Explain why, as a spacecraft travels from the Earth to the Moon along the line joining their centres, the magnitude of the net gravitational field strength first decreases, reaches zero at one point, and then increases again.

IB DP Physics Higher Level (2023 syllabus) — D.1 Gravitational fields · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A spacecraft travels in a straight line from the surface of the Earth to the surface of the Moon. Both bodies exert gravitational forces on the spacecraft throughout its journey.

Model answer (4 marks)

The field from Earth and Moon act in opposite directions along the line joining the centres, so the net field is the vector difference of the two contributions.

Near Earth the Earth's field is much larger than the Moon's, so the net field points towards Earth and its magnitude is large.

As the spacecraft moves away from Earth its field decreases as 1/r², while the Moon's field increases, so at a particular distance the two fields are equal in magnitude but opposite in direction and the net field becomes zero.

Further along the line the Moon’s field dominates, the net field points towards the Moon and its magnitude increases again.

Examiner tips

  • Use the word ‘opposite’ to show the vector difference; mention 1/r² dependence; identify the point where fields cancel; describe the change in direction after the neutral point.

Common mistakes

  • Confusing the direction of the net field with the direction of the larger field; forgetting that the net field is zero where the magnitudes are equal; not recognising that the net field increases again after the neutral point.

Mark scheme (4 marks)

  1. The gravitational field strengths due to Earth and Moon act in opposite directions (towards each respective body), so the net field is the vector difference of the two contributions.
  2. Close to Earth the Earth's contribution dominates, so the net field points towards Earth and is large; as the spacecraft moves away from Earth its contribution decreases (field strength ∝ 1/r²).
  3. At one specific point, the field strengths due to the Earth and the Moon are equal in magnitude but opposite in direction, so the net gravitational field strength is zero.
  4. Beyond this neutral point, as the spacecraft approaches the Moon, the Moon's field dominates and the net field increases in magnitude, now directed towards the Moon.

Key terms in this question

gravitational field strength · net gravitational field

Related

More Gravitational fields questions

▶ Try answering this question with AI marking (free) →