Superlesson
Project 7-1
Advanced Algebra
Chapter 7, Investigating Roots and Powers
To the casual observer, starlight is just an intriguing twinkle in the night sky. To astronomers, starlight is an endless source of information about our universe.
Part A, Inverse, Combined, and Joint Variation;
Part B, Positive Integer Exponents
1. The brightness of a distant light, as you see it, depends on the actual intensity of the light (Is it a tiny 25-watt bulb or a giant spotlight?) as well as its distance from you. The same is true of starlight. A star's brightness, as you see it, depends on the star's absolute brightness and its distance. Absolute brightness is different from a star's magnitude, which is a measure of the intensity of the star's light as you see it.
a. Find the magnitude and distance of the two stars Barnard's Star and Ross 154.
b. Read about magnitude beneath the star table. What does the difference in the magnitudes of the two stars tell you about how much brighter Barnard's Star appears in the night sky than Ross 154 appears?
c. The absolute brightnesses of Barnard's Star and Ross 154 are almost identical. The difference in their magnitudes is due to the fact that their distances from Earth are different. Brightness varies inversely as the square of an object's distance from the observer. Use this fact and your answer to 1b to find how many times farther from Earth is Ross 154 than is Barnard's Star. Explain your method.
d. Compare your answer to 1c with the data on star distances you found in the table. Are the data compatible with your answer?
Part C, Properties of Exponents and Powers;
Part D, Making Connections
2. Moonlight captured on a photograph can be used to estimate the height of a moon crater.
a. The moon's mass is 7.35 X 1022 kg. Its density is 3.34 X 103 kg/m3. Use the fact that density = (mass / volume) to find the moon's volume.
b. The volume V of a sphere with radius r is given by V = (4 / 3) πr3. Use your answer to a to find the moon's radius in meters.
c. Find the moon photo titled L2-7 days (1st quarter). Click on the photo for a detailed image. Locate the crater with a wide shadow on the Web site photo. Use the picture shown here to help locate the crater. With a millimeter ruler, take these measurements from the Web site photo:
s = width of shadow in crater
d = distance of shadow from moon's shadow line
r = radius of moon (you may have to scroll to get this)
d. If h represents the height of the crater wall, why does (r / d) = (s / h)?
e. Use the proportion to find h in millimeters.
f. In the Web site photo, what fraction of the radius of the moon r is represented by the height of the crater wall h?
g. Dimensions on the photo are proportional to actual dimensions on the moon. Use your answers to 2b and 2f to approximate the height of the crater wall.
