Astro 210 Homework 6 - Astronomy 210 Spring 2011 Homework...

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Astronomy 210 Spring 2011 Homework Set #6 Due in class: Friday, March 11 Total Points: 50 + 10 bonus 1. On the Lookout for the Asteroid of Doom . While most asteroids have orbits that confine them to the asteroid belt between Mars and Jupiter, there are still many that are found in the inner solar system, to include some with orbits which cross the Earth’s. Just one asteroid impact can ruin your entire day, as the dinosaurs discovered 65 million years ago. (a) [5 points] Consider a near-Earth asteroid which collides with the Earth. The asteroid begins its fall at a great distance r R and with an initial speed v 0 . Calculate the speed v hit with which the asteroid impacts the Earth (i.e., arrives at the Earths’ surface r = R ). Energy conservation will be useful here. You should find that v hit v esc , that is, the impact speed is always at least the escape speed. (b) [5 points] Find an expression for the kinetic energy of an asteroid impacting the Earth at the escape speed. You may assume the asteroid is spherical with radius s and with uniform density ρ . Evaluate this impact energy for a medium-sized s = 1 km asteroid with density ρ = ρ rock = 3000 kg / m 3 . Compare your answer to the energy released from a “small” nuclear explosion (equivalent to 1 kTon of TNT, 4 × 10 12 Joules), and a large explosion (1 MTon of TNT, 4 × 10 15 Joules), and comment on possible effects for the impact region and for global civilization. For comparison, the global nuclear arsenal represents about 10 4 MTon. (c) [5 points] It is obviously of interest to identify and track near-Earth asteroids. The upcoming
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