Orbital motionEdexcel International A Level Physics: Subtopic test

1. 1
   The International Space Station (ISS) moves in a circular orbit at a height of 4.0 × 10⁵ m above the Earth's surface. The Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m. G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   What provides the centripetal force that keeps the ISS in orbit?

   [1 mark]

   • AThrust from the station's engines
   • BA centrifugal force acting outwards
   • CThe gravitational attraction between the Earth and the station
   • DAir resistance acting on the station

   (b)

   What is the orbital speed of the ISS?

   [1 mark]

   • A5.9 × 10⁷ m s⁻¹
   • B3.2 × 10⁴ m s⁻¹
   • C7.91 × 10³ m s⁻¹
   • D7.67 × 10³ m s⁻¹

   (c)

   Calculate the time taken for the ISS to complete one orbit.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A geostationary communications satellite remains above the same point on the Earth's surface. The Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m, and it rotates once in 8.62 × 10⁴ s (one sidereal day). G = 6.67 × 10⁻¹¹ N m² kg⁻².

   (a)

   Which statement must be true for the satellite to be geostationary?

   [1 mark]

   • AIt orbits in a plane that passes through the poles
   • BIt orbits in the plane of the equator, in the same direction as the Earth's rotation
   • CIt orbits just above the Earth's atmosphere
   • DIts acceleration is zero

   (b)

   What is the radius of the orbit of the satellite, measured from the centre of the Earth?

   [1 mark]

   • A4.21 × 10⁷ m
   • B3.58 × 10⁷ m
   • C7.49 × 10²² m
   • D1.8 × 10⁵ m

   (c)

   Explain why a geostationary satellite must orbit in the plane of the equator.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Mars moves in an approximately circular orbit of radius 2.28 × 10¹¹ m around the Sun, which has mass 1.99 × 10³⁰ kg. G = 6.67 × 10⁻¹¹ N m² kg⁻². Take one year to be 3.16 × 10⁷ s.

   (a)

   Show that the orbital period T of a planet in a circular orbit of radius r around the Sun is given by T² = 4π²r³/GM, where M is the mass of the Sun.

   [3 marks]

   (b)

   Calculate the orbital period of Mars in years.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Satellites in the Global Positioning System (GPS) move in circular orbits of radius 2.66 × 10⁷ m around the Earth, which has mass 5.97 × 10²⁴ kg. G = 6.67 × 10⁻¹¹ N m² kg⁻². The Earth rotates once in 8.62 × 10⁴ s.

   (a)

   Explain, using Newton's laws of motion and the law of gravitation, why the orbital speed of a satellite depends on the radius of its orbit but not on its mass, and why a satellite in a higher orbit has a longer period.

   [6 marks]

   (b)

   Calculate the orbital speed and the period of a GPS satellite, and hence deduce how many orbits it completes in one rotation of the Earth.

   [6 marks]

   Total for question 4: 12 marks

End of questions