Near Star weirdness

[Evil Dr Ganymede]

I'm not sure if my co-ordinate conversions have gone a bit wacky, or if this is something real... I used the stars from this list:

http://www.chara.gsu.edu/RECONS/TOP100.htm

and converted the RA/Dec into galactic lat/lon, and then converted those into X/Y/Z co-ordinates (The XY plane is the galactic plane, +X points to the Galactic core, +Y points to the left of +X if you look down from the north galactic pole, +Z point up toward the north galactic pole), and then plotted it out using a program called CHview. (Sorry - I can't persuade Celestia to do this yet )

I was somewhat surprised to find that all 100 nearest stars can be found basically on one side of Sol - while there were stars in three quadrants around Sol on the XY plane, there were no stars that had -X and -Y co-ordinates. You can see this in this top down view:



(+X (galactic core) is to the right, +Y is to the top of the image) each grid square is 1 ly. Sol is the yellow star on its own in the centre-left.

What's suspicious about this is that there does seem to be a diagonal line (marked by Eta Casseiopei (bottom right), Sol (centre left), and WD 1142-645 (top left)) behind which there are no stars. Which leads me to believe that either (a) something screwy is going on with my co-ordinates, (b) this is something wacky caused how the RECONS survey was made (though it's seeing stars in the northern and southern hemispheres), or that there really is this big gap in the stellar placement around the Sun, so that the nearest stars are all to one side of it.

According to my calculations, stars can be found on the X-axis between extremes of -7.35 to 20.12 ly, on the Y-axis between extremes of -16.18 and 19.90 ly, and on the Z-axis between -18.75 and 20.31. The galactic longitudes calculated from the RECON tables go from about -57 up to +117 (going through 0)... so that does seem to cover about 174 degrees of sky.

So... do any of the astronomy types here have any clue what's going on here? Is this real, or is something weird going on with my numbers??

[Cormoran]

Greetings, Dr. G,

Nice to see I'm not the only one who used CHView

I had a look at some of my data files, and while our coordinate systems are slightly different (My +Y axis goes towards the Galactic centre), I can see the relative positions of some of the stars in your image compared to my own.



I hate to say it, but I think it might be your Math.

I've posted a copy of the CHV file I've been using so you can do a comparison if you like.


http://homepage.ntlworld.com/jdchapman66/150-Gal4.CHV

Hope its useful,

Cormoran

[Evil Dr Ganymede]

Yeah... it does rather look like something's gone screwy in my conversion from RA/Dec to galactic co-ordinates...

Thanks for the file and picture, that helps!

[Cormoran]

Dr G,

This file might be useful too, when you come to getting your Traveller maps sorted out.

http://homepage.ntlworld.com/jdchapman66/BigStars.CHV

Its basically a CHV that contains the positions of well-known stars irrespective of distance.

Same coordinate system as the last one.

Cheers,

Cormoran

[Evil Dr Ganymede]

Dr G,
This file might be useful too, when you come to getting your Traveller maps sorted out.

Now, whatever gave you the impression that this was for Traveller?

Its basically a CHV that contains the positions of well-known stars irrespective of distance.

Ta muchly, squire

[Guest]

Greetings Evil Dr G,

ah, you appear to have succumbed to the pesky inverse tangent ambiguity bloatoid in calculating galactic longtude, l! Omicron 2 Eridani in your maps gives it away: it's opposite to the galactic centre, but you have it to the right - towards the galactic centre.

Your problem looks very much like a symptom of the infamous inverse tan ambiguity problem that folds all angles between 180° and 360° back into a restricted range, sometimes 0° and 180°, sometimes -90° to +90°. Since you mentioned in your thread "Co-ordinate systems?" (http://www.shatters.net/forum/viewtopic.php?t=4517) that you’re using Excel, I can tell you that you can easily fix this by switching from =ATAN(r) to =ATAN2(x,y). What are x and y to be? Well, looking back to "Co-ordinate systems?" and recalling what granthutchison supplied to you on Mon Mar 01, 2004 7:10 pm:

l = 33 + atan{[sin(delta)-sin(b)*sin(27.4)]/[cos(delta)*sin(alpha-192.25)*cos(27.4)]}

you take the denominator of the atan argument to be x = cos(delta)*sin(alpha-192.25)*cos(27.4) and the numerator to be y = sin(delta)-sin(b)*sin(27.4)

Note Excels's ATAN2() takes x before y.

Spiff.

P.s., good luck!


Extra, for other's who are interested in avoiding common mistakes that Everyone Suffers From When Learning Applied Computing In Mathematics and Sciences...: Why is this necessary?

It's from trigonometry. Taking the co-ordinates of a star to be (x, y) - with the origin being where the Sun would be - the tangent of that angle anti-clockwise around from the x-axis is found by dividing y by x:

tan(a) = r = y / x

so tan(a) is a function of r. If you know r, you know tan(a), but how do you find a from r? Mathematically, we write:

a = arctan(r).

The problem is that r doesn't tell you what x and y were, and that is the problem. Try these examples:

1. If a = 45°, x = 1 and y = 1, so tan(a) = 1/1 = 1. Good.
2. If a = 135°, x = -1 and y = 1, so tan(a) = 1/-1 = -1. Good.
3. If a = 225°, then x = -1, and y = -1, so tan(a) = -1/-1 = 1. Wait! that's the same as for 45°. The sign information of x and y has been lost in the division. This is why the ATAN() function taking only one argument can never tell where the angle really is. Worse, some languages guess the angle to be within the first two quadrants: 0° to 180°, and others such as Excel's ATAN() guess the angle to be within the first and fourth quadrants: -90° to +90°.

Excel's ATAN2() function solves this by taking the x and y arguments separately, so the sign information is preserved. If you ever need to write code for an inverse tangent function yourself, there are nine cases you must compute for depending on the sign of x and y:

1. x = 0, y = 0. No answer (0, Infinity, Not-a-Number - you need to decide).
2. x > 0, y = 0. a = 0°.
3. x > 0, y > 0. 0° < a < 90°.
4. x = 0, y > 0. a = 90°.
5. x < 0, y > 0. 90° < a < 180°.
6. x < 0, y = 0. a = 180°.
7. x < 0, y < 0. 180° < a < 270°.
8. x = 0, y < 0. a = 270°.
9. x > 0, y < 0. 270° < a < 360°.

After checking for the obvious cases: 1, 2, 4, 6 and 8, you can use the 1 argument function (ATAN() in Excel, or whatever's native to your programming language) to get the answer in restricted quadrants (experiment to find out which ones). Then add the correct angles to get the final answer into the right quadrant. For Excel, in cases 3, 5, 7 and 9 where =ATAN() would give an answer, you would need to add nothing for case 3, 180° for cases 5 and 7, and 360° for case 9.

Here endeth the lesson.

[Evil Dr Ganymede]

Thanks Spiff. That was most educational (I didn't have a clue about any of that ).

So I need to phrase it as:

l = 33 + ATAN2{[cos(delta)*sin(alpha-192.25)*cos(27.4)],[sin(delta)-sin(b)*sin(27.4)]}

right?

[Cormoran]

Why did I think it was for Traveller? Oh, I dunno... maybe I have Zhodani blood

Heck, I did the chv files to map an SF campaign setting, so I see no reason not to spread the joy

Regards,

Cormoran

[Guest]

... must remember to log in before replying ... grumble...mutter...

Ahem, yes, that substitution is correct. For 1950.0 epoch.

Whipping out my trusty ol' Duffett-Smith "Practical Astronomy With Your Calculator", 2nd ed., I note that the same formulae as presented in "Co-ordinate systems?"are there on p.48 for 'Equatorial to galactic co-ordinate conversion', and the numbers are for 1950.0 epoch. The 192.25° is the R.A. of galactic centre, and the 27.4° is declination of galactic centre, The 33° is the ascending node of the galactic plane on the celestial equator. I appear to have made a note that for epoch 2000.0, the numbers change to 194.7°, 27.1°. The 33° appears to stay the same. Give it a whirl in your formaulae to eliminate precession as the source of those residuals errors...

Spiff.

[selden]

Spiff,

My guess is that you're actually logging out. Don't! If your browser has cookies enabled, you'll always still be logged in when you return.

[Evil Dr Ganymede]

Whipping out my trusty ol' Duffett-Smith "Practical Astronomy With Your Calculator", 2nd ed., I note that the same formulae as presented in "Co-ordinate systems?"are there on p.48 for 'Equatorial to galactic co-ordinate conversion', and the numbers are for 1950.0 epoch. The 192.25° is the R.A. of galactic centre, and the 27.4° is declination of galactic centre, The 33° is the ascending node of the galactic plane on the celestial equator. I appear to have made a note that for epoch 2000.0, the numbers change to 194.7°, 27.1°. The 33° appears to stay the same. Give it a whirl in your formaulae to eliminate precession as the source of those residuals errors...

Nope. That change seems to make it much worse, if anything

[Spaceman Spiff]

... right, I *think* I'm logged in this time ...

Hello Selden,

thanks, but no, it was because I had multiple windows open to compare threads. I logged in on one, and replied on another. Tsk! Cookies were set, but I think you have to refresh all open windows to set cookies amongst all (?).

Hello Evil Dr G,

My next reply on the co-ord matter is over on the "Co-ordinate systems?" thread.

Spiff.

[granthutchison]

<Jaw drops>
For, oh these many years, I've been puzzled by a claim in Larry Niven's novel Protector, in which he claimed that if you were heading into the Sun's vicinity from the galactic core, you'd see the local G stars concentrated to one side of the Sun. It never looked that way to me.

But (gasp) do you think the Divine Niven might have just bollixed his arctans when converting coordinates? Excel shifts them all towards the galactic core, but it's an equally likely error to place them all one side or the other of the zero galactic meridian.

If so ... GOOD company, Evil Dr!

Grant

[Cormoran]

Given when Protector was written, I think Larry can be forgiven.

He had to do all the calculations by hand!!!

Be thankful we live when we do

Cormoran

[granthutchison]

Given when Protector was written, I think Larry can be forgiven.

He had to do all the calculations by hand!!!

I'm all for forgiving Niven, of course.
But the reason it didn't look that way to me was because I'd already done all the calculations by hand before Protector was ever published, and drawn the map. It was actually more easy to remember these little subtleties when you were figuring them with a slide rule and a set of trig tables, compared to nowadays when you just click on a formula and hope for the best.

Grant

[Eburacum]

Anyone know if there is an on-line calculator for this? It does my head in trying to calculate xyz for stars when all I've got is Ra/dec/ly.

[selden]

If I understand your question correctly, you're looking for a coordinate conversion calculator for transforming between RA, Dec and l2,b2.

If so, then you might take a look at Precess: http://cxc.harvard.edu/toolkit/precess.jsp. It converts among Galactic, Equatorial and Ecliptic, both B1950 & J2000 as well as handling precession for arbitrary dates. It can only convert one set of coordinates at a time, though.

Alternatively, if you know anything about Fortran and want to do the calculations en-masse on your own system, you might investigate the freeware astronomical subroutine library provided by StarLink at http://star-www.rl.ac.uk/

[Evil Dr Ganymede]

It occurs to me that I should post an image of the correct map of the area around Sol . So here you go.



And yes, Cormoran, those are Traveller directions around the edges .

[Cormoran]

Dr. G,

Very nice work, and it has increased my confidence in my own star maps, as a direct point for point comparison shows that our figures agree to within rather fine tolerances . How far does your map extend, btw?

Only one point, can you confirm that the galaxy rotates clockwise in the view both are databases use, because I rather like the 'coreward, spinward' naming convention (though in deference to my pagan wife, I think I might use 'Widdershins' instead of trailing )

Cheers,

Cormoran

[granthutchison]

... though in deference to my pagan wife, I think I might use 'Widdershins' instead of trailing

In which case you should use deasil instead of spinwards, too ... it's the fortunate Celtic opposite of widdershins.

Grant

PS: Yes, the galaxy does rotate deasil when seen from galactic north.