Momentum: nudging an asteroid
In 2022 a spacecraft deliberately hit an asteroid moon to change its orbit. Momentum explains how a tiny spacecraft could move a body millions of times heavier.
- Calculate momentum using p = mv.
- Apply conservation of momentum to a collision.
- Explain why the ejecta made DART's push more effective.
Links to: GCSE physics, forces (higher tier): momentum, p = mv, and conservation of momentum in collisions; maths: standard form.
Momentum
Momentum is mass multiplied by velocity: p = mv, measured in kg m/s. Like velocity, it has a direction. In a collision with no outside forces, the total momentum before equals the total momentum after. This is conservation of momentum.
The DART test
NASA's DART spacecraft, with a mass of about 580 kg, struck Dimorphos, a moon about 150 m across orbiting the asteroid Didymos, at about 6.1 km/s on 26 September 2022. Dimorphos has a mass of roughly 4 × 10⁹ kg, millions of times more than DART.
The impact shortened Dimorphos's orbit around Didymos by about 33 minutes, from 11 hours 55 minutes. Telescopes on Earth measured the change by timing how the pair's brightness dipped as one passed in front of the other.
The ejecta bonus
The impact blasted a huge plume of rock and dust off Dimorphos. That debris flew away in roughly the opposite direction to DART's motion, carrying momentum with it. By conservation of momentum, Dimorphos received an extra push in DART's direction. The ejecta made the push several times bigger than the spacecraft's momentum alone, good news for planetary defence.
How much did DART change Dimorphos's speed?
DART: m = 580 kg, v = 6,100 m/s. Dimorphos: M = 4.3 × 10⁹ kg. Ignoring the ejecta, estimate the change in Dimorphos's velocity.
- DART's momentum: p = mv = 580 × 6,100 ≈ 3.5 × 10⁶ kg m/s.
- If all of it is transferred, change in velocity = p ÷ M = (3.5 × 10⁶) ÷ (4.3 × 10⁹).
- 3.5 ÷ 4.3 ≈ 0.81, and 10⁶ ÷ 10⁹ = 10⁻³, so Δv ≈ 0.81 × 10⁻³ m/s = 0.8 mm/s.
- The ejecta multiplied this by about three to four times, to roughly 3 mm/s.
Answer: Less than 1 mm/s from DART alone, about 3 mm/s with the ejecta. A tiny change, but applied a decade or more ahead it would add up to thousands of kilometres.
Use two trolleys, or two coins on a smooth table, to show conservation of momentum: a moving one strikes a stationary one. Then explain in writing why hitting an asteroid years before a possible impact is far more effective than hitting it days before.
Quiz
5 questions. Choose an answer to see whether you are right and why. Finish the quiz to complete the lesson.
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Question 1What is the momentum of a 2,000 kg spacecraft moving at 3.0 m/s?
p = mv = 2,000 × 3.0 = 6,000 kg m/s.
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Question 2What does conservation of momentum state?
In a closed system, momentum is neither created nor destroyed.
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Question 3What did DART change?
Dimorphos's orbital period around Didymos shortened by about 33 minutes.
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Question 4Why did the ejecta increase the push on Dimorphos?
By conservation of momentum, material thrown backwards gives the asteroid an extra forward push.
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Question 5Why is early warning so important for deflecting an asteroid?
A change of a few mm/s, applied years ahead, shifts the asteroid's position by a large distance by the time it would reach Earth.