15
tan heta =(v)/(c)
(Equation 13.1)
tan
FIGURE 13.2 Aberration of falling raindrops.
Suppose raindrops are falling straight down with a speed of 15 feet per second. Use Equation 13.1 to compute the tilt of the umbrella when the person carrying the umbrella moves at (a) 5 feet per second, (b) 10 feet per second, and (c) 15 feet per second.
Use your answers from Part 1 to write a statement describing how the tilt of the umbrella depends on the raindrops' velocity and the velocity of the person carrying the umbrella.
Suppose raindrops are falling straight down with a speed of 15 feet per second. This time you observe a person walking through the rain with an umbrella tilted at an angle of 10 degrees. Use Equation 13.1 to compute the velocity of the person.
Figure 13.1(b), which illustrates the analogous situation for starlight entering an Earth-based telescope, suggests that we can apply the trigonometric principle described in Equation 13.1 to the phenomenon of stellar aberration-and thereby compute the orbital velocity of Earth. James Bradley imagined the right triangle in Figure 13.3 formed by line segments representing the velocity of light c (the longer side) and the orbital velocity of Earth v (the shorter side). The triangle's hypotenuse indicates the direction Bradley had to point his telescope to intercept starlight from Gamma Draconis. (The triangle is not drawn to scale.) Figure 13.3 suggests that were Earth moving close to the speed of light, the majority of stars would appear huddled in one portion of the sky!
tan
person. E (c15 feet per second. 1. would appear huddled in one portion of the sky! velocity and the velocity of the person carrying the umbrella. through the rain with an umbrella tilted at an angle of 10 degrees. Use Equation 13.1 to compute the velocity of the Suppose raindrops are falling straight down with a speed of 15 feet per second. This time you observe a person walking Use your answers from Part I to write a statement describing how the tilt of the umbrella depends on the raindrops' Suppose raindrops are falling straight down with a speed of 15 feet per second. Use Equation 13.1 to compute the FIGURE 13.2 Aberration of falling raindrops. 0- al< tan0= (Equation 13.1)