1. An angle of one degree contains 60 minutes of arc, and a minute of arc contains 60 seconds of arc. How many arcseconds are in a full circle (360º)?
2. The Sun's angular diameter is 30 arcminutes. What is its angular diameter in degrees and in arcseconds?
3. The Moon takes 27.0 days to orbit once around the Earth. How far must the Moon travel each day, in units of degrees per day? How far must it travel each hour? How does this hourly distance compare with the angular diameter of the Moon, which is one-half of a degree? Would this motion be easily observed?
4. Suppose the scale of the Universe were changed so that the Earth was the size of a marble with a diameter of 1.0 cm. Using this scale, determine: (a) the scaled diameter of the Sun (express your answer in meters), and (b) the scaled distance between the Sun and Pluto (express your answer in kilometers). The actual diameter of the Earth is 1.3 x 107 m, the actual diameter of the Sun is 1.4 x 109m, the actual distance between the Earth and the Sun is 1.5 x 108 km, and the actual distance from the Sun to Pluto is 39.4 AU. [Note that 1 km = 1,000 m and 100 cm = 1 m.]
5. Suppose the scale of the Universe were changed so that the distance between the Earth and the Moon was 2.0 cm. On this scale, the scaled distance to the brightest star in the constellation Taurus, Aldebaran, is 2.9 x 104 km. Determine the actual distance to Aldebaran (express your answer in light years (ly)). The actual distance between the Earth and the Moon is 3.8 x 105 km, and 1 ly = 9.5 x1015 m. [Note that 1 km = 1,000 m and 100 cm = 1 m.]
6. Calculate the time light takes to travel: (a) from the Sun to Earth (express your answer in minutes), and (b) from the Sun to Jupiter (express your answer in minutes). The distance between the Earth and the Sun is 1.5 x 108 km, the distance between Jupiter and the Sun is 5.2 AU, and the speed of light is 3.0 x105 km/s.