To approximate the distance from the Earth to stars relatively close by. astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with ∠ P S E = 90 ° . The length of is the distance between the Earth and Sun. approximately 92 , 900 , 000 mi . The parallax angle (or simply parallax) is denoted by p . Use this information for Exercises 31-32. a. Find the distance between the Earth and Barnard's Star if the parallax angle is 0.547 arcseconds. Round to the nearest hundred billion miles. b. Write the distance in part (a) in light-years. Round to 1 decimal place. (Hint 1 light-year is the distance that light travels in 1 yr and is approximately 5.878 × 10 12 mi .)
To approximate the distance from the Earth to stars relatively close by. astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with ∠ P S E = 90 ° . The length of is the distance between the Earth and Sun. approximately 92 , 900 , 000 mi . The parallax angle (or simply parallax) is denoted by p . Use this information for Exercises 31-32. a. Find the distance between the Earth and Barnard's Star if the parallax angle is 0.547 arcseconds. Round to the nearest hundred billion miles. b. Write the distance in part (a) in light-years. Round to 1 decimal place. (Hint 1 light-year is the distance that light travels in 1 yr and is approximately 5.878 × 10 12 mi .)
Solution Summary: The author calculates the distance between the earth and Barnard's star, if the parallax angle is 0.547arcseconds.
To approximate the distance from the Earth to stars relatively close by. astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly
6
months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with
∠
P
S
E
=
90
°
. The length of is the distance between the Earth and Sun. approximately
92
,
900
,
000
mi
. The parallax angle (or simply parallax) is denoted by
p
. Use this information for Exercises 31-32.
a. Find the distance between the Earth and Barnard's Star if the parallax angle is
0.547
arcseconds. Round to the nearest hundred billion miles.
b. Write the distance in part (a) in light-years. Round to
1
decimal place. (Hint
1
light-year is the distance that light travels in
1
yr
and is approximately
5.878
×
10
12
mi
.)
A 20 foot ladder rests on level ground; its head (top) is against a vertical wall. The bottom of the ladder begins by being 12 feet from the wall but begins moving away at the rate of 0.1 feet per second. At what rate is the top of the ladder slipping down the wall? You may use a calculator.
Explain the focus and reasons for establishment of 12.4.1(root test) and 12.4.2(ratio test)
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