AQA A Level Physics

Topic Questions

7.3 Orbits of Planets & Satellites

1a4 marks

Figure 1 shows a satellite orbiting the Earth in a clockwise direction.  

Figure 1

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Draw an arrow on Figure 1 to show: 

(i)
The centripetal force acting on the satellite when it is in orbit.  Label this arrow F.
(ii)
The linear velocity of the satellite.  Label this arrow v. 
1b4 marks

The equation used to calculate the centripetal force is: 

         F =fraction numerator m v squared over denominator r end fraction

Explain what each symbol in the equation represents.

1c1 mark

State the name of the force which provides the centripetal force required to keep the satellite orbiting in a circular path. 

1d2 marks

The orbital radius of the satellite can be calculated using the equation: 

         r =begin mathsize 16px style fraction numerator G M over denominator v squared end fraction end style

(i)
State how the radius of the orbit would change if the linear speed of the satellite was doubled 
(ii)
Explain your answer to part (i).

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2a4 marks

The equation from Kepler’s third law is given below: 

      T2 = fraction numerator 4 straight pi squared straight r cubed over denominator G M end fraction

Explain what each symbol in the equation represents.

2b1 mark

State the time period for any geostationary satellite orbiting the Earth.

2c3 marks

Use the following data to show that the orbital radius of a geostationary satellite is 4.22 × 107 m: 

   Gravitational constant, G = 6.67 × 10–11 N m2 kg–2

   Mass of the Earth, ME = 5.97 × 1024 kg

2d2 marks

Hence, calculate the height of a geostationary satellite above the Earth’s surface.

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3a2 marks

Describe two features of a geostationary satellite.

3b2 marks

A geostationary satellite orbits the Earth with an orbital radius, ro, of 4.22 × 107 m, as shown in Figure 1. 

Figure 1

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Calculate the distance the satellite travels during 1 complete orbit.

3c3 marks
(i)
State the orbital period of the geostationary satellite
(ii)
Using your answer to part (b), calculate the orbital speed of the geostationary satellite.    
3d4 marks

The satellite has a mass of 1 200 kg.  When it is travelling in a geostationary orbit the total energy of the satellite is 6.93 × 1010 J. 

When the satellite is travelling in a geostationary orbit, calculate its: 

            (i)         Kinetic energy 

            (ii)        Gravitational potential energy.

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4a3 marks

Give the definition of escape velocity.

4b2 marks

The equation to calculate the escape velocity from a planet is given below: 

      v = begin mathsize 16px style square root of fraction numerator 2 G M over denominator r end fraction end root end style

Calculate the escape velocity at the surface of the Earth.

4c1 mark

State the orbital period of the Earth around the Sun. 

4d3 marks

When comparing the orbital period, T, and the orbital radius, r, of Earth and Mars around the Sun, Kepler’s third law can be written as: 

          begin mathsize 16px style open parentheses T subscript E close parentheses squared over open parentheses r subscript E close parentheses cubed equals open parentheses T subscript M close parentheses squared over open parentheses r subscript m close parentheses cubed end style

Where T subscript E  and  T subscript M are the orbital periods of Earth and Mars respectively and r subscript E and r subscript M are the orbital radii of Earth and Mars respectively.

Use the following data to calculate the orbital radius of Mars, r subscript M

            Orbital radius of the Earth r subscript E= 15 × 1010 m

            Period of orbit of Mars  T subscript M= 1.9 Earth years

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5a3 marks

State Kepler’s Third Law in words.

5b2 marks

High quality photographs of the Earth’s surface can be obtained from low orbit satellites, as shown in Figure 1. 

Figure 1

7-3-s-q--q5b-easy-aqa-a-level-physics

State two additional applications of low orbit satellites.

5c2 marks

The satellite in Figure 1 has an orbital radius of 320 km. 

Use the equation:

      T2 =fraction numerator 4 straight pi squared straight r cubed over denominator G M end fraction 

To calculate the orbital period of the satellite.

5d3 marks

Impulse engines are used to move the satellite between orbit X and orbit Y, as shown in Figure 2.   

Figure 2

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State whether the following quantities increase or decrease when the satellite is in orbit Y: 

            (i)         Gravitational potential energy 

            (ii)        Orbital speed 

            (iii)       Orbital period.

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1a2 marks

The orbits of the Earth and Jupiter are very nearly circular, with radii of 150 × 109 m and 778 × 109 m respectively. It takes Jupiter 11.8 years to complete a full orbit of the Sun.

Show that the values in this question are consistent with Kepler’s third law.

1b5 marks

Data from the orbits of different planets around our Sun is plotted in a graph of log (T2) against  log (R3) as shown in Figure 1, where T is the orbital period and R is the radius of the planets orbit.

Figure 1

7-3-s-q--q1b-hard-aqa-a-level-physics

Calculate the percentage error for the mass of the Sun obtained from the graph in Figure 1.

1c3 marks

The Sun is about 8 kpc (kilo-parsecs) from the centre of the Milky Way Galaxy and moves at about 230 km/s.  Calculate the orbital period of the Sun around the centre of the Milky Way Galaxy.

      1 kpc = 3260 light years

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2a2 marks

Pluto is a dwarf planet with a radius of 1.19 × 106 m.  It orbits the Sun in an orbital radius which is 25.9 times greater than that of Mars.

Calculate how many times Mars will completely orbit the Sun in the time it takes Pluto to complete one full orbit of the Sun.

2b2 marks

A small mass is released from rest and takes 5.69 s to fall 10 m onto the surface of Pluto. 

Assuming that there is no atmosphere above the surface of Pluto that could provide any resistance to motion, calculate the mass of Pluto.

   The radius of Pluto is 1.19 × 106 m.  

2c4 marks

A meteorite hits Pluto and ejects a lump of ice from the surface that travels vertically at an initial speed of 1600 m s–1.

Determine whether this lump of ice can escape from Pluto.

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3a2 marks

A satellite X of mass m is in a concentric circular orbit around a planet of mass M, as shown in Figure 1.The radius of the orbit is 4R, where R is the radius of the planet. 

Figure 1

7-3-s-q--q3a-hard-aqa-a-level-physics

Show that the kinetic energy of X, can be expressed as:

      KE =begin mathsize 16px style fraction numerator G M m over denominator 8 R end fraction end style

3b2 marks

The orbital radius of satellite X is reduced to a distance r from the centre of the planet.

Show that the gravitational potential difference between the surface of the planet and a point on satellite X’s new orbit can be expressed as:

         V = GMopen parentheses fraction numerator r minus R over denominator R r end fraction close parentheses

3c4 marks

A satellite in the closest orbit to the Earth has a period of 90 minutes.

Calculate the kinetic energy of a 1000 kg satellite in the closest orbit to Earth.

3d2 marks

Unused satellites are often referred to as ‘space junk’. 

1000 kg of the explosive TNT yields approximately 4.1 × 109 J. 

Suggest why ‘space junk’ poses a significant problem to future space missions.

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4a2 marks

A space mission is being planned to launch a spacecraft from Earth to land a robotic probe on a comet which is in deep space where the gravitational field strength is negligible. The total mass of the spacecraft is 3000 kg.

Calculate the change in the gravitational potential energy of the spacecraft to move it from the surface of the Earth to the comet.

4b4 marks

The comet has a mass of 1.7 × 1013 kg.  It is planned that the robotic probe, of mass 145 kg will separate from the spacecraft and land on the comet at a distance of 1.8 km from the comets centre of mass.  The robotic probe will drill a hole into the surface of the comet to anchor itself. The drill will exert a force of 32 N for 5 s.

Determine whether the drilling process would cause the probe to escape from the surface of the comet.

4c6 marks

On another mission a spacecraft of mass 1050 kg is being returned to the Earth from the moon. 

Use the information below to calculate the speed at which the spacecraft must be launched from the surface of the moon if it is to reach the surface of the Earth.

   Mass of the moon,  m subscript m = 7.35 × 1022 kg

   Radius of the moon,  r subscript m = 1.74 × 106 m

   Separation distance between Earth and moon,  r subscript E M end subscript = 3.85 × 108 m

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5a6 marks

A satellite of mass 150 kg moves from an orbital radius of 6500 km to an orbital radius of 5 500 km above the surface of the Earth.

Calculate the change of energy of the satellite as it moves between the two orbits and state whether the total amount of energy has increased or decreased as the satellite moves between the orbits.

5b2 marks

The escape velocity, v subscript 1 , from a  planet of mass M is 0.5 × 104 m s-1

The escape velocity, v subscript 2 , from a  planet of mass 4M is 1.5 × 104 m s-1.

Calculate the ratio of the radii of the planets, r subscript 2 over r subscript 1.

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1a2 marks

Explain why it is preferable to have a satellite in a geostationary orbit for TV and telephone signals.

1b4 marks

Calculate the radius of a geostationary orbit.

1c3 marks

Calculate the increase in potential energy of a satellite of mass 830 kg when it is raised from the Earth’s surface into a geostationary orbit.

1d3 marks

Using the centripetal acceleration, calculate the speed of the satellite when it is in a geostationary orbit.

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2a4 marks

Kepler’s Third Law defines the relationship between the period, T and the radius, r of an orbit as:

            T squared ∝ r cubed 

Derive the full equation for Kepler’s Third Law. State one assumption made.

2b3 marks

The Earth’s orbit is of mean radius 1.50 × 1011 m and the Earth’s year is 365 days long. The mean radius of the orbit of Mars is 2.32 × 1011 m. 

Calculate the length of one Mars year in days.

2c3 marks

Jupiter orbits the Sun once every 12 Earth years. 

Calculate the ratiofraction numerator distance space from space Sun space to space Jupiter over denominator distance space from space Sun space to space Earth end fraction

2d2 marks

Jupiter has the shortest day compared to any other planet in our solar system at 10 hours. 

Calculate the angular speed of Jupiter’s rotation.

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3a2 marks

Determine the equation for the escape velocity, v, of a planet with mass M and radius R.

3b4 marks

Calculate the escape velocity of the Moon using the following data: 

   Mass of the Moon = 7.33 × 1022 kg

    Density of the Moon = 3300 kg m–3

3c3 marks

A dwarf planet Q has the same mass as the moon but a radius twice as large. 

Calculate the escape velocity on planet Q.

3d2 marks

State two reasons why rockets launched from the Earth’s surface do not need to achieve escape velocity to reach their orbit.

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4a4 marks

Compare the advantages and disadvantages of polar and a geostationary orbit.

4b2 marks

State and explain one possible use for a satellite travelling in a polar orbit.

4c3 marks

A satellite travels in a polar orbit at an altitude of 300 km. 

Show that the time period of its orbit is around 90 minutes.

4d2 marks

Calculate the speed of the satellite when it travels in a polar orbit at an altitude of 300 km.

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5a3 marks

The International Space Station (ISS) orbits travels around the Earth once every 93 minutes. 

Calculate the angular speed of the ISS, stating an appropriate unit.

5b4 marks

Hence, or otherwise, calculate the distance of the ISS above the Earth’s surface.

5c4 marks

The Soyuz is a Russian spacecraft that carries astronauts to and from the international space station (ISS). The ISS has a mass of approximately 4.2 × 105 kg. 

Calculate the change in kinetic energy of a Soyuz travelling from the Earth’s surface to the ISS.

5d2 marks

Without performing any further calculations, explain how the change in kinetic energy relates to the change of the potential energy when the Soyuz travels from the Earth’s surface to the ISS. 

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