21st Century Astronomy
21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 22, Problem 9QP
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=350,000csc(π/30*x). a. Select the graph of g(x) on the interval [0,35]. b. Evaluate g(5). Enter the exact answer. c. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? d. Find and discuss the meaning of any vertical asymptotes on the interval [0,35].
A space probe with a diameter of 2.50m is moving past Saturn's moon Enceladus. An observational platform on Enceladus measures the shortest length of the ellipsoidal probe to be 1.25m. How fast is the probe moving relative to the moon? a) .999c b) .995c c) .957c d) .883c e)  .866c
1. For centuries, we accpeted Newton's 2nd Law as the standard model for motion. Then Einstien came along and siggested a modification in cases of high velocity. The Lorenz factor:                                         γ(v)=(1/square-root of 1−(v^2/c^2)) a) The constant (c) is the speed of light, which is 3 * 10^8 m/s. What is the lim as v approaches 400 γ(v)? You will have to track many decimal places to see a difference from 1. A bullet travels 400 m/s; this limit indicates that time dilation is extremely small (and basically negigible) at that speed.    b) In the movie Interstellar, time dialation occurs as 1 hour on the water planet corresponds to 7 years on earth. What is the factor γ in this case (what is the ratio of 7 years to 1 hour)?   c) If we rearrange the equation for γ and solve for v, we get:                                    v = c square-root of (γ^2 - 1/γ^2) What velocity v is necesary to get the γ you found in part (b)?   d) What is the lim as v approaches c γ(v) ?…
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