Howardites

The answer sheet for the worksheet Gravitational fields and escape. Each answer comes with the reason, so it can be used to mark or to go over the questions with the class.

Back to the worksheet

A-level · Ages 16 to 18 (Years 12 and 13)Answer sheet for teachers

Answers: Gravitational fields and escape

  1. A: About −1.3 × 10⁷ J kg⁻¹V = −GM/r = −4.28 × 10¹³ ÷ 3.39 × 10⁶ ≈ −1.3 × 10⁷ J kg⁻¹. Zero potential is at infinity, not at the surface, so V here is negative.
  2. B: Vesta, Moon, Mars, EarthThe values are about 0.36, 2.4, 5.0 and 11.2 km s⁻¹ for Vesta, the Moon, Mars and Earth.
  3. A: 2.5 × 10⁷ JE = ½mv² = 0.5 × 2.0 × (5.0 × 10³)² = 2.5 × 10⁷ J. Forgetting to square the speed gives only 5,000 J.
  4. D: Ejecta need only about 360 m s⁻¹ to escapeVesta's escape velocity is only about 360 m s⁻¹, roughly the speed of sound in air, so modest ejection speeds are enough.
  5. C: Accelerating rock to 5 km s⁻¹ was expected to melt itIt seemed that any shock strong enough to reach Martian escape velocity would melt or destroy the rock, until spallation was understood.
  6. True (It cannot escape: its kinetic energy is less than GMm/r)Escape needs ½mv² ≥ GMm/r. Below 362 m s⁻¹ the rock stays bound to Vesta whatever its mass or launch direction.
  7. True (About 40 times)Vesta's surface field is about 0.25 N kg⁻¹ against about 9.8 N kg⁻¹ for Earth, a ratio of roughly 40.
  8. The field strength they experience (accept any answer with the same meaning)Field strength is force per kilogram, g = GM/r², which depends only on the planet; force, weight and escape energy all scale with the object's mass.
  9. A high escape velocity and a thick atmosphere (accept any answer with the same meaning)Venus, like Earth, has a high escape velocity and a dense atmosphere that slows ejecta, so no meteorites from it have been identified.
  10. Taking the square root of 2GM/r (accept any answer with the same meaning)For Vesta 2GM/r ≈ 1.31 × 10⁵ m² s⁻²; its square root gives the correct escape velocity of about 362 m s⁻¹.

Task

Answers will vary. The task comes from the lesson: Calculate the escape velocity of the Moon (M = 7.35 × 10²² kg, r = 1.74 × 10⁶ m) and of Mars (M = 6.42 × 10²³ kg, r = 3.39 × 10⁶ m). Then plot escape velocity against radius for Vesta, the Moon, Mars and Earth (M = 5.97 × 10²⁴ kg, r = 6.37 × 10⁶ m) and comment on the trend.

Look for work that uses the key words correctly and gives a reason for each point.

Howardites · teacher copy: keep it separate from the pupil worksheets