Parapegma for Astronomical Twilight at Salt Lake City, Utah

Revised 6/26/2006

A parapegma is a table of rising constellations after sunset. In Greek and Roman times, persons would memorize their parapegma as common knowledge - much like we would memorize multiplication tables today. Using the table of rising constellations at sunset and knowing the number of seasonal hours at night for given month, it is possible to tell time at night. For example, in June Sagittarius is the rising zodiac constellation at astronomical twilight. There are 45 minutes or 3/4 of a standard hour to a seasonal hour. In 6 seasonal hours - or (6 * .75) 4 1/2 standard hours, Sagittarius will transit. That will occur at approximately 2:30 am in the morning.

The columns labelled "Zenith Constellation", "Transiting Equator", and "Transiting Zodiac" are useful for observation planning. Those are the constellations that will be most favorably positioned for viewing. Use this table to enter your guidebooks that are organized by constellation name. It is useful to look at the following month in the table when planning a night. Two hours after astronomical twilight, transiting constellations will be the ones listed in the following month.

In modern amateur practice, an analogous table is Table 1 - Approximate Sidereal Time in Volume One of Burnham's Celestial Handbook (p. 59). Such planning is normally done with a planisphere - an inexpensive disk that can be purchased at your local planetarium.

Table 1 - Parapegma for Astronomical Twilight at Salt Lake City, Utah

Date	Astronomical Twilight Time	Ecliptic Transit Altitude	Seasonal Hour	Due East Rising	Rising Zodiac	Zenith Constellation	Transit Right Ascension J2000	Transiting Equator	Transiting Zodiac	Setting Zodiac	Due West Setting	Season	Overnight Temp F	Percent Cloudy
3/1	19:50_MST	72	1:03	Vir	Vir	Cep	5h29m	Ori	Gem	Psc	Psc	Winter	31	52
4/1	21:27_MDT	67	0:56	Vir	Vir	Lyn	8h41m	Hyd	Cnc	Psc	Cet	Spring	38	47
5/1	22:09_MDT	52	0:50	Oph	Sco	Uma	11h21m	Leo	Leo	Tau	Ori	Spring	46	39
6/1	22:56_MDT	41	0:45	Aql	Sgr	Boo	14h10m	Vir	Vir	Gem	Hyd	Spring	55	20
7/1	23:08_MDT	27	0:44	Aqr	Cap	Her	16h21m	Oph	Sco	Cnc	Sex	Summer	64	13
8/1	22:33_MDT	45	0:48	Psc	Psc	Her	17h47m	Oph	Sgr	Vir	Vir	Summer	62	13
9/1	21:36_MDT	44	0:54	Psc	Psc	Lyr	18h53m	Aql	Sgr	Vir	Vir	Summer	51	17
10/1	20:41_MDT	44	1:01	Cet	Psc	Cyg	19h56m	Aql	Cap	Lib	Vir	Fall	40	29
11/1	18:56_MST	34	1:07	Cet	Tau	Cyg	21h09m	Aqr	Cap	Sco	Ser	Fall	31	47
12/1	18:36_MST	42	1:12	Ori	Gem	Lac	22h51m	Psc	Aqr	Sgr	Oph	Fall	22	58
1/1	18:49_MST	56	1:13	Mon	Cnc	And	1h07m	Psc	Psc	Cap	Aql	Winter	19	61
2/1	19:19_MST	69	1:09	Hyd	Leo	Per	3h39m	Ari	Tau	Aqr	Aqr	Winter	25	57

Prepared by and report errors or broken links to: K. Fisher 6/2006 fisherka@csolutions.net.