Shock, craters and deflecting an asteroid
Hypervelocity impacts generate shock pressures that transform minerals. This final lesson connects shock metamorphism, crater evidence and the momentum physics of deflecting an asteroid.
- Describe shock metamorphism and the minerals it produces.
- Use impulse and momentum, including the enhancement factor β, to calculate a deflection.
- Explain why small velocity changes produce large position changes over time.
Links to: A-level physics, momentum and impulse; A-level geology: impact structures, shock metamorphism and high-pressure minerals.
Shock metamorphism
In a hypervelocity impact, a shock wave compresses rock to pressures of tens to hundreds of gigapascals in microseconds. Minerals respond in characteristic ways: quartz develops planar deformation features; feldspar turns to a diaplectic glass such as maskelynite without melting; quartz transforms to the high-pressure polymorphs coesite and stishovite; olivine can transform to ringwoodite. Shatter cones form at lower pressures.
Meteorites record shocks on their parent bodies on the same principle, graded as shock stages S1 to S6. Many L chondrites are heavily shocked by a break-up of their parent body about 470 million years ago.
Deflection by impact
A kinetic impactor delivers an impulse to an asteroid equal to its momentum, mv, plus the momentum carried away by ejecta. This is written Δp = βmv, where the momentum enhancement factor β is 1 if there is no ejecta and greater than 1 when ejecta is thrown backwards. The asteroid's velocity change is Δv = βmv/M.
For the DART impact on Dimorphos in 2022, β was estimated at about 3.6, with a plausible range of about 2 to 5, depending on Dimorphos's uncertain mass. The orbital period around Didymos fell by about 33 minutes.
Lead time
A change in velocity of millimetres per second sounds trivial, but its effect accumulates. A change in an asteroid's orbital speed alters its orbital period, so the asteroid arrives earlier or later at each subsequent pass. Over many orbits, the along-track shift grows roughly in proportion to elapsed time, and can exceed Earth's radius. Years to decades of warning therefore turn a small nudge into a miss.
DART's velocity change
DART: m = 580 kg, v = 6.14 × 10³ m s⁻¹. Dimorphos: M = 4.3 × 10⁹ kg. Calculate Δv for β = 1 and β = 3.6.
- mv = 580 × 6.14 × 10³ = 3.56 × 10⁶ kg m s⁻¹.
- For β = 1: Δv = 3.56 × 10⁶ ÷ 4.3 × 10⁹ = 8.3 × 10⁻⁴ m s⁻¹.
- For β = 3.6: Δv = 3.6 × 8.3 × 10⁻⁴ ≈ 3.0 × 10⁻³ m s⁻¹.
Answer: About 0.8 mm s⁻¹ without ejecta and about 3 mm s⁻¹ with it, consistent with the observed change in Dimorphos's orbit.
Estimate the along-track shift produced by Δv = 3 mm s⁻¹ applied 10 years before a predicted impact, assuming as a rough approximation that the shift is about 3Δv × t. Compare your answer with Earth's radius (6,370 km). Then list three reasons why a real deflection campaign would be more complicated.
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 1Which mineral is a high-pressure form of SiO₂ produced by impacts?
Coesite and stishovite are high-pressure polymorphs of quartz found at impact sites.
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Question 2What is maskelynite?
Shock disrupts the plagioclase structure into a diaplectic glass while the grain keeps its shape.
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Question 3What does β > 1 mean for a kinetic impactor?
Momentum carried by ejecta in the opposite direction gives the target extra forward momentum.
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Question 4A 1,000 kg impactor at 5,000 m s⁻¹ hits a 1.0 × 10¹⁰ kg asteroid with β = 2. What is Δv?
Δv = βmv/M = 2 × 1,000 × 5,000 ÷ 1.0 × 10¹⁰ = 1.0 × 10⁻³ m s⁻¹.
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Question 5Why is warning time crucial for deflection?
A tiny change in orbital period shifts the arrival time more with every orbit.