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Answer: Navigating in the Big Dipper. All of the stars of
Chapter 1, Problem 1.91(choose chapter or problem)
Navigating in the Big Dipper. All of the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. Figure P1.91 shows the distances from the earth to each of these stars. The distances are given in light-years (ly), the distance that light travels in one year. One light-year equals 9.461 * 1015 m. (a) Alkaid and Merak are 25.6o apart in the earths sky. In a diagram, show the relative positions of Alkaid, Merak, and our sun. Find the distance in light-years from Alkaid to Merak. (b) To an inhabitant of a planet orbiting Merak, how many degrees apart in the sky would Alkaid and our sun be?
Questions & Answers
QUESTION:
Navigating in the Big Dipper. All of the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. Figure P1.91 shows the distances from the earth to each of these stars. The distances are given in light-years (ly), the distance that light travels in one year. One light-year equals 9.461 * 1015 m. (a) Alkaid and Merak are 25.6o apart in the earths sky. In a diagram, show the relative positions of Alkaid, Merak, and our sun. Find the distance in light-years from Alkaid to Merak. (b) To an inhabitant of a planet orbiting Merak, how many degrees apart in the sky would Alkaid and our sun be?
ANSWER:Step 1 of 2
(a)
Given information:
The angle between Alkaid and Merak 
Schematic diagram:
Relative positions of Alkaid, Merak, and our Sun.
Here, point A denotes the position of Earth, point B denotes the position of Sun, Point C denotes the position of Merak and point D denotes the position of Alkaid.
The distance between the Alkaid and Merak is given as,
Substituting all known values,
Therefore, the distance from Alkaid to Merak is ly .