Gravitational fields and Newton's law of gravitationEdexcel A-Level Physics: Subtopic test

1. 1
   A mission planner is comparing the gravitational field of Mars with that of the Earth before designing a rover. Mars may be treated as a uniform sphere of mass 6.42×10²³ kg and radius 3.39×10⁶ m. The gravitational constant is G = 6.67×10⁻¹¹ N m² kg⁻².

   (a)

   Which statement correctly defines the gravitational field strength at a point on the surface of Mars?

   [1 mark]

   • AThe work done per unit mass in bringing a small mass from infinity to that point
   • BThe gravitational force acting per unit mass on a small mass placed at that point
   • CThe total gravitational force exerted by Mars on the rover
   • DThe mass of Mars divided by the volume of Mars

   (b)

   What is the gravitational field strength at the surface of Mars?

   [1 mark]

   • A0.93 N kg⁻¹
   • B7.46 N kg⁻¹
   • C3.73 N kg⁻¹
   • D9.81 N kg⁻¹

   (c)

   A rover of mass 185 kg is on the surface of Mars. Calculate the gravitational force on the rover.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A communications satellite of mass 850 kg moves in a circular path at a distance of 4.22×10⁷ m from the centre of the Earth. The Earth may be treated as a point mass of 5.97×10²⁴ kg at its centre.

   (a)

   The satellite is moved so that its distance from the centre of the Earth is trebled. What happens to the gravitational force on the satellite?

   [1 mark]

   • AIt becomes one ninth of its original value
   • BIt becomes one third of its original value
   • CIt becomes three times its original value
   • DIt becomes nine times its original value

   (b)

   A student says that the Earth pulls on the satellite with a much larger force than the satellite pulls on the Earth, because the Earth is far more massive. Which statement is correct?

   [1 mark]

   • AThe student is correct because F is proportional to the mass of the attracting body
   • BThe student is correct because the satellite is closer to the Earth's centre than the Earth's centre is to the satellite
   • CThe satellite pulls more strongly because it has the smaller mass
   • DThe forces are equal in magnitude and opposite in direction

   (c)

   Calculate the gravitational field strength of the Earth at the position of the satellite.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A lunar lander is travelling along the straight line joining the centres of the Earth and the Moon. The mass of the Earth is 5.97×10²⁴ kg, the mass of the Moon is 7.35×10²² kg, the radius of the Moon is 1.74×10⁶ m and the distance between their centres is 3.84×10⁸ m. Take G = 6.67×10⁻¹¹ N m² kg⁻².

   (a)

   Show that the gravitational field strength at the surface of the Moon is about 1.6 N kg⁻¹.

   [3 marks]

   (b)

   There is a point on the line between the Earth and the Moon where the resultant gravitational field strength is zero. Calculate the distance of this point from the centre of the Earth.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The International Space Station (ISS) orbits 400 km above the surface of the Earth. Some students claim that the astronauts float inside it because there is no gravity at that height. Take the radius of the Earth as 6.37×10⁶ m, its mass as 5.97×10²⁴ kg, the surface field strength as 9.81 N kg⁻¹ and G = 6.67×10⁻¹¹ N m² kg⁻².

   (a)

   Use g = GM/r² to calculate the gravitational field strength at the height of the ISS, and hence evaluate the students' claim.

   [6 marks]

   (b)

   A second satellite is to be placed at a point where the field strength is 2.45 N kg⁻¹, one quarter of the surface value. Determine its height above the surface of the Earth. Explain why changing the mass of the satellite would change the gravitational force on it but not the field strength at that point.

   [6 marks]

   Total for question 4: 12 marks

End of questions