Assigning co-ordinates to objects

[george7378]

Hello,

I was just wondering - if I were to point out the location of an object using coordinates, would it be expected for me to give an RA/DEC value, or would I be OK just giving altitude and azimuth values along with a latitude and UT time? Does anyone work in alt/az, or is pretty much everything done in RA/DEC? Also, does anyone have any formulas to convert between alt/az and RA/DEC?

Thanks.

[FraserClarke]

Depends who you are pointing it out to I think??

RA/Dec would be preferred for anything scientific.

[george7378]

Thanks. I have been looking around and I have found some formulae. I can calculate Dec. easily enough, but when you do RA, you need to calculate the Hour Angle (which I can also do) and then you need take LST (local sidereal time) from the hour angle to get RA, but I don't know how to calculate LST. Any ideas? Thanks again.

[mark7331]

LST can be worked out thus:-

LST = GMST + (L / 15)

Where L is geographic longitude in degrees east of Greenwich and GMST is Greenwich Mean Sidereal Time.

If you'd like any more of the maths let me know.

Mark

[george7378]

Thanks Mark. Is GMST just the current GMT? Also, how would I enter GMST into the formula (it should give me a value to take from the hour angle, so I presume I would't just put hours, minutes and seconds into it).

[mark7331]

Yes GMST is effectively the time at the Greenwich meridian. To enter the value convert the H:M:S into seconds then there's a simple conversion from seconds to sidereal seconds:-

1s = 1.002738 sidereal seconds.

There's a way to convert from equatorial to Altitude and horizon (alt-az) cooridinates directly using sin/cos maths if you need it.

Interestingly the (local)Hour angle can be calculated from the right ascension subtracted from the LST.

[george7378]

Thanks again - I think I get it now. I have seen the formulae to convert from equatorial to horizontal - I am interested in doing it the other way. I am just going to try an example of a conversion from Alt/Az to RA/Dec - can you spot any errors, or is it OK?

Say I want to find the RA/Dec of Vega, which is at Alt 45.2 and Az 277.3 @ 19:59:43. I am at 53.3768 N and 0.7099 W.

Declination:

sin DEC = sin LAT sin ALT + cos LAT cos ALT cos AZ

sin Dec = (sin 53.3768 X sin 45.2) + (cos 53.3768 X cos 45.2 X cos 277.3)

sin Dec = 0.6229, Dec = 38.5

Hour angle:

cos H = (sin ALT - sin DEC sin LAT)/(cos DEC cos LAT)

cos H = (sin 45.2 - sin 38.5 X sin 53.3786)/(cos 38.5 X cos 53.3768)

cos H = 0.4491, H = 63.32

LST:

LST = GMST + (L / 15)

GMST (in seconds) = 43 + (59 X 60) + (19 X 60 X 60) = 71,983

LST = (71,983 X 1.002738) + (0.7099 / 15)

LST = 72180.1

RA:

RA = H - LST

RA = 63.62 - 72180.1

RA = -72180.136S, = -20.05H?

[mark7331]

George, looks like you're bang on to me.

I'll run it through a few checks tomorrow because I have a different approach for the hour angle but a quick substitution resolves to your solution. The numbers look good.

[george7378]

Thanks - I would love to see your method when you have time. Also, I think the RA was a little out as it is apparently just over 18.5H, but I'm sure there is a simple reason for this.

[mark7331]

Ok I've plugged your numbers into my model with a quick bash of the calculator and get an Hour Angle of 62.98 resulting in RA of 71917.157 or 19h 58.62m.

I've just noticed that your LST calc is wrong in that the sign of the Longitude should be negative as it's degrees West and the formula requires degrees East. You should have -0.7099.

I've also put in your Lat/Long/Time into Stellarium for a quick check and found that Vega is at 278.48/+44.97.

What I'll do in the morning (as I am now being stared at by the she who must be obeyed) is work through the whole set of calculations and verify each step. I'll PM you when I have the results.

It looks pretty good though and won't take much to get it running.

Cheers.

Mark

[george7378]

Hi - thanks for putting that right! I wonder why we got differing hour angle values? Probably the number of decimal places or the slight differences in alt/az. Thanks for your time!

[FraserClarke]

Hi George,

Your equations for Dec and HA are correct, and LST is OK too, though make sure you check you're not 'over-running' the day, and subtract 24 hours if you need.

GMST is more complex I'm afraid and depends on the date (otherwise objects would appear at the same place at the same time each night, which we know doesn't happen). Here's a PDF I found with equations in it giving the GMST and the changing 'constants' you need for the calculation;

http://www.astro.umd.edu/~jph/GST_eqn.pdf

The problem comes with leap years etc, which screw up a normal day->GST conversion. So usually one first converts the day to the julian date, which takes into account the leap years.

Also, the last line should be the other way around;

RA = LST - HA

[brianb]

Why not:

(1) image the object and the surrounding star field and use astrometric software to obtain the position of the object directly (given catalogue positions for some of the objects in the field)

(2) use a crossbar micrometer and a stopwatch to measure the position wrt catalogued objects if observing visually with an undriven scope (or one whose tracking can be truned off)