All 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 P1.101 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.

(a) Alkaid and Merak are 25.6^o apart in the earth's 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?

Figure P1.101:

Transcribed Image Text:

Dubhe Megrez 81 ly 105 ly Mizar 73 ly Merak Alioth 77 ly 64 ly Phad Alkaid 138 ly 80 ly