if a body of mass m placed in a gravitational field is halved?

1c2 marks

Figure 1 shows two of the orbits, P and D of two of Mars’ moons, Phobos and Deimos respectively that are in circular orbit above Mars, M. 

Figure 1

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The gravitational potential due to Mars of each of these orbits is: 

      Orbit P: –7.19 MJ kg–1

      Orbit D:  –2.13 MJ kg–1 

The mass of Mars is 0.107 times the mass of Earth. 

Calculate the radius, from the centre of Mars, of orbit P.

1d3 marks

Calculate difference in distance between orbits P and D.

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2a3 marks

Figure 1 shows the gravitational equipotential lines around a planet. The gravitational potential at point A is –40 MJ kg–1. 

Figure 1

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Determine which of the following potentials equate to points B, C and D. 

            (i)         –20 MJ kg–1

            (ii)        –40 MJ kg–1

            (iii)       –50 MJ kg–1

2b4 marks

A 400 kg probe is sent to the asteroid Ceres to collect rock samples before returning to Earth. Ceres has a gravitational field strength, g on its surface is –0.27 N kg–1. 

The gravitational potential, V, at the surface of the asteroid is –1.33 × 105 J kg–1. 

Calculate the gravitational potential 35 km above the surface of the asteroid.

2c2 marks

The radius of the asteroid is 470 km. 

Calculate the mass of the asteroid Ceres.

2d3 marks

Calculate the work done by the probe as it travels from the surface to a point 2000 m above the surface.

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3a3 marks

The graph in Figure 1 shows how the gravitational potential varies with distance in the region above the surface of the Earth. R is the radius of the Earth. At the surface of the Earth, the gravitational potential is −63 MJ kg–1. 

Figure 1

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Explain what is meant by the gravitational potential and why the values on Figure 1 are negative.

3b3 marks

Use Figure 1 to determine the increase in gravitational potential between a distance 2R and 3R from the centre of the Earth.

3c3 marks

Using Figure 1, calculate the decrease in potential energy of a 1500 kg satellite has it is brought to the surface of the Earth from a circular orbit of 3R.

3d3 marks

By use of Figure 1, calculate the gravitational field strength at distance 2R from the centre of the Earth.

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4a4 marks

The gravitational field associated with a planet is radial, as shown in Figure 1, but near the surface it is effectively uniform, as shown in Figure 2. 

Figure 1

7-2-s-q--q4a-medium-aqa-a-level-physics

Figure 2

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Sketch a graph to show how the gravitational potential, V, associated with the planet varies with distance r for: 

(i)         Figure 1 

(ii)        Figure 2

4b2 marks

Explain how the graphs in part (a) would change for a planet with the same radius, but larger mass.

4c3 marks

Titan is the largest moon of Saturn. 

Using the following data to calculate the gravitational potential at the surface of Saturn. 

   Mass of Titan = 2.38 × 10–4 × mass of Saturn

   Radius of Titan = 0.0455 × radius of Saturn

   Gravitational potential at surface of Titan = –3.50 MJ kg–1

4d3 marks

Sketch a graph on Figure 3 to indicate how the gravitational potential varies with distance along a line outwards from the surface of the Earth to the surface of the Moon. 

Label any values on the axes. 

Figure 3

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5a2 marks

Table 1 shows how the gravitational potential varies for three points about the centre of Earth. 

Table 1

Distance from centre of Earth / 106 m

Gravitational potential / 107 J kg–1

7.5

–5.2

50

–0.8

200

­–0.2

 

Show that the data suggest that the potential is inversely proportional to the distance from the centre of the Earth.

5b3 marks

Figure 1 shows two points, P and Q, at distances r and 2r from the centre of Earth. 

Figure 1

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The gravitational potential at P is −36 kJ kg−1. 

Show that the work done on a 12 kg mass when it is taken from P to Q is 216 kJ.

5c2 marks

Mercury has a diameter approximately 0.38 that of a planet Y, and a mass 0.06 that of planet Y. The gravitational potential at the surface of planet Y is −50 MJ kg–1. 

Calculate the approximate value of the gravitational potential at the surface of Mercury. .

5d2 marks

Which planet, Mercury or planet Y requires more work to be done to move a satellite of mass 200 kg from its surface to a distance point? Explain your answer.

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