“PA” – you see those letters frequently on this web site and in various books and catalogs of double stars. They stand for “position angle” and position angle is one of the most fundamental tools in the double star observer’s tool belt. It tells us what direction to look for what frequently is a star’s faint and almost-too-close-for-splitting companion. Knowing the PA also can give you assurance that the starry companion you think you have found is really the correct one. But directions in the sky can be different than directions on Earth and different telescopes flip things around differently and this all tends to overwhelm someone trying to get a handle on it for the first time – or second!
Don’t let it. It is all very simple. The key is to break the problem into two bite-sized chunks – first make sure you understand directions in the sky as you see them with the naked eye – then tackle what the telescope does to these.
The source of all the confusion is that stars move in circles around the celestial poles – not straight lines – and the circles get smaller as you approach the poles. This is different from the apparently flat, common sense world we walk around on each day. So here are two new rules to apply to help you get things right in the stellar environment.
1. Whatever direction the stars appear to move, that is west.
2. The direction from a star to Polaris is north.
Notice that these are new definitions. We are not talking about the cardinal directions – north, south, east, and west – as they appear on the horizon, though these are closely related. These sky directions are a bit different because we are looking at a sphere from the inside – the dome of the sky. They are absolutely essential, however, for talking intelligently and usefully about where things are in the sky in relation to one another. Terms such as “above” and “below” are relative and not always that helpful when trying to find your way around the sky dome. Nor is it helpful to relate what you see in the eyepiece to a clock face. Instead, learn to think in terms of the cardinal directions, north, south, east, and west.
So face south and look up. This puts east to your left and west to your right. Hey that was easy!
Yes it was. Now face north. East is now to your right and west to your left. Wow – there’s nothing to this!
Nope. Nothing to it – until you look at the section of sky beneath the North Star. Now east and west get flipped. Now – in the sky – west is to your right and east to your left! Remember – this is the special case that applies only to objects that are below the North Star. This chart should help you understand why.Notice the stars appear to move from left to right, down to up, right to left, and then up to down as they circle the pole – and all these directions are the same – they are all west.
Why the change in direction? Nothing has changed really. Remember Rule 1: The star always appear to rotate to the west. Since they appear to circle the North Star – the North Celestial Pole really – then beneath it they will appear to move from left (east) to right (west.) It is confusing because the western point of the horizon is still to your left – but you are not dealing with the horizon – you are now dealing with the sky dome.
Now lets look at the second rule. It applies everywhere in the sky, no matter what direction you face. North is always toward the North Star. We’ll illustrate this by looking north.
Second bite – the telescope
Digested the directions as seen with the naked eye? Feel confident you know west from east? Good. Now let’s see what the telescope does to this. Look at the sky and make sure you know which way is west.
Once you have determined west, there are two simple rules that apply depending on the type of telescope you are using.
3. If you are using a telescope with a diagonal mirror (refractor, SCT, or Maksutov), then the other directions are read clockwise from west – north,east, south.
4. If you are using a Newtonian reflector, whether on a Dobsonian mount or equatorial, then the other directions are read counterclockwise from west – north, east, south.
Got it? Diagonal – clockwise. Reflector – counterclockwise. Not too big a bite.
Now it’s easy, with some telescopes, to forget about the naked eye view and directions and determine west by simply looking in the eyepiece. If you are using a manual telescope – or one with a simple clock drive that tracks the stars, this is easy. Turn off the tracking motor if you are using one. Now when you look in the eyepiece you will notice in just a few seconds that the stars are drifting through it. The direction they are drifting is west. Depending on where and when you are looking the stars may leave your field of view at any point in a 360 degree circle. But place a star near the center of your field of view and follow its drift to the exit point. Wherever that exit point is, that is west. So we are simply applying Rule 1 above to the telescope view. Now use either Rule 3 or Rule 4 , depending on what type of telescope you are using, to determine the other directions.
But the PA is a number?
Yes, and you are probably familiar with these numbers. They frequently appear on a compass. They are used to determine “azimuth” on land. And they are simply the 360 degrees of a circle. All you have to remember is that they start with “0” as north and progress clockwise around the circle, so that 90 marks due east, 180 due south, 270 due west. I suggest you make one or more simple discs – let’s call then “training wheels” – for your telescope and slip your eyepiece through them before loading it into the telescope so they serve as a memory jogger. Soon you will find you don’t need them, but they should help at first.
This wheel implements Rule 3.
And this wheel implements Rule 4.
Put it to the test – right here and now!
Want to see this in action? Here’s a simulation prepared using Starry Nights Pro software and looking at the famous double, Albireo. It’s fairly low in the northwest at this time of year (December) as I write this and here’s how it would appear in the early evening now in a refractor/SCT’/Mak telescope that uses a diagonal mirror. Be patient – follow the drift. This is a real time video simulation, but I made the field of view just 6-arc-minutes in diameter so it should go quite quickly. (The stars and their split are not to scale, but the PA and drift are correct.)
From watching this you should be able to deduce that West is in the direction marked on this still image.
Now remember, we are using a telescope with a diagonal mirror, so we need to apply Rule 3 – that is, North is clockwise from West. (Mentally lay the first training wheel on top of this.) So when we look at Albireo and its companion, we should see in our mind’s eye something that looks like this.
OK – the PA of Albireo’s companion is 55°! Were you near that? Within ten or fifteen degrees? That’s all I hope for and all I find useful most of the time. We’re not trying to make scientific measurements for the record here. We just want to know where we should look for the secondary star. Or, we want to confirm our observation. I frequently make a quick sketch at the eyepiece, always indicating “west” on it. Then I look up the PA to make sure I have the right star. When we check close double it’s not unusual to be fooled, especially in poor seeing. Sometimes you just aren’t sure, but you think you have it right. So in many instance I make it a point not to remember the PA when I’m deciding what double to look at – then I check my notes against the published figures. It’s always fun to know you have it right.
But wait – I have a GOTO Scope!
Oops – sorry. This is an instance where the technology can tend to get in the way a tad. You can, of course, turn the “goto” off and the stars will drift and you can determine direction as above. But that will be a pain when you have to start up again. You certainly don’t want to be on a double star, then have to shut down and go through all that alignment stuff and find the star again just to determine PA. But don’t despair, just do this.
- Use Rule 1 above to determine with your naked eye which way is west – which way the stars, Sun, Moon, and Planets all seem to be moving.
- Now remember that your telescope – either type – flips left and right. People tend to forget this and assume that the telescope flips east and west. Not always. It flips the horizontal axis and whether thatis east-to-west or north-to-south depends on which way you are facing. So the trick is to know whether left-to-right represents east/west or north/south.
Pause and think. A double star you want to observe is rising in the east. If it’s pretty close to the horizon – say within 30 degrees – then north is basically to your left, east is down, and west is up. So in this case it is north and south that are left and right – so they get swapped in the eyepiece.
If you’re looking south, east and west get swapped.
This leads to a general rule – if you’re looking either north or south, east and west get swapped. If you’re looking east or west, then north and south get swapped. Remember, the goal is to identify “west” in your eyepiece. Then you can use the appropriate training wheel – or choose from rule 3 or 4 depending on the type of telescope you’re using.