By the way, if someone is interested, I made up a "London Underground" style nodemap on excel. File attached. IMHO it indeed clears the picture quite a bit.
Arcanum, do you know how to convers sphere co-ordinates into cartesian co-ordinates? Because if you do, you can simply convert the locations of real stars into xyz-co-ordinates from declination, right ascension and distance. You can use equatorial co-ordinates because the distance between Sol and Earth is so small that you can approximate Sol and Earth to exist in same location.
If you don't know how, I can tell you. It's not really very complicated. In fact, since I have spare time, I tell anyway, even if you already know how to do it...
Read if you want to.
Stellar locations are announced in spherical co-ordinates fixed to equator plane of Earth and Vernal Equinox (or Aries point).
Right Ascension (RA or Ra) tells us in which direction of the equatorial plane the object is. It is announced in hours, minutes and seconds, because of historical reasons as well as producing convenient calculations if local time is involved.
The right ascension zero point is fixed into Equinox; that's the point where RA co-ordinate has value 00h 00min 00.00sec. The point in the opposite direction has RA value of 12h 00min 00.00sec, and so on. To convert RA values into degrees, we define how much one hour, one minute and one second equal in degrees:
1 h = 360 degrees / 24 h = 15 degrees
1 minute = 15 degrees / 60 min = 0.25 degrees
1 second = 0.25 degrees / 60 s = 1/240 degrees
Declination (DE or Dec) announces the angle in which the star's direction elevates from equatorial plane. Declination is announced in degrees, arc minutes and arc seconds. But these minutes and seconds aren't the same minutes and seconds used in a clock... A minute in this context is 1/60 degrees, and correspondingly a second is 1/3600 degrees.
For example, Polaris has Dec value of nearly 90 degrees. An object near the equatorial plane would have Dec value of ~0 degrees. Objects on northern hemisphere of sky have positive declination, objects on southern side have negative declination.
Now that we know what RA and Dec values are and how they are used, let's take an example of how to convert RA, Dec and distance into cartesian co-ordinate values.
First of all, we point z-axis to north pole (near Polaris). X-axis we point at the Equinox point. Y axis is pointed so that it is normal to both x and z axes, and so that the co-ordinate system used is right-handed (default in modelling programs). I recommend using light years as units, they are rather convenient in this kind of task.
Okay, now how do we convert RA/Dec/Distance into convenient xyz co-ordinates?
When we have converted RA and Dec values into decimal degree values, we define the cartesian xyz co-ordinates with the help of these two angles and known distance S.
x = S * cos RA
y = S * sin RA
z = S * cos DE
Really simple, isn't it? This gives the exact co-ordinates of the star in an XYZ system used in all modelling programs, for exampl. Just throw a star object onto the program, feed in these values and the object is automatically moved into correct location.
Example.
Beta Aquilae has following co-ordinates:
Right ascension 19h 55m 18.8s
Declination +06° 24′ 24″
Distance 44.7 light years
First we have to convert RA and Dec values into simple, decimalic degree values to more easily calculate them.
As shown before, it goes like this:
RA = 19 * 15 degrees + 55 * 0.25 degrees + 18.8/240 degrees = 285 + 13.75 + 0,07833... degrees = 298,8283 degrees = ~298,8 degrees
Dec = 6 degrees + 24/60 degrees + 24/3600 degrees = 6,4067 degrees = ~6,4 degrees
x = S * cos RA = 44.7 ly * cos 298,8 deg = ~ 21.53 ly
y = S * sin RA = 44.7 ly * sin 298,8 deg = ~ -39,17 ly (note the negative value, it is important to remember to put it in...)
z = S * sin DE = 44.7 ly * sin 6.4 deg = ~ 4,98 ly
x = 21.53
y = -39,17
z = 4,98These are the co-ordinates of Beta Aquilae. Convert all the other existing star co-ordinates in similar fashion and you get an accurate model of relative locations of stars.
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