In the material following the letter, I've gone some steps further and used some basic celestial mechanics and geometry to determine the appearance of the Vulcan sky--for those who are interested.
First, Gene's letter:
This year we celebrate the 25th anniversary of the launch of two important enterprises. One is the HK Project at Mount Wilson Observatory, where astronomers have been monitoring surface magnetic activity on 100 solar-type stars to understand our own Sun's magnetic history. The other is the starship Enterprise on the television series "Star Trek."
Surprisingly, the two have more in common than their silver anniversaries.
One of the TV show's main characters, Mr Spock, hails from the planet Vulcan. The star around which Vulcan orbits was never identified in the original series or in any of the feature films based on it and so has never been officially established. But two candidates have been suggested in related literature, and both stars have been studied by the HK project.
"Star Trek 2" by James Blish (Bantam, 1968) and "Star Trek Maps" by Jeff Maynard and others (Bantam, 1980) name the star 40 Eridani as Vulcan's sun. "The Star Trek Spaceflight Chronology" by Stan and Fred Goldstein (Pocket, 1980) cites Epsilon Eridani instead.
We prefer the identification of 40 Eridani as Vulcan's sun because of what we have learned about both stars at Mount Wilson. The HK Project takes its name from the violet H and K lines of calcium, both sensitive tracers of stellar magnetism. It turns out that the average level of magnetic activity inferred from the H and K absorptions relates to a star's age; young stars tend to be more active than old ones (Sky & Telescope: December 1990, page 589). The HK observations suggest that 40 Eridani is 4 billion years old, about the same age as the Sun. In contrast, Epsilon Eridani is barely 1 billion years old.
Based on the history of life on Earth, life on any planet around Epsilon Eridani would not have had time to evolve beyond the level of bacteria. On the other hand, an intelligent civilization could have evolved over the aeons on a planet circling 40 Eridani. So the latter is the more likely Vulcan sun.
In that case, Mr Spock's daytime star is a 4.4-magnitude multiple system about 16 light-years from Earth. Presumably Vulcan orbits the primary star, an orange main-sequence dwarf of spectral type K1. Data from the HK Project reveal that it has a starspot cycle of roughly 11 years, just like the Sun. [Diagram here of 40 Eridani's starspot cycle, showing that the latest peak in starspot activity was in 1989.]
Two companion stars--a 9th-magnitude white dwarf and an 11th-magnitude red dwarf--orbit each other about 400 astronomical units from the primary. They would gleam brilliantly in the Vulcan sky with apparent magnitudes -8 and -6, respectively.
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Now the more detailed stuff.
40 Eridani--also known as Omicron 2 Eridani--is a fascinating trinary system located at a distance of only 4.9 parsecs (about 16 light-years) from Earth. The system consists of three stars: 40 Eridani A, B, and C.
The following information is in three parts:
1. A Technical Description of the 40 Eridani System: for those who understand and are interested in the technical details.
2. A View From Vulcan: What the system would look like from Vulcan.
3. A View From Earth: How to go out and see the system for yourself.
40 Eridani A, the primary star (and Vulcan's sun) is an orange main-sequence dwarf of spectral type K1 V, which makes it a cousin to our own Sun. (It's interesting that the star is an orange one; I seem to remember--from ST:TMP-- that the light on Vulcan is decidedly orange.) Below are the star's other specs, as compared to those of the Sun:
Surface temperature: 5000 deg K (Sun = 6000 deg K)
Luminosity: 30% of the Sun's
Diameter: 783,000 mi. = 90% of the Sun's
Mass: 75% of the Sun's
Density: 4% greater than the Sun's (almost identical)
Absolute magnitude: 6.0 (Sun = 4.75)
40 Eridani B and C, the other two stars in this trinary system, are both situated 400 AU (about 2 light-days or 40 billion miles) from 40 Eridani A-- an enormous distance. 40 Eridani B and C orbit *each other* every 248 earth- years, at an average distance from each other of 44 AU (about 4.1 billion miles, greater than the distance from the Sun to Pluto). In turn, 40 Eridani B and C--*together*--orbit 40 Eridani A every 8000 or so earth-years.
40 Eridani B is a white dwarf of spectral type A VII. Below are the star's other specs, as compared to those of the Sun:
Surface temperature: 13,000 deg K (Sun = 6000 deg K)
Luminosity: 0.27% of the Sun's
Diameter: 17,000 mi. = 1.9% of the Sun's
Mass: 44% of the Sun's
Density: 65,000 times greater than the Sun's
Absolute magnitude: 11.2 (Sun = 4.75)
The enormous density of 40 Eridani B is typical of a white dwarf: 44% of the Sun's mass crammed into a sphere only twice the diameter of the earth. The stellar material of 40 Eridani B is 90,000 times denser than water; a cubic inch of it weighs 2 tons, and the surface gravity of the star is 37,000 times that of Earth.
40 Eridani C is a very faint red main-sequence dwarf of spectral type M4e V. Below are the star's other specs, as compared to those of the Sun:
Surface temperature: 3000 deg K (Sun = 6000 deg K)
Luminosity: 0.08% of the Sun's
Diameter: 374,100 mi. = 43% of the Sun's
Mass: 20% of the Sun's
Density: 80% greater than the Sun's
Absolute magnitude: 12.3 (Sun = 4.75)
In order for 40 Eridani A (Vulcan's sun) to shine in the Vulcan sky at approximately the same magnitude as the Sun does in ours, Vulcan must orbit the star at a distance of 0.56 AU or 52,360,000 mi. (equivalent to a solar orbit about halfway between Mercury and Venus). At this distance, 40 Eridani A would appear from Vulcan as a disk 0.86 arc-degrees in diameter, about 62% larger than the Sun appears to us.
40 Eridani B and C are much too far away from 40 Eridani A to appear as disks to an observer on Vulcan; they would appear as points of light to the naked eye, albeit very *bright* points of light. 40 Eridani B would appear as a blazing silver-white star shining at magnitude -7.4 in the Vulcan sky (some 16 times brighter than the brightest that Venus ever appears in our sky). 40 Eridani C would appear as a brilliant blood-red star of magnitude -6.3 (about 6 times brighter than the brightest Venus we ever see). Of course, the apparent distance between B and C would change as they orbit each other, but to an observer on Vulcan, B and C would always appear near each other--in fact, even when B and C are as far apart as they ever get, they would appear together in the Vulcan sky only as far apart as the width of your fist held out at arm's length.
Both B and C are bright enough to be easily visible in Vulcan's daytime
sky, though (at their distance) they wouldn't really be contributing much
to Vulcan in the way of light and heat. At night, they would shine with
a combined magnitude of -7.8, some 22 times brighter than our brightest
Venus--though still only about 1/47th of the brightness of our full Moon.
Enough to cast a dim shadow, maybe, and annoy the hell out of Vulcan astronomers
around the time that B and C are in opposition, but dim enough to let night
Can you go out tonight and find Vulcan's sun and its two companion stars? You bet. The trinary system 40 Eridani (Omicron 2 Eridani in some star atlases) is located in the constellation Eridanus at RA 4h 13m D -07d 44m; the system shines in our sky at magnitude 4.4 (easily visible, but not conspicuously so). Small telescopes will show 40 Eridani A next to a single white star (actually B and C, but small telescopes won't show them as separate). A larger telescope--say, an 8-incher--will be able to show B and C as separate. 40 Eridani B--the white dwarf--has the distinction of being the easiest-to-see white dwarf in Earth's night sky.
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