## Answers to Example Questions

1. 10 full moons fit within 5 degrees (the moon is 0.5 degree across). Since the sun and moon have the same angular size (remember a total eclipse of the sun --- they are the same size !) 10 suns would also fit across 5 degrees.

2. Number of arcsec in 360 degrees is 360 x 60 x 60 = 1,296,000 (quite a lot!). Recall there are 60 arcmins in 1 degree and 60 arcsecs in one arcmin.

3. 10 degrees. Try to remember the "handy angles" : finger=1 degree; three fingers=5 degrees; fist=10 degrees; index-pinky=15 degrees; outstreached hand=20 degrees.

4. False. The dipper is an ASTERISM --- only a part of the constellation of Ursa Major

5. Lyra; Ursa Minor; Cygnus. You should know these by now from the labs.

6. First magnitude star is brightest (recall, smaller magnitude numbers are brighter).

7. Difference is 10 magnitudes. Recall that 5 magnitudes is a factor of 100 in brightness. So 10,000=100x100 is 5+5=10 magnitudes different.

8. False. Gamma rays are at the shortest wavelength end of the EM spectrum. Recall the sequence: Radio, Microwave, infra-red, optical, ultra-violet, X-rays, gamma rays.

9. X-ray; Gamma-ray; Ultra-violet; Far infra-red.

10. nano means 10-9 or one billionth. Recall : micro=10-6 milli=10-3; kilo=103; mega=106; giga=109.

11. I cant do sketches on the web easily: look at figure 38c in appendix C of the manual. The important parts are: the thin corrector lens; the primary concave mirror (with a hole in it); the secondary convex mirror up in the center of the corrector lens; the eyepiece behind the primary.

12. The longer the focal length of the eyepiece the SMALLER the magnification and the LARGER the field of view.

13. A 4 meter mirror at f/8 has an effective focal length of 4x8=32 meters. (Recall, f-ratio is the ratio of the focal length of the element to its diameter). To get a magnification of x100 we need an eyepiece with a focal length of 1/100 x 32 meters = 0.32 meters = 32 centimeters. (Recall, magnification is the focal length of the primary divided by the focal length of the eyepiece).

14. 16 inch telescope has 4 times the collecting area of a 8 inch telescope (16/8 = 2 squared). The faintest stars can therefore be 4 times fainter. This corresponds to a difference in magnitudes of 2.5xLog(4) = 1.5 magnitudes. So the limiting magnitude is 14 + 1.5 = 15.5.

15. False. The zodiac constellations are grouped around the ECLIPTIC, not the equator.

16. False. The point overhead is the zenith. (The NCP is only overhead for an observer standing at the north geographic pole).

17. Meridian: great circle passing through the NCP and the zenith, it cuts the horizon due north and due south. Zenith: the point directly overhead. Horizon Plane: the tangent plane to the earth at the observer's location. Transit: the moment when an object crosses the meridian (moves from the eastern hemisphere into the western hemisphere; Synodic vs Sidereal: the synodic period is the period between two consecutive similar phases or positions of a planet or sun in the sky. The sidereal period is the time between two consecutive alignments with the same star --- it is the true orbit or rotation period.

18. The altitude of a transiting object (SALT) = 90-Lat+Dec. So we want this to equal 90 (directly overhead). So 90-Lat+Dec=90, so Lat=Dec. Now the Dec of the mid-summer sun is +23.5 so the latitude in question is +23.5. This is also called the Tropic of Cancer.

19. 11 pm EST (Use your star wheels to do this).

20. Cassiopeia is circumpolar in Charlottesville. It is the only one sufficiently far north to be within 38 degrees of the NCP so that it never sets.

21. The Equator. At latitude zero, the circumpolar zones have NO size, and so there is no region of the celestial sphere that is permanently below the horizon.

22. On March 21 the sun is at the vernal equinox, moving eastwards from the southern celestial hemisphere into the northern celestial hemisphere.

23. Dec of the sun is largest on June 21, the summer solstice, when it has a value of +23.5 degrees.

24. a) Altitude of NCP is 38 degrees (ie the latitude). b) altitude of the celestial equator is 52 degrees (ie 90-lat). c) 14 degrees because the altitude on the meridian is 90-Lat+dec = 90-38+(-38) = 14.

25. At sidereal time 20 hours, RA=20 hours is on the meridian, suggesting that it was 4 hours ago that RA=16 hours was on the meridian. Hence an object with RA=16 hours is WEST of the meridian (ie it has already passed by the meridian).

26. On March 21 the sun is at RA=0; on June 21 it is at RA=6h so on July 21 the sun is at RA=8h. Hence at midnight the RA opposite the sun on the meridian (ie the sidereal time) is 8+12=20 hours. So at 10pm on July 21 the sidereal time is 18 hours (ie two hours earlier). A galaxy with coordinates RA=4h20m has an hour angle HA=ST-RA = 18h - 4h20m = 13h40m. Since this is so large, the object is clearly below the horizon.

27. Midnight (recall, the 3rd quarter moon leads the sun by 90 degrees in their westward diurnal motion, so the moon is on the eastern horizon when the sun is directly beneath us at midnight.

28. Waxing crescent of age 3 days has a phase angle of 3/29x360 = 37 degrees (there are 29 days in the synodic month). So 37 degrees separate the moon from the sun, with the sun to the west of the moon (since it is a waxing moon).

29. Precession of the earth's axis refers to the gradual circular motion executed by the Celestial poles as the axis of the earth's rotation also moves in a circle. The polar motion is such that the inclination of the axis to the ecliptic remains 23.5 degrees, so the circle described by the NCP in the sky has a radius of 23.5 degrees and is centered on the pole of the ecliptic. Similarly, the position of the vernal equinox moves around the ecliptic (a great circle) with the same 26000 year period (about 50 arcmin per year). Spring continues to occur on March 21 because our calendar is DEFINED so that March 21 occurs when the sun is on the vernal equinox, whether or not it has moved. The astrological sign of someone born at the end of march is always Aries, even though the constellation in which the sun appears at the end of march continually changes due to precession. In other words, western astrology does not account for the effects of precession (unlike, for example, Indian astrology which does).

30. The precession period is about 26000 years.

31. Since a complete precession cycle is 26,000 years, then in 100 years the equinox moves 100/26000 x 360 degrees = 1.384 degrees.

32. False. Although the sun and moon exert a force which tries to pull the earth's equatorial bulge into alignment with the ecliptic, because the earth is rotating, it instead executes precession, a motion in which the equatorial bulge is always inclined relative to the ecliptic, but the rotation axis slowly describes a circular motion.

33. False. Since precession slowly changes the direction of the earth's rotation axis, this means that a given season (eg summer, when the axis is pointing towards the sun) will occur at a different part in the earths orbit. This consequently means the part of the sky which is visible during a given season also changes. While Orion is presently a winter constellation, in 13,000 years it will be a summer constellation.

34. A partial solar eclipse.

35. c = at new or full moon. Obviously, the shadow of either the moon must fall on the earth or visa versa. Thus, the sun moon and earth must all lie in a line. This will only occur at new or full moon.

36. Some sunlight is scattered as it passes through the earth's atmosphere near the earth's terminator. Some of this scattered light goes into the umbra. Hence the umbra isn't totally dark, and one can see the moon even when it enters the umbra.

37. Moon's orbit is inclined 5 degrees to the ecliptic. The nodes are the points in the moon's orbit where the moon crosses the ecliptic (there are two, the ascending node and the decending node, on opposite sides of the orbit). Obviously, for an eclipse to occurr, both the earth and moon must be in the ecliptic plane (since that is where the shadow is), and so since the earth is (by definition) in the ecliptic, the moon must be at one of its nodes.

38. False. The 26,000 year period refers to the precession of the earths rotation axis. The period for the precession of the moon's orbital axis is 18.6 years --- significantly shorter.

39. False. They occur every 5.6 months -- ie in consecutive eclipse seasons. Remember, eclipses must occur when the sun and moon lie on the line of nodes. Although one might expect this to occur every 6 months, the precession of the moon's orbital plane causes the line of nodes to move around (regress) slowly, so that the true interval between eclipse seasons is more like 5.6 months instead of 6.

40. Never. Remember, planets only pass through the zodiac constellations and Orion is not one of them. Note that precession wont help here either, since that only changes the plane of the earth's equator, not the ecliptic plane.

41. True. Since they are inferior planets, they each have a maximum elongation which is less than 90 degrees (which is the elongation needed to make quadrature).

42. Recall that at greatest elongation, the direction of the earth to the planet is now tangent to its orbit (assumed circular). Hence we have a right angled triangle with the earth sun side as the hypotenuse. Since this has length 1 AU, then the distance from the sun to the planet is just sin 33 = 0.544 AU.

43. False. Although it is 90 degrees for the angle Mars-Earth-Sun, since Mars is on an outer orbit, the angle Earth-Mars-Sun (which defines the phase of the planet) is significantly more than 90 degrees. Hence Mars is in a gibbous phase.

44. b = Saturn. The planet is at opposition, and hence must be superior relative to Mars. Saturn is the only one in the list.

45. False. This is confusing sidereal period with synodic period. Clearly, the sidereal period is 7 months. But in general this will NOT be the synodic period, which is what is needed to find the period between one greatest elongation and the next one.

46. False. They each undergo retrograde motion near opposition, which is approximately once per year (since they are so far away they hardly move much during the year anyway). Hence they go through retrograde motion equally often, and about once per year.

47. Westwards (ie it is in retrograde motion). Planets usually move eastwards, except near opposition when they move "backwards" in the sky, which is westwards.

48. Saturn is big and rotates fast so its equatorial regions experience significant centrifugal force compared to higher latitudes. This pulls Saturn into an oblate spheroid. Since Saturn is not as massive or dense as Jupiter, it has a higher oblateness than Jupiter (though noticing this is tricky with the rings present).

49. The asteroids which get perturbed into the so-called "Earth Crossing" group simply dont survive long because of the possible collision with the terrestrial planets (we suffer a major impact about every 100 million years). For comets, the answer is slightly different -- since the comet nucleus is made of ice, a few meters of it evaporates each time it passes through perihelion --- and after a few hundred passages the nucleus is all gone.

50. False. Comet tails do not result from material being left behind in the orbit --- the sun pushes the evaporated gas directly away from the sun, and that creates the tail.

51. Meteors seen in a meteor shower result from small "sand" grains which have been shed by a comet relatively recently. They are therefore in orbits which are similar to the orbit of the comet. When the earth passes through this orbit, we run into the grains of sand which are visible as meteors. The meteor shower is characterized by an increase in the frequency of meteors, as well as the fact that they appear to come from a particular place in the sky (the radiant). Meteors at other times of the year are called sporadics. They have a more random distribution of orbits and so show no particular tendency to move in one direction or another. The originate, mostly, from fragments of asteroids resulting from asteroid/asteroid collisions.