Math Rocks: A Lesson in Asteroid Dynamics
This activity is related to a Teachable Moment from April 19, 2017. See "How NASA Studies and Tracks Asteroids Near and Far."
Asteroids are rocky, airless worlds that orbit our sun, but are too small to be called planets. They are remnants left over from the early formation of our solar system about 4.6 billion years ago. Tens of thousands of these minor planets are gathered in the main asteroid belt, a vast doughnut-shaped ring between the orbits of Mars and Jupiter. Asteroids that pass close to Earth are called near-earth objects.
They become meteors -- or shooting stars -- when they fall through a planet's atmosphere; leaving a bright trail as they are heated to incandescence by the friction of the atmosphere. Pieces that survive the journey and hit the ground are called meteorites.
Meteorites may vary in size from tiny grains to large boulders. One of the largest meteorite found on Earth is the Hoba meteorite from southwest Africa, which weighs roughly 54,000 kg (119,000 pounds).
ProceduresOn Feb. 15, 2013, a small asteroid entered Earth's atmosphere over Chelyabinsk, Russia, and startled onlookers with its fiery appearance and shockingly loud noise. NASA estimates the asteroid was approximately 17 meters in diameter with a mass of approximately 11,000 metric tons and traveled approximately 18 kilometers per second. Infrasound stations nearby and as far away as Antarctica detected the low-frequency sound waves generated by the meteor. The infrasound data indicates that the event, from atmospheric entry to the meteor's airborne disintegration took 32.5 seconds. The entry angle to horizontal was about 15° and the terminal part of the fireball was at about 20 km altitude.
- What is the straight-line distance the meteor traveled through Earth's atmosphere?
- Compute the volume of the asteroid, assuming it was nearly spherical.
- Compute the density of the asteroid. What does this tell you about the physical composition of the asteroid?
- Is it primarily ice? Rock? Iron?
- How much energy was released by the event? Give answer in Joules and kilotons.
- At what altitude did atmospheric entry occur? What layer of the atmosphere is this?