Astronomy 350: Worksheet 1 - Positional Astronomy• 1. Why is the sidereal day shorter than the solar day?• 2. What is the difference between a sidereal month and a synodic month?Between a sidereal year and a tropical year?• 3. What is apparent solar time and what is the difference between this andmean solar time?• 4. What are the fall and spring equinoxes and the winter and summersolstices in terms of the Earth’s o r bit around the Sun?• 5. What are declination and right ascension? How are they similar anddifferent to lat itude and longitude on Earth?• 6. How and why do t he Sun’s celestial coordinates change over the courseof a year?• 7. At the North Pole, where is the Celestial equator in the sky and theNorth Celestial Pole? Describe the motions of the stars here. Do the samefor the equator.• 8. Describ e the Sun’s paths through the local sky on the equinoxes andsolstices for latitude 40◦N. Do the same for the North Pole, South Pole andequator.• 9. What is special about the tropics of Cancer and Capricorn? Describe theSun’s path on the solstices at t hese latitudes. Do the same for the Arcticand Antarctic circles.• 10. Briefly describe how you would use the Sun or stars to determine yourlatitude and longitude.• 11. Describe why the following statements do or do not make sense: a) theapparent solar time was noon, but the Sun was just setting. b) my meansolar clock said it was 2.00pm but a friend who lives east of here had a meansolar clock that said it was 2.11pm. c) when the standard time is 3.00pmin Baltimore, it is 3.15pm in Washington DC. d) Last night I saw Jupiterat an altitude of 45◦ in the south. e) The latitude of stars in Orion’s beltis about 5◦ f) today the Sun is at an altitude of 10◦ on the celestial sphere.g) Los Angeles is west of New York by about 3 hours of right ascension h)the summer solstice is east of the vernal equinox by about 6 hours of rightascension.• 12. The time from one spring equinox to the next is a) sidereal day b)tropical year c) synodic month.1• 13. Your wristwatch tells you a) apparent solar time b) universal time c)standard time• 14. A star that is located 30◦ north of the celestial equator has a) declination=30◦b) right ascension of 30◦ c) latitude=30◦.• 15. A stars path thro ug h the night sky depends on your latitude and thestar’s a) declination b) right ascension c) both.• 16. At 50◦N, the celestial equator crosses the meridian at altitude a) 50◦inthe south b) 50◦in the north and c) 40◦in the south.• 17. AT the North Pole on the summer solstice, the Sun a) remains station-ary in the sky b) reaches zenith at noon c) circles the horizon at an altitude23.5◦.• 18. If you know a star’s declination, you can determine your latitude ifyou also a) measure its altitude when it crosses the meridian b) measureits right ascension c) know the universal time.• 19. If you measure the Sun’s position in your local sky, you can deter-mine your longitude if you also a) measure its altitude when it crosses themeridian b) know its right ascension c) know the universal time.• 20. If the Earth did not precess would there be any difference between thesidereal and tropical year?• 21. Answer the following for a latitude of about 40◦N :– a) Where is the No r th Celestial Pole in yo ur sky?– b) Describe the location of the meridian in your sky. Specify threedistinct points on it. Is there a meridian at the North Pole?– c) Describe the location of the celestial equator in your sky. Specifythree distinct point s along it.– d) Does the Sun ever appear at your zenith? If not, why not?– e) What r ange of declinations makes a star circumpolar in your sky?What range of declinations for stars makes it impossible to see in yoursky?• 22. Its Feb 15 and your sundial tells you the apparent solar time is 3.30pm.What is the mean solar time?• 23. It is 4pm on the spring equinox. What is the local sidereal time?• 24. The local sidereal time is 19.30. When will Vega (RA=18h35m). Whenwill Vega cross your meridian?2• You observe a star that has an hour angle of 3 hours when the local siderealtime is 8:15. What is the star’s RA?• 25. The Orion Nebula has a declination of about −5.5◦ and RA=5h25m. Ifyou are at latitude 40 ◦ N and the local sidereal time is 7:00, approx wheredoes the Orion Nebula appear in your