Astronomy Quiz #3

19. What is the full moon's approximate visual size in degrees? in arcminutes?

0.5° or 30 arcminutes

20. What is the sun's approximate visual size in degrees? in arcminutes?

0.5° or 30 arcminutes

17. How many degrees are in a circle? How many arcminutes are in a circle? How many arcseconds are in a circle?

360° in a circle 21,600 arcminutes in a circle (360 x 60 = 21,600) 1,296,000 arcseconds in a circle (360 x 60 x 60 = 1,296,000)

14. On what approximate date does the sun attain an RA of 12h and a DEC of 0°? What is that day called?

September 23....the Autumnal Equinox or Fall Equinox or the First Day of Fall

11. When a celestial object's right ascension value (RA) and the local sidereal time (LST ) are equal, what happens?

transit....the object is momentarily on the celestial meridian

18. Each degree of arc can be divided into how many arcminutes? Each arcminute can be divided into how many arcseconds?

60 arcminutes per degree 60 arcseconds per arcminute

16. The sun changes its RA value by about how many degrees per day? How many minutes of change does this represent? What causes this change to occur?

About 1° per day....the sun's movement in right ascension is actually a reflection of the earth's own movement around the sun. The earth must complete a full orbit of the sun (360°) in one year (365.25 days). 360° / 365.25 days = a little less than 1° per day. 1° is 1/360 of an orbit or 1/360 of 24h of RA. 24h / 360 = .0666h of RA per day, and .0666h x 60m/hr = 4m. The sun "appears" to move about 1° per day around the sun or, viewed another way, it seems to add about 4 minutes per day to its right ascension value, beginning from 0h on the First Day of Spring. In actuality, it is the earth which is moving, not the sun, but since it is not possible to sense our own movement on earth, we note our own orbital movement indirectly by watching the sun "seem" to move against the back- ground of stars in right ascension every day.

9. What common terms are used for 24-hour time at the prime meridian?

Greenwich Mean Time (GMT) Universal Time (UT) Universal Coordinated Time or Universal Time Coordinated (UTC) Zulu Time (Z)

7. Explain how to find the celestial equator in the sky. Why is this line particularly important?

Calculate the MCP for your latitude. Then locate this point along the celestial meridian. Finally, connect this point with the east point on the horizon and the west point on the horizon. For observers at Chattanooga, this means connecting the east point, a point on the celestial meridian which is 55° above the south point, and the west point. Any point on the celestial equator represents 0° declination (DEC). All stars with a positive declination lie north of this line. All stars with a negative declination lie south of this line.

4. How can you easily determine which stars will be circumpolar at your location?

Calculate your MCP value: MCP = 90° - Latitude. Any stars with a declination (DEC) value greater than the MCP will be circumpolar at Chattanooga. At Chattanooga: MCP = 90° - 35° = 55°. Any star with a DEC value between +55° and +90° will be circumpolar. For an observer at 50° N latitude: MCP = 90° - 50° = 40°. Any star with a DEC value between +40° and +90° will be circumpolar at this location. For an observer at 90° N latitude (the north pole): MCP = 90° - 90° = 0°. Any star with a DEC value between 0° and +90° will be circumpolar, and since the celestial equator lies on the horizon at the north pole, all visible stars there will be circumpolar.

3. Stars which never rise or set have a special name. What is it? Why do they not rise or set?

Circumpolar stars. They lie so close to Polaris that they trace circles around it without ever dropping below the horizon.

6. Explain how to find the celestial meridian in the sky, and explain again why this line is particularly important. How often do most stars cross this line? A few stars will cross it twice each day....which stars are these? What are the terms for the two transits?

Connect the north point on the horizon, the zenith, and the south point on the horizon. All celestial objects must cross this north-south line at least once in every 24 hour period (a few stars will cross it twice). For those stars which transit only once, the moment of transit will coincide with the object's highest altitude and therefore with its most optimum observation time. Circumpolar stars will cross this line twice in every 24 hour period (every 12 hours). They will cross the line above the NCP (Polaris) and then below the NCP. These two transits are called "upper transit" and "lower transit." Upper transit will occur higher in the sky, and lower transit will occur closer to the horizon.

21. Be able to solve a simple transit problem at Chattanooga for today using Heavens-Above.

Data needed for any transit calculation: a. LST (from app if the calculation is for today) b. Clock Time (AM or PM)—taken at the moment LST is recorded Both times rounded off to the nearest half-hour (round up at 15m and 45m) c. RA of a celestial object d. DEC of the same celestial object Transit Time Procedure: a. Always work from LST to RA b. Figure out how much time to add (+) or subtract (-) from LST to get to RA c. Note +hrs or -hrs (count carefully!) d. Apply +hrs or -hrs to Clock Time = Transit Time (note AM or PM) Transit Altitude Procedure: a. Find the MCP for your latitude (MCP = 90° - Latitude) b. If the DEC is positive, add it to the MCP c. If the DEC is negative, subtract it from the MCP d. The result is Transit Altitude in degrees above the south point on the horizon EX: LST = 4h Clock = 2 PM RA = 10h DEC = - 20° Latitude = 35° N (Chattanooga) LST→ RA 4h + 6h = 10h 2 PM + 6h = 8 PM Transit Time MCP = 55° (at Chattanooga) - 20° = 35° Transit Altitude

15. On what approximate date does the sun attain an RA of 18h and a DEC of -23.5°? What is that day called?

December 21.....the Winter Solstice or the First Day of Winter

23. Given the LST during the day, determine what hour circles will be visible that night at a particular observation time. Know which hour circles will be east and which ones will be west of the meridian at that time.

Here's the procedure: a. For today, find the LST using your app and make note of Clock Time when you do so. For a day other than today, find the LST at local noon using the procedure in #22 above. b. Settle on a specific observation time that evening. c. Determine how many hours must elapse until the observation time. d. Add x hours to LST to find the LST at your observation time. e. This will be the hour circle on the celestial meridian at your observation time. Assume you are facing the southern end of the celestial meridian. Hour circles with higher numbers will be east of the meridian and rising. They will be toward your left. Hour circles with lower numbers will be west of the meridian and setting. They will be toward your right. Graphic solution: a. Draw a horizontal line to represent the horizon with your observation time under it b. Label the left end of the line EAST and the right end WEST c. Draw a vertical line perpendicular to the horizon at the midpoint d. Label the vertical line CELESTIAL MERIDIAN or CM e. Label it also with the LST at your observation time f. Draw a spoke half way between the horizon and CM on the east side of the CM g. Draw a spoke half way between the horizon and CM on the west side of the CM h. Draw two more spokes above and below these half-way spokes...on both sides i. You should now have 5 spokes between the horizon and vertical on both sides j. All spokes should be equally spaced...each will represent 15° of arc (1 hour of time) k. Label each spoke to the left (EAST) of the CM by adding an hour to each one l. Label each spoke to the right (WEST) of the CM by subtracting an hour from each one Don't forget that one hour less than 1h RA is 0h RA, and one hour less than that is 23h. Also, 23h + 1h = 0h. EX: Suppose the current LST is 13h and the current time is 11 AM. Find the range of hour circles which will be visible at 10 PM tonight. CURRENT CLOCK: 11 AM CURRENT LST: 13h HOURS TO OBSERVATION TIME: 11h LST AT OBSERVATION TIME: 13h + 11h = 24h = 0h Label your vertical CM line 0h Spoke labels moving leftward (EAST): 1h 2h 3h 4h 5h 6h (horizon line) Spoke labels moving rightward (WEST): 23h 22h 21h 20h 19h 18h (horizon line) Remember: Your LST clock at the observation time will read 0h. The sky rotates east to west or from your left to your right. The hour circle 15° to your left will line up with the celestial meridian in one hour, and at that moment your LST clock will read 1h. LST and RA are always equal at transit. Thus, the higher LST hours to come must lie eastward, and the lower elapsed LST times must be westward.

13. On what approximate date does the sun attain an RA of 6h and a DEC of +23.5°? What is that day called?

June 21.....the Summer Solstice or the First Day of Summer

12. On what approximate date does the sun attain an RA of 0h and a DEC of 0°? What is that day called?

March 21.....the Vernal Equinox or the First Day of Spring

Do all stars rise and set for an observer at the north pole? for an observer at the equator? for an observer at the latitude of Chattanooga?

No. All stars are circumpolar for an observer at the north pole, since Polaris lies at the zenith. All stars simply trace circles around Polaris. Yes. All stars rise and set for an observer at the equator, including Polaris. Of course, celestial objects near the horizon are notoriously difficult to see. Some but not all stars rise and set for an observer at Chattanooga's latitude. Those lying close to Polaris simply circle it and are always in the sky. Those farther away from Polaris will rise and set.

5. Are all stars visible to an observer at the north pole? If not, what stars are not visible? Are all stars visible to an observer at the south pole? If not, what stars are not visible? Are all stars visible to an observer at the equator? If not, what stars are not visible? Are all stars visible to an observer at the latitude of Chattanooga? If not, how can you determine which stars will not be visible?

No. An observer at the north pole can only see stars with positive declination values (0° to +90° DEC). That is because the NCP (Polaris) is at the zenith and the celestial equator is on the horizon (the DEC of the celestial equator is 0°). All negative values of DEC will be invisible. No. An observer at the south pole can only see stars with negative declination values (0° to - 90° DEC). The SCP is at the zenith, and the celestial equator is on the horizon. All stars with a positive DEC value lie below the horizon and are invisible. Yes, at least theoretically. A thick blanket of air at the horizon, however, makes observation of objects near the horizon difficult or impossible. Only observers near the equator, however, can see virtually all of the stars of the celestial sphere. No. Some stars will always lie below the horizon at Chattanooga because they simply lie too far south on the celestial sphere. An observer at Chattanooga can see all stars with a positive DEC value but only some stars with negative DEC values. Stars which are invisible at a particular latitude north of the equator are those whose DEC values are more negative than the MCP value. Since the MCP at Chattanooga is 55°, any stars with DEC values between - 55° and - 90° will be invisible. They will simply never rise at Chattanooga. This fact can be confirmed by the Transit Altitude formula: TA = MCP +/- DEC = 55° - 55° = 0° This object (DEC = - 55°) will just graze the horizon at transit TA = MCP +/- DEC = 55° - 85° = - 30° This object (DEC = - 85°) will still be 30° below the horizon at transit

8. Be able to plot a planet's daily altitude and azimuth using Heavens-Above (see your notes for Day #10).

See your class notes for Day #10. Collect Altitude and Azimuth data from Heavens- Above for every hour of the day when the altitude is positive. Plot the points and connect the dots.

10. How is the earth's equator related to the celestial equator? How is a line of declination related to a line of latitude? How is a line of right ascension (also called an "hour circle") related to a line of longitude?

The celestial equator is just the earth's equator expanded out into space. Similarly, a line of latitude extended out into space becomes a line of declination, and a line of longitude extended out into space becomes a line of right ascension or hour circle.

For observers in the northern hemisphere, what does the altitude of the North Star (Polaris) above the northern horizon indicate? Why is this not true for observers in the southern hemisphere?

The observer's approximate latitude Because Polaris lies below the horizon and is not visible to observers south of the equator.

22. Be able to solve a simple transit problem at Chattanooga for a day different from today using Heavens-Above.

The procedure for doing a transit calculation for a different day than today is the same as in #21 above, EXCEPT: You must find Clock Time and LST by going to Heavens-Above, logging in, and doing the following: a. Go to the SUN link b. Note the time under MAX ALTITUDE If the time is 13:00 or later, subtract 12h and express it as PM This time is the sun's local transit time on that day c. At the same time, note the sun's RA....this value will be the LST at solar transit Round off both times to the nearest half hour Now proceed as usual in #21 above EX: Calculate Transit Time and Transit Altitude for this celestial object: Date: November 21, 2018 RA: 18h DEC: +45° Latitude: 35° N (Chattanooga) Clock = Max Alt = 12:27 PM = 12:30 PM LST = RAsun = 15h47m = 16h LST → RA 16h + 2h = 18h 12:30 PM + 2h = 2:30 PM Transit Time MCP = 55° (at Chattanooga) + 45° = 100° Transit Altitude