Orbital motionEdexcel A-Level Physics: Subtopic test

1. 1
   An Earth-observation satellite moves in a circular orbit at a height of 600 km above the surface of the Earth. The mass of the Earth is 5.97×10²⁴ kg, its radius is 6.37×10⁶ m and the gravitational constant is G = 6.67×10⁻¹¹ N m² kg⁻².

   (a)

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

   [1 mark]

   • AGM/r
   • B√(GM)/r
   • C√(GM/r)
   • DGM/r²

   (b)

   The satellite is moved into a higher circular orbit. Which row describes the change in its orbital speed and orbital period?

   [1 mark]

   • Aspeed decreases, period increases
   • Bspeed increases, period increases
   • Cspeed increases, period decreases
   • Dspeed stays the same, period increases

   (c)

   Calculate the orbital speed of the satellite.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A television company uses a communications satellite that is placed in a geostationary orbit above the Earth. The mass of the Earth is 5.97×10²⁴ kg, its radius is 6.37×10⁶ m and the gravitational constant is G = 6.67×10⁻¹¹ N m² kg⁻². One day is 8.64×10⁴ s.

   (a)

   Which row lists conditions that a satellite must satisfy to be in a geostationary orbit?

   [1 mark]

   • AOrbit passes over the poles, period 24 hours
   • BOrbit above the equator, period 24 hours, moves in the same direction as the Earth's rotation
   • COrbit in any plane, period 12 hours
   • DOrbit at a height of about 600 km above the equator

   (b)

   Satellite P orbits the Earth at four times the orbital radius of satellite Q. What is the ratio (period of P) / (period of Q)?

   [1 mark]

   • A2
   • B4
   • C16
   • D8

   (c)

   Calculate the orbital radius of the satellite.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The Moon orbits the Earth in an approximately circular path of radius 3.84×10⁸ m. Its orbital period is 27.3 days. Take G = 6.67×10⁻¹¹ N m² kg⁻².

   (a)

   Use the motion of the Moon to calculate the mass of the Earth.

   [3 marks]

   (b)

   Calculate the orbital speed of the Moon and explain why this speed would be the same if the Moon had twice its mass.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A navigation satellite is in a circular orbit at a height of 2.02×10⁷ m above the surface of the Earth. The mass of the Earth is 5.97×10²⁴ kg, its radius is 6.37×10⁶ m and the gravitational constant is G = 6.67×10⁻¹¹ N m² kg⁻². A geostationary satellite has an orbital radius of 4.22×10⁷ m.

   (a)

   Calculate the orbital period of the navigation satellite and explain why a satellite in a higher circular orbit has a lower speed.

   [6 marks]

   (b)

   A student suggests that the navigation satellite could be used as a geostationary satellite. Evaluate this suggestion and describe the conditions for a geostationary orbit.

   [6 marks]

   Total for question 4: 12 marks

End of questions