Orbits of planets and satellitesAQA A-Level Physics: Subtopic test

1. 1
   An Earth-observation satellite is in a circular orbit 600 km above the Earth's surface. Take the Earth's mass as 5.97 × 10²⁴ kg and its radius as 6.37 × 10⁶ m.

   (a)

   Which statement about the satellite's orbital speed is correct?

   [1 mark]

   • AIt depends on the orbital radius but not on the mass of the satellite
   • BA satellite of greater mass must orbit faster at the same radius
   • CIt increases as the orbital radius increases
   • DIt is zero relative to the Earth's centre

   (b)

   Which expression gives the orbital speed v of a satellite in a circular orbit of radius r about a body of mass M?

   [1 mark]

   • Av = GM/r
   • Bv = √(2GM/r)
   • Cv = √(GMm/r), where m is the mass of the satellite
   • Dv = √(GM/r)

   (c)

   Calculate the orbital speed of the satellite. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A telecommunications company operates a satellite in a geostationary orbit to relay television signals. A weather-monitoring agency separately uses satellites in low polar orbits.

   (a)

   Which statement describes a geostationary orbit?

   [1 mark]

   • AAn orbit over the poles with a period of 12 hours
   • BAn orbit in any plane with a period of 24 hours
   • CAn orbit in the equatorial plane, in the same direction as the Earth's rotation, with a period equal to the Earth's rotation period
   • DAn orbit in the equatorial plane, in the opposite direction to the Earth's rotation, with a period of 24 hours

   (b)

   Which statement gives an advantage of a low polar orbit over a geostationary orbit for monitoring the weather?

   [1 mark]

   • AThe satellite stays above the same point of the surface all the time
   • BThe satellite is closer to the surface, so gives higher resolution images and, as the Earth rotates beneath it, covers the whole surface over time
   • CThe satellite has a longer orbital period, so makes fewer orbits per day
   • DThe satellite needs no centripetal force

   (c)

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

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student investigates the relationship between the orbital period and the orbital radius of satellites moving in circular orbits around the Earth, which has mass 5.97 × 10²⁴ kg.

   (a)

   Derive the relationship between the orbital period T and orbital radius r for a satellite in a circular orbit, showing that $T^2 \propto r^3$.

   [3 marks]

   (b)

   A geostationary satellite has an orbital period of 24 hours. Calculate the radius of its orbit from the centre of the Earth and its height above the Earth's surface, which has radius 6.37 × 10⁶ m. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A communications satellite of mass 800 kg moves in a circular orbit of radius 8.0 × 10⁶ m about the Earth. The Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m. Rockets launching spacecraft from its surface must overcome the Earth's gravitational field.

   (a)

   Calculate the kinetic energy, the gravitational potential energy and the total energy of the satellite in its orbit, and state what the sign of the total energy shows. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [6 marks]

   (b)

   Calculate the escape velocity from the surface of the Earth, explaining your method in terms of energy. Use $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$.

   [6 marks]

   Total for question 4: 12 marks

End of questions