ESSENTIAL COSMIC PERSPECTIVE PKG
ESSENTIAL COSMIC PERSPECTIVE PKG
15th Edition
ISBN: 9780133982688
Author: Bennett
Publisher: PEARSON
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Chapter 9, Problem 45EAP

Room to Roam. It's estimated that there are a trillion comets in the Oort cloud, which extends out to about 50,000 AU. What is the to1al volume of the Oort cloud, in cubic AU? How much space does each comet have in cubic AU, on average? Take the cube root of the average volume per comet to find the cornets' typical spacing in AU. (Hints: For the purpose of this calculation, you can assume the Oort cloud fills the whole sphere out to 50,000 AU. The volume of a sphere is given by 4 3 π r 3 , where r is the radius.)

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You observe a comet 0.46 AU from Earth with a tail that is 1.7 degrees long. How long is the tail in AU? How long is the tail in kilometers? How many times could the U.S. fit along the length of the tail? (The width of the U.S. is 4,313 km.)
A typical comet contains some 1013 kg of water ice. How many comets would have to strike Earth in order to account for the roughly 2×1021 kg of water presently found on our planet?  If this amount of water accumulated over a period of 500 million years, how frequently must Earth have been hit by comets during that time?
It is believed there are 2.7 x 1012  comets in the Oort Cloud, which has a radius of 71000.0 AU. Calculate the average volume that each comet has to itself. Then take the cube root of the average volume per comet to find their typical spacing in AU.
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