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Astronomy Assignment #1b Solutions Text Problems: Unit Number 2 5 Problems 10c 10, 11, 14 Problem Solutions: Unit 2 10. If the Milky Way were the size of a nickel (about 2 centimeters). Object a. How big would the visible Universe be? Use a proportion to solve questions like this where different objects appear at the same scale. Required information Diameter of a nickel = 2 cm Radius of the Milky Way = 50,000 lyrs (See Table 2.1 Radius of the visible Universe = 13.2 billion lyrs (See Table 2.1) Scales of the Universe Table 2.1 Approximate Radius Earth R = 6,400 km Moon’s Orbit 380,000 km Sun Solar System to Pluto R = 700,000 km = 110 R 1 AU = 150 Million km = 210 R = 23,100 R 40 AU = 8500 R Nearest Star 4.2 ly = 270,000 AU Milky Way Galaxy 50,000 ly Local Group 1.5 Million ly Local Super Cluster 40 Million ly Visible Universe 13.2 Billion ly Earth’s Orbit Solve the following proportion for the diameter of the visible Universe 2 cm x 2 50,000 ly 2 13.2 109 ly 2 cm x 2 13.2 109 ly 5.28 105 cm 5.28 103 m 5.28 km 2 50,000 ly The scaled down visible would be 5.28 km ( about 3 ¼ miles) in diameter. Problem Solutions: Unit 5 10. What are your latitude and longitude? What are the latitude and longitude at the point on the Earth exactly opposite you? What geographic features are located there? A Google search of “latitude and longitude of Syracuse, NY” yields our latitude is about 43 longitude is about 76 degrees W. degrees N and Just opposite us on the globe implies that we (1) take the same latitude but opposite hemisphere and (2) add 180 degrees to the longitude (and then play with the number so that it is between zero and 180 degrees either E or W. So…the point opposite Syracuse, NY on the Earth has a latitude of 43 degrees S and the longitude is (76 W + 180 = 256 W = ) 104 degrees E longitude. On the map below the position of Syracuse, NY and its opposite point are marked with Xs. You can see that our opposite point is in the middle of the ocean off the southwest corner of Australia. X X 11. Your observatory lies at a latitude of 45N and a longitude of 90W. You wish to observe three celestial objects that have declinations of +87, -40, and -67. Which of these objects can you observe? This question requires a fairly complete understanding of the celestial coordinate system and the celestial sphere model. According to the last sentence on page 43 “if a star’s declination matches your latitude it will pass over through zenith”. This means that the declination of your zenith is just your latitude. Observing from 45 N will mean that 45 declination will be directly over your head. Following Figure 5.4A on page 42, you can see that the horizon is 90 from the zenith. Thus, any star that is within 90s from the declination of your zenith will be visible. As seen from 45N, all stars between +90 declination and -45 declination will eventually be visible over the horizon. So, you will be able to see the objects at +87 and -40 declination, but not the object at -67 declination.. Pictorially, we can draw the simplified celestial sphere as shown below. The three stars in the question are plotted in red. Clearly the stars at 87 degrees dec and -40 degrees dec are visible from this location because they appear above the horizon. The star at -67 degrees dec appears below the horizon and thus is not visible from that latitude. Zenith (dec= 45) Celestial Equator (dec = 0) dec = 87 NCP (dec = 90) dec = -40 (dec = -45) S The Southernmost Visible Star 45 Horizon Line 45 45 45 45 Horizon Line N (dec = 45) The Boundary of the Circumpolar Region dec = -67 SCP (dec = -90) Like 13. Boston and Rome are at the same latitude, but Boston is at a longitude of 71 W, while Rome is at 12E. If M31 passes through the zenith at a particular time in Rome, how many hours later will it pass through the zenith in Boston? This question was not assigned, but questions like it may appear on the exam, as stated in the study guide. This question requires knowledge of the relationship between the celestial coordinate system and the rotation of the Earth. As stated on page 43, “Each hour of RA equals 15;…if a star at RA =2h is overhead now, a star at RA =5h will be overhead three hours from now.” Thus, if were to calculate the number of degrees longitude between Boston and Rome, then divide that difference by 15 per hour, we would have the time in hours between M31 passing over both cities. Number of degrees longitude between Boston and Rome is 83. This divided by 15 per hour gives a time difference between M31 over Rome than Boston as 5.53 hours or 5 hours and 32 minutes. 14. How far is the celestial equator from your zenith if your latitude is 42N? 34S? This question requires a fairly complete understanding of the celestial coordinate system and the celestial sphere model. According to the last sentence on page 43 “if a star’s declination matches your latitude it will pass over through zenith”. This means that the declination of your zenith is just your latitude. Observing from 42N will mean that 42 declination will be directly over your head. Since 42 declination is 42 away from the celestial equator, the celestial equator must be 42 away from your zenith at this location. Observing from 34S latitude, will mean that the celestial equator is 34 away from your zenith at that location. The picture you could draw for each location appears below. Be certain that you understand how to construct these pictures to answer similar questions. If you were observing at 42N latitude the picture would be as follows: As you can see the celestial equator is 42 south of the zenith. Zenith (dec = 42) Celestial Equator (dec = 0) NCP (dec = 90) 42 (dec = -47) S 47 42 Horizon Line 47 Horizon Line N (dec = 47) 42 The Southernmost Visible Star The Boundary of the Circumpolar Region SCP (dec = -90) If you were observing at 34S latitude the picture would be as follows: As you can see the celestial equator is 34 north of the zenith. Notice that the circumpolar region is in the southern sky, not the northern sky, and that there is a portion of the northern hemisphere that is never visible. Zenith (dec = -34) Celestial Equator (dec = 0) SCP (dec = -90) 56 (dec = 47) S The Boundary of the Circumpolar Region Horizon Line 34 34 56 Horizon Line -34 N (dec = -56) The Northernmost Visible Star NCP (dec = 90)
