Vision: A Resource for Writers

Putting
Your Stars in Their Places
By
s
science fiction writers, we're free to range far beyond earth in our stories, from the moon
to the farthest stars we can see. However, there are times when this can pose
worldbuilding problems that writers in other genres don't need to worry about. For
a story I recently wrote, I had to find out how far apart Tau Ceti and BY
Draconis were so I could figure out how long a message between the two systems
would take for a round trip. Given that this message would be traveling at FTL
speeds, I could just wave my writer's wand and make messages travel
instantaneously. However, this would violate the rules I'd already set up in the
story for this form of communication, and maintaining internal consistency is
crucial to maintaining your reader's willing suspension of disbelief. I
already knew how far each star was from Earth, and in which direction, and I
knew there had to be some way to translate this into the distance between the
two stars. I found it, and it's not difficult to handle at all. Astronomers
locate the objects they study with a coordinate system comprised of three
elements: Right Ascension, Declination, and Distance. Right Ascension (hereafter
RA) and Declination might sound mysterious, but don't worry  they're really
not hard to understand. RA and declination are precisely analogous to longitude
and latitude. The difference is that we can't specify the location of
astronomical objects relative to the surface of the Earth, because the Earth
rotates. Therefore, we use an imaginary reference grid in the sky to locate our
objects, with the zero points defined by the point where the Sun crosses the
equator on the first day of Spring for RA and the celestial equator and poles
for declination. RA is measured in hours, minutes, and seconds (24 hours equals
360 degrees of "longitude"; RA increases in the eastward direction).
Declination is measured in degrees (0 at the equator; 90 at the Celestial North
Pole; objects below the celestial equator are assigned negative declinations). Now that we know how astronomers locate things, we can use stellar catalog information to locate our stars and figure out the distance between them. Taking the two stars I mentioned earlier as our example, we find the location from Earth of each star is as follows:
Armed
with this information, we're ready to begin. Here's where the math kicks in. To
find the distance between stars, we need to convert from the Earthcentered
polar coordinate system astronomers use to a Cartesian XYZ coordinate system.
It sounds scary at first, but it really isn't. If you have spreadsheet software
handy that can handle trig functions, it's very easy to create a spreadsheet
that does all this for you. First,
we need to convert RA to degrees. We'll call this value A: A
= (hours * 15) + (minutes * 0.25) + (seconds * 0.004166) Doing
so gives us: Tau
Ceti: 26.017046 BY
Draconis: 278.482530 Save
these answers; we'll need them later. Next,
we need to find the value of what we'll call B. As declination is already
measured in degrees, this is pretty simple. B
= ( ABS(Dec_degrees) + (Dec_minutes / 60) + (Dec_seconds / 3600)) *
SIGN(Dec_Degrees) Note that, as declination can range between 90° and negative 90°, we need to take the absolute value of the degrees term (the value as a positive number) and restore the sign after we've done our math. Otherwise, we'll get an inaccurate value for B. Using our two stars we get:
C is just the distance in light years (You can use parsecs if you prefer. It does you no good to use light years with one star and parsecs with the other, though!):
Now
that we have all our polar coordinates in the same units, we can convert that to
Cartesian XYZ coordinates. The
formula for the conversions is: X
= (C * cos(B)) * cos(A) Y
= (C * cos(B)) * sin(A) Z
= C * sin(B) Using our values for A, B, and C for each star, plugging in our numbers gives us:
Now
we've got things located in familiar Cartesian coordinates, with the scale in
light years, centered on Earth. With this, we're finally ready to find the
distance between our two stars. The
formula for finding the distance between two points in a Cartesian coordinate
system is: Distance^{2 }= (X1  X2)^{2} + (Y1  Y2)^{2} + (Z1  Z2)^{2 } Altering
this to a form more suitable for pocket calculator use gives us: Distance
= SQRT((X1  X2)^{2} + (Y1  Y2)^{2} + (Z1  Z2)^{2}) Putting
our numbers in gives us the distance between two stars (and you though we'd
never get here!) Distance
between Tau Ceti and BY Draconis: 60.991494 light years Now,
this may seem like a lot of work to get a number which you might not explicitly
use in a story, but details like this matter when you're building a world. Even
in hard SF we're allowed to break some of the laws of physics, but we need to
make sure we've explained the ground rules of our world to the reader, and then
rigorously stick with those rules. Otherwise, you'll risk losing your reader's
willing suspension of disbelief  and possibly that that reader's desire to
keep reading your story. Sustain that willing suspension of disbelief by making
your imaginary worlds vivid, detailed, and internally selfconsistent, though,
and you'll likely have a reader staying up past her bedtime, totally absorbed in
the world you're showing her. Resources: The
Internet Stellar Database: http://www.stellardatabase.com/
A
searchable online database of most of the stars within 75 light years of Earth.
Also gives you Earthcentered X,Y,Z coordinates, so you can save a bit of number
crunching. 3D
Starmaps: http://www.projectrho.com/starmap.html
If
you're interested in more information on the math involved, there's an extensive
discussion here. Also includes extensive links to more information sources,
online star catalogs, and software.
