Understanding Our Universe
Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 5, Problem 38QAP

(a)

To determine

The density of the asteroid Vesta considering it to be spherical in shape.

(b)

To determine

The difference in the composition of the rock of the asteroid Vesta as compared to the water and primitive rocks.

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A 0.872 km diameter asteroid will make a crater about 10 km in diameter. Let the asteroid have a density of 3000 kg/m3 and impact the surface at 22 km/sec. Assuming a spherical asteroid, what is the kinetic energy (in joule) of the asteroid? Convert the answer to megatons of TNT, where 1 megaton is about 4 × 1015 joule. For comparison, the most energetic weapon in the human arsenal is about 100 megatons.
On February​ 15, 2013, Asteroid 2012 DA14 passed within​ 17,200 miles​ [mi] of the surface of the Earth at a relative speed of 7.8 kilometers per second​ [km/s]. This is considerably closer than the orbit of geosynchronous satellites​ (26,200 miles). This is the closest recorded approach of an object this large. The asteroid 2012 DA14 was estimated to have a diameter of 30 meters​ [m] and a specific gravity of 3. If 2012 DA14 had hit the​ Earth, what is the total amount of energy that would have been released​ (i.e., what was the kinetic energy of the​ asteroid)? Express your answer in megatons​ [Mton]. One megaton is the energy released by one million metric tons of TNT explosive. A metric ton equals​ 1,000 kilograms​ [kg], and the explosive energy of TNT is 4,184 joules per gram​ [J/g].
The Tunguska asteroid is estimated to have had a diameter of 50 m, and to have produced an explosion equivalent to 10 megatons of TNT (1 megaton = 4.2 x 1015 joules). Assume that the asteroid was a sphere with density 2 g/cm3. Using the kinetic energy formula K = ½ mv2, where m is the mass and v is the speed, to estimate the speed of the asteroid. Assume that all kinetic energy is converted into the energy of the explosion. Give your answer in km/s with one significant figure.
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