The kinetic energy of space rocks
Because they move so fast, even small meteoroids carry huge amounts of energy. This lesson uses the kinetic energy equation to explain fireballs, airbursts and craters.
- Use Eₖ = ½mv² to calculate kinetic energy.
- Explain why speed matters more than mass for impact energy.
- Compare the energy of real events using TNT equivalents.
Links to: GCSE physics, energy: kinetic energy stores and Eₖ = ½mv²; maths: standard form, squaring and unit conversion.
Speed squared
Kinetic energy is given by Eₖ = ½mv², with mass in kg, speed in m/s and energy in joules (J). Because speed is squared, doubling the speed quadruples the energy. Meteoroids move at 11 to 72 km/s, thousands of times faster than everyday objects, so even a small one carries astonishing energy.
Scientists often compare impact energies with the energy released by exploding TNT: one tonne of TNT releases about 4.2 × 10⁹ J, and a kilotonne about 4.2 × 10¹² J.
Airbursts
Most meteoroids larger than a few metres do not reach the ground intact. The air pressure on their front face becomes greater than the strength of the rock, so they break apart. The fragments then slow down and heat up so quickly that most of the energy is released in the air as an airburst.
On 15 February 2013 an asteroid about 18 metres across entered the atmosphere over Chelyabinsk, Russia, at about 19 km/s. It exploded about 30 km up with an energy of roughly 500 kilotonnes of TNT. The shock wave broke windows across the region, and about 1,500 people were injured, mostly by flying glass.
Craters
Larger or stronger bodies, especially iron ones, can reach the ground with much of their speed. Then the kinetic energy is transferred to the ground almost instantly, producing a shock wave that excavates a crater many times larger than the impactor. The iron that made Meteor Crater in Arizona, about 1.2 km across, is estimated to have released energy equivalent to several megatonnes of TNT, perhaps as much as 10.
Energy of a small meteoroid
A 1.0 kg meteoroid enters the atmosphere at 20 km/s. Calculate its kinetic energy and its TNT equivalent (1 kg of TNT releases 4.2 × 10⁶ J).
- Convert speed: 20 km/s = 20,000 m/s = 2.0 × 10⁴ m/s.
- Eₖ = ½ × 1.0 × (2.0 × 10⁴)² = ½ × 4.0 × 10⁸ = 2.0 × 10⁸ J.
- TNT equivalent = (2.0 × 10⁸) ÷ (4.2 × 10⁶) ≈ 48 kg.
Answer: 2.0 × 10⁸ J, the energy of about 48 kg of TNT, carried by a stony rock about the size of an orange. Almost all of it is released harmlessly high in the atmosphere.
Use the impact calculator on this site. Keep the size fixed and double the speed, then keep the speed fixed and double the diameter. Record the energy each time. Use Eₖ = ½mv² to explain why doubling the diameter has a bigger effect than you might expect (hint: how does mass depend on diameter?).
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 happens to kinetic energy if speed doubles and mass stays the same?
Eₖ = ½mv², so doubling v multiplies Eₖ by 2² = 4.
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Question 2Calculate the kinetic energy of a 2.0 kg meteorite falling at 100 m/s.
Eₖ = ½ × 2.0 × 100² = 1.0 × 10⁴ J.
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Question 3What is an airburst?
When air pressure exceeds a meteoroid's strength it fragments and releases most of its energy in the air.
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Question 4What injured most people in the Chelyabinsk event of 2013?
The airburst's shock wave shattered windows over a wide area.
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Question 5Why can iron impactors reach the ground more often than stony ones of the same size?
Strong iron bodies resist the air pressure that shatters weaker stony ones.