version 4.0 - February 12th, 2001   Positions of the real stars   1. Table of the real stars   2. Table of the real DSOs   3. Explanations on the tables   4. Maps on the tables   5. Three-dimensional view

With this exclusive collection of all real stars or deep sky objects (DSOs) mentioned in Star Trek, their coordinates and distances in a never achieved precision, thanks to the use of the most recent data from the HIPPARCOS catalogue, and their calculated two-dimensional distances and relative coordinates in the galactic plane, you are now able to draw exact maps of the Star Trek universe for the first time.

The already fourth version of the "Positions of the real stars" contains heavily extended and much more precise information on 39 stars (four additional ones compared with former versions) and on 4 deep space sky objects (in this version for the first time). Also for the first time, the given, different absolute coordinates are based on the revised distance of the sun from the Galactic center: 7.9kpc (25800 ly).

This unique data collection based on a Microsoft Excel spreadsheet, which has been continuously developed since October 1999, would not have been possible without the theoretical preliminary work of Masao Okazaki, who helped me to understand what galactic coordinates are and how I can calculate map distances and directions with them, and Bernd Schneider of Ex Astris Scientia, who submitted the first HIPPARCOS figures of the most important stars to me.

1. Table of the real stars

Identification			Celestial coordinates		Distance		Galactic coordinates			Position relative to Earth			Position in the Galaxy		Cartesic position		Polar position		Additional information
Appearance	Name	Bayer notation	a	d	Parallax	Dist (ly)	l	b	Plane dist	XRel (ly)	YRel (ly)	ZRel (ly)	X (ly)	Y (ly)	X0 (ly)	Y0 (ly)	r (ly)	phi (�)	Arity	Spectrum / Luminosity
	Acamar	Theta Eridani	-	-	20	163.091	244	-61	79.07	71.07	34.66	-142.64	50071.07	75834.66	71.07	-25834.66	25834.7588	270.1576	binary	A3, A2
	Aldebaran	Alpha Tauri*	68.98	16.51	50	65.236	181.33	-19.65	61.44	1.43	61.42	-21.94	50001.43	75861.42	1.43	-25861.42	25861.4206	270.0032	quartern�r	K5III, M2V, -, -
		Alpha Centauri*	219.92	-60.835	742.12	4.395	315	-1.08	4.39	3.11	-3.11	-0.08	50003.11	75796.89	3.11	-25796.89	25796.8928	270.0069	trinary	G2V, K4V, M5eV
		Alpha Eridani*	24.428	-57.237	23	141.818	290	-58.95	73.15	68.74	-25.02	-121.50	50068.74	75774.98	68.74	-25774.98	25775.0737	270.1528	single	B3pV
	Altair	Alpha Aquilae*	297.695	8.867	194.44	16.775	47.39	-9.8	16.53	-12.17	-11.19	-2.86	49987.83	75788.81	-12.17	-25788.81	25788.8116	269.9730	single	A7V
	Antares	Alpha Scorpii*	247.352	-26.432	5.4	604.039	352	14.47	584.88	81.40	-579.19	150.93	50081.40	75220.81	81.40	-25220.81	25220.9451	270.1849	binary	M1Ib, B4V-VI
	Arcturus	Alpha Bootis**	213.918	19.187	88.85	36.711	16	68.51	13.45	-3.71	-12.93	34.16	49996.29	75787.07	-3.71	-25787.07	25787.0724	269.9918	single	K2peIII
	Bellatrix	Gamma Orionis*	81.283	6.35	13.42	243.056	197.24	-15.36	234.37	69.46	223.84	-64.38	50069.46	76023.84	69.46	-26023.84	26023.9369	270.1529	single	B2III-V
		Beta Aurigae*	89.882	44.947	39.72	82.120	167.76	10.98	80.62	-17.09	78.78	15.64	49982.91	75878.78	-17.09	-25878.78	25878.7899	269.9622	single	A2IV
	Betelgeuse	Alpha Orionis**	88.793	7.407	7.63	427.498	200.11	-8.37	422.94	145.42	397.16	-62.23	50145.42	76197.16	145.42	-26197.16	26197.5633	270.3180	single	M2Ib
	Canopus	Alpha Carinae*	95.988	-52.696	10.43	312.734	262	-25.14	283.11	280.35	39.40	-132.86	50280.35	75839.40	280.35	-25839.40	25840.9220	270.6216	single	F0Ib
	Capella	Alpha Aurigae*	79.172	45.999	77.29	42.202	162.91	5.12	42.03	-12.35	40.18	3.77	49987.65	75840.18	-12.35	-25840.18	25840.1808	269.9726	quartern�r	G5III, G0III, M2V, M4V-VI
	Cor Caroli	Alpha Canum Ventat.	-	-	30	108.727	118	78	22.61	-19.96	10.61	106.35	49980.04	75810.61	-19.96	-25810.61	25810.6204	269.9557	single	A0
	Deneb	Alpha Cygni*	310.358	45.28	1.01	3229.516	84.61	1.87	3227.80	-3213.52	-303.20	105.39	46786.48	75496.80	-3213.52	-25496.80	25698.5110	262.8165	single	A2Ia
		Epsilon Hydrae			24	135.909	221	29	118.87	77.98	89.71	65.89	50077.98	75889.71	77.98	-25889.71	25889.8287	270.1726	single	G0
		Epsilon Indi*	330.823	-56.78	275.76	11.828	339	-48.57	7.83	2.80	-7.31	-8.87	50002.80	75792.69	2.80	-25792.69	25792.6931	270.0062	single	K5eV
		Gamma Hydrae	-	-	25	130.472	311	39	101.40	76.52	-66.52	82.11	50076.52	75733.48	76.52	-25733.48	25733.5919	270.1704	single	G5
		Gamma Tauri	-	-	-	326.000	179	-24	297.82	-5.20	297.77	-132.60	49994.80	76097.77	-5.20	-26097.77	26097.7710	269.9886	single	K0
		Gamma Trianguli	-	-	-	91.000	143	-26	81.79	-49.22	65.32	-39.89	49950.78	75865.32	-49.22	-25865.32	25865.3674	269.8910	single	A0
	Izar	Epsilon Bootis*	221.247	27.074	15.55	209.763	39.04	64.27	91.06	-57.36	-70.73	188.96	49942.64	75729.27	-57.36	-25729.27	25729.3336	269.8723	single	K0
	Merak	Beta Ursae Majoris	165.46	56.382	41.07	79.421	148.98	55.28	45.24	-23.31	38.77	65.28	49976.69	75838.77	-23.31	-25838.77	25838.7767	269.9483	single	A1V
	Mintaka	Delta Orionis*	83.002	-0.299	3.56	916.239	204.14	-17.17	875.41	358.01	798.85	-270.48	50358.01	76598.85	358.01	-26598.85	26601.2593	270.7711	single	B0
	Mira	Omicron Ceti			-	418.000	167	-57	227.66	-51.21	221.82	-350.56	49948.79	76021.82	-51.21	-26021.82	26021.8746	269.8872	single	M6eIII
	Mizar	Zeta Ursae Majoris	200.981	54.925	41.73	78.165	112.37	61.75	37.00	-34.21	14.08	68.85	49965.79	75814.08	-34.21	-25814.08	25814.1032	269.9241	binary	A2, A6
	Pollux	Beta Geminorum*	116.331	28.026	96.74	33.717	192.6	24.01	30.80	6.72	30.06	13.72	50006.72	75830.06	6.72	-25830.06	25830.0590	270.0149	single	K0IIIb
	Regulus	Alpha Leonis*	152.094	11.967	42.09	77.496	227	49.39	50.44	36.89	34.40	58.83	50036.89	75834.40	36.89	-25834.40	25834.4282	270.0818	trinary	B7V, K1V, MV
	Rigel	Beta Orionis*	78.634	-8.202	4.22	772.941	209.47	-24.69	702.28	345.50	611.41	-322.86	50345.50	76411.41	345.50	-26411.41	26413.6739	270.7495	single	B8Ia
	Sheliak	Beta Lyrae*	282.52	33.363	3.7	881.571	63.4	14.45	853.68	-763.32	-382.24	219.98	49236.68	75417.76	-763.32	-25417.76	25429.2149	268.2799	binary	B8, B2
		Sigma Draconis*	293.086	69.665	173.41	18.810	101.41	21.93	17.45	-17.10	3.45	7.02	49982.90	75803.45	-17.10	-25803.45	25803.4575	269.9620	single	K0V
	Sirius	Alpha Canis Majoris*	101.289	-16.713	379.21	8.602	227	-8.44	8.51	6.22	5.80	-1.26	50006.22	75805.80	6.22	-25805.80	25805.8035	270.0138	single	A1V
	Sol	keine**	-	-	-	0	0	0	0.00	0.00	0.00	0.00	50000.00	75800.00	0.00	-25800.00	25800.0000	270.0000	single	G2V
	Spica	Alpha Virginis**	201.298	-11.161	12.44	262.204	316	50.45	166.96	115.98	-120.10	202.18	50115.98	75679.90	115.98	-25679.90	25680.1620	270.2588	binary	B1V, B7V
		Tau Ceti*	26.021	-15.94	274.17	11.897	173.9	-72.85	3.51	-0.37	3.49	-11.37	49999.63	75803.49	-0.37	-25803.49	25803.4883	269.9992	single	G8pV
		Theta Cygni	-	-	-	60.690	87	14	58.89	-58.81	-3.08	14.68	49941.19	75796.92	-58.81	-25796.92	25796.9851	269.8694	binary	F4V, MV
	Vega	Alpha Lyrae*	279.234	38.783	128.93	25.299	67.61	18.94	23.93	-22.13	-9.11	8.21	49977.87	75790.89	-22.13	-25790.89	25790.8946	269.9508	single	A0V
	"Velara"	Plejaden, Tau**	56.75	24.7	-	415.000	166.57	-22.52	383.35	-89.04	372.87	-158.95	49910.96	76172.87	-89.04	-26172.87	26173.0229	269.8051	single	G?
	"Vulcan"	o� (40) Eridani A*	63.823	-7.645	198.24	16.454	200.97	-37.46	13.06	4.67	12.20	-10.01	50004.67	75812.20	4.67	-25812.20	25812.1961	270.0104	trinary	K1eV, DA4wd, M4eV
	Wolf 359	keine*	-	-	-	7.803	247	54	4.59	4.22	1.79	6.31	50004.22	75801.79	4.22	-25801.79	25801.7924	270.0094	single	M6eV
	Zibal	Zeta Eridani	-	-	-	130.400	171	-52	80.28	-12.56	79.29	-102.76	49987.44	75879.29	-12.56	-25879.29	25879.2969	269.9722	single	A5

2. Table of the DSOs

Identification			Celestial coordinates		Distance		Galactic coordinates			Position relative to Earth			Position in the Galaxy		Cartesic position		Polar position		Additional information
Appearance	Name	Catalogue number	a	d	Parallax	Dist (ly)	l	b	Plane dist	XRel (ly)	YRel (ly)	ZRel (ly)	X (ly)	Y (ly)	X0 (ly)	Y0 (ly)	r (ly)	phi (�)	Classification	Diameter
	Crab nebula	M1 / NGC1952, Tau	83.625	22.1	-	3260	184.82	-5.14	3246.89	272.82	3235.41	-292.06	50272.82	79035.41	272.82	-29035.41	29036.6901	270.5383	Diffuse nebula	10 ly
	Helical nebula	NGC 7293, Aqr	337.4	-20.48	-	450	37.6	-57.52	241.65	-147.44	-191.46	-379.61	49852.56	75608.54	-147.44	-25608.54	25608.9658	269.6701	Planetary nebula	1.75 ly
	Orion nebula	M42 / NGC 1976, Ori	83.725	-5.32	-	1630	209.16	-18.88	1542.30	751.49	1346.84	-527.45	50751.49	77146.84	751.49	-27146.84	27157.2351	271.5857	Diffuse nebula	30 ly
	Pleiades	M45 / NGC 1432, Tau	56.75	24.7	-	415	166.57	-22.52	383.35	-89.04	372.87	-158.95	49910.96	76172.87	-89.04	-26172.87	26173.0229	269.8051	Open cluster	40 ly

3. Explanations on the tables

Identification (stars) - appearance (not to scale), Arabic designation and Bayer notation of the real star or star system.
Stars whose distances or galactic coordinates were altered or replaced by more precise values in this version are marked with a (�). All stars which have a (**) were newly added to the table.
Our sun ("Sol") is per definition a "real Star Trek star", too, even though this may sound paradoxical first. Fictitious Star Trek stars like Velara and Vulcan are marked by inverted commas. They were added to the list because we know their real reference star or the real reference region of space. These references are given in the second column.

Identification (DSOs) - a real mini-photo, the common designation of the real deep sky object (mostly nebulae), its catalogue number and the constellation where it can be found. "M" refers to the historical Messier catalogue, "NGC" to the also quite old, but still often-used New General Catalogue.

Distance - the parallax of the star and the derived distance from Earth in light years (Distance=1pc/parallax p; 1pc=3.26 ly). All distances are super-precise and up-to-date figures from the HIPPARCOS catalogue, except the deep sky objects and the following stars: Gamma Hydrae, Gamma Tauri, Gamma Trianguli, Velara, Zibal.  These distances taken from other sources do not include parallaxes.

Celestial coordinates - The coordinates of the object in the Earth-bound equatorial system, which is, however, independent of time and place. The figures include the right ascension RA and the declination d. Both values are given in degrees. The right ascension refers to the arc between vernal point (the intersection of equator and ecliptic) and the declination circle running through the celestial object, measured on the celestical equator. The angles are between 0� and 360�. The declination is the object's angular distance from the celestial equator. The declination, including values between -90� and +90�, is positive if the object is located north from the equator, and negative if it is situated south of the equator. The celestial coordinates, however, are only available here if they have been used for the calculation of the corresponding galactic coordinates (and therefore all positions of the real stars).

Galactic coordinates - Galactic longitude and latitude in degrees. The galactic longitude is the direction angle of the object projected on the hypothetical galactic sphere, relative to its center, Earth. The galactic longitude is based on a counter-clockwise system, i.e. l=0 puts the object right to the north of Earth and l=90� puts it right to the west of Earth etc., provided that we look at the galactic sphere/Milky Way from above. The galactic latitude b is the elevation angle. A galactic latitude of more than 0� means that the object is located above the "equator" of the galactic sphere (therefore in the same height like Earth), and a latitude of less than 0� that the is located below the equator. The galactic latitude determines decisively the apparent distance of the object relative to Earth, if we consider the galactic sphere, looked at from above, as a two-dimensional galactic plane. The bigger is the amount of the galactic latitude, the smaller will appear the distance of the object relative to Earth on the map. This is the third figure, the distance on the galactic plane, calculated by trigonometry with the real distance and the galactic latitude.

Position relative to Earth - X and Y distances of the object from Earth in light years, calculated by trigonometry with the direction angle (galactic longitude) and the plane distance, and Z distance from Earth in light years, derived from the elevation angle (galactic latitude) and the real distance. If you want to create a map of the galactic plane (top view) scaled 1 ly = 1 px, you can directly use the X and Y values (horizontal / vertical distances) as pixel distances.

Position in the Galaxy - The absolute, two-dimensional coordinates in the Milky Way, based on a Cartesian coordinate system with the upper left corner (0;0) and the lower right corner (100000;100000). In this system, Earth is located at the coordinates (50000;74000).

Cartesic position - The absolute coordinates in a different Cartesian coordinate system of the plane. The point (0;0) being located in the center of the Galaxy, the 4 quadrants of the coordinate system correspond to the 4 galactic quadrants (Alpha=III, Beta=IV, Gamma=II, Delta=I). Consequently, the system has the advantage that the galactic quadrant can be derived from the sign of the x and y coordinates: position in Alpha Quadrant - x negative, y negative; position in Beta Quadrant - x positive, y negative; position in Gamma Quadrant - x negative, y positive and position in Delta Quadrant - x positive, y positive.

Polar position - The absolute galactic position in a polar coordinate system. The point (0;0) is again located in the center of the Galaxy, but in this system, the position of the star is unambiguously determined by its distance r to the point (0;0) and its angle phi (between 0� and 360�, counter-clockwise) between the x axis and the line running through the object and the point (0;0). Consequently, the galactic quadrant in which the object is located can be easily derived from the angle phi: Delta Quadrant -  phi from 0� to 90�; Gamma Quadrant - phi from 90� to 180�; Alpha Quadrant - phi from 180� to 270� and Beta Quadrant - phi from 270� to 360�=0�.

Additional information (stars) - Further characteristics of the stars not relevant to their position in the Galaxy, which are nevertheless important for creating galactic maps: the spectrum of the star (and the accompanying stars in case it is a star system), from which the size and color can be derived, and the classification of the star as single star or member of a complex system (binary/trinary/quaternary).

Additional information (DSOs) - A classification of the deep sky object and determination of its diameter, which are not relevant to their position in the Galaxy but could be necessary for creating maps. Differentiated categories are nebulae (diffuse/planetary) and (open) clusters.

4. Maps on the tables

The following maps in the format 630x650 pixels (file size app. 165 KB each) were created with a program on the basis of the positions of the stars and DSOs in the Galaxy and have been subsequently heavily post-edited in order to be both graphically convincing and user-friendly. For a better overall view, the maps 1 to 4 are not named but numbered. Hence, please pay attention to the legend below.

5. Three-dimensional view

Beside the usual two-dimensional maps of the galactic planes, also a real 3D view of the galaxy can be created using the x , y and z distances of the stars from Earth. However, a 3D system is needed to transform the coordinates into a visual image. The following script, that was recreated for version 4 of "Positions of the real stars", uses the established 3D markup language VRML 1.0 to display all real stars of Star Trek in space. Therefore, using a VRML viewer (i.e. the Platinum plugin for Internet Explorer 5.0, shipped as "vrml2c.exe" with the installation files), you can now make a virtual trip through the Galaxy for the first time.

Back to the Star Trek Cartography overview

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