In consultation with the other members of your group, solve the problem highlighted below. If you finish your assigned problem quickly, try one of the other problems as well.
Note: Bloomington is located at latitude 39o 09.9' and longitude 86o 31.5'.
1. Draw the view of the celestial sphere from Bloomington.
Label the cardinal directions, the north celestial pole (NCP), the altitude of the
NCP, zenith, horizon, and meridian. What is the declination
at zenith?
The altitude of the NCP = latitude = 39.165o.
The declination at zenith = latitude = 39.165o
2.
What declination ranges will be circumpolar in Bloomington; what declination ranges
will be circumpolar for the following four observatories?
| Observatory | longitude | latitude | height (m) |
| deg min | deg min | ||
| Kitt Peak, AZ | -111 36.0 | +31 57.8 | 2120 |
| Palomar, CA | -116 51.8 | +33 21.4 | 1706 |
| Mauna Kea, HI | -155 28.2 | +19 49.4 | 4214 |
| Cerro Tololo, Chile | -70 48.9 | -30 09.9 | 2215 |
The declination range for circumpolar stars are given by:
90 - latitude < declination < 90o for northern hemisphere
-90 - latitude > declination > -90o for southern hemisphere
Bloomington: 50.84o < decl. < 90.o
Kitt Peak: 58.04o < decl. < 90.o
Palomar: 56.64o < decl. < 90.o
Mauna Kea: 70.18o < decl. < 90.o
CTIO: -59.84 o > decl. > -90.o
3. What is the declination at zenith for the four observatories listed in Problem 2? What is the altitude of the north celestial pole for the four observatories listed in Problem 2?
The declination at zenith = latitude; the altitude of the NCP = latitude.
Bloomington: decl. at zenith= 39.165o; altitude of NCP = 39.165o
Kitt Peak: decl. at zenith= 31.963o; altitude of NCP = 31.963o
Palomar: decl. at zenith= 33.357o; altitude of NCP = 33.357o
Mauna Kea: decl. at zenith= 19.823o; altitude of NCP = 19.823o
CTIO: decl. at zenith= -30.165o; altitude of NCP = ...
(for CTIO, the NCP is below the horizon).
4. The Subaru telescope is located atop Mauna Kea, HI at a latitude of N 19.82o. On how many days of the year, if any, is the Sun at the zenith at midday as seen from the Subaru dome? On how many days is the Sun at the zenith as seen from Palomar Observatory (latitude = N 33.36o)?
The sun is at zenith twice during the year as seen from Mauna Kea, once shortly before summer solstice, as the sun is moving towards its apex at decl. = 23.5o, and once shortly after summer solstice, as the sun's declination decreases.
The sun is never seen at the zenith at Palomar Observatory since the maximum declination of the sun is 23.5o, well short of the 33.357o of Palomar's zenith.
5. What is the sidereal time when the vernal equinox rises? On what date is the sidereal time nearly equal to the solar time?
The sidereal time is the equivalent of the right ascension of objects going through upper transit. The vernal equinox (by definition) has a right ascension of 0hr. If the vernal equinox is rising, the sidereal time must be 6 hours prior to its transit, or LST = 18:00.
The sidereal time is nearly equal to the solar time on the autumnal equinox.