Astrometry with CCD (or CMOS) cameras can be very useful tool for measuring separation and position angle of double and multiple stars. When position of stars is determined with good accuracy it is pretty straightforward then to calculate separation of any star pair. In the example below I used free AstroImageJ software, but any other software that can handle plate solving and astrometry can be used for this (like MaxIm DL, MPO Canopus or Astrometrica). With some care it is possible to achieve accuracy of 0.1″ or better, so for some cases you can observe changes in position after a year or two (like for example 70 Oph, Gamma Virginis, or Zeta Cnc). There is also dedicated software REDUC for double stars measurements, but I do not have yet a chance to use it.
The whole process consists of following steps:
- after image is opened you need to run plate solve on it, so the image scale, coordinates and orientation is calculated
- then you need to select stars, so software will determine its center and calculate position
- and this data you need to export to spread sheet and calculate separation and position angle.
So, starting from top. After you start AstroImageJ you open image file (File -> Open). Then you can pan and zoom image to find your object. Also you can use sliders at the bottom to adjust levels, so the object to measure will be well defined.
If plate solve was not yet done in the line with image description you can notice (No WCS) string and you need to do plate solve now. You can use for it nova.astrometry.net server or to use local astrometry server. If you do more than few plate solves I recommend to install local server – like ANSVR. From WCS menu you need to select Plate solve using astrometry.net (with options). If you have local server you need to put its URL here. If you use nova.astrometry.net server, you need to enter your user key, that you received after signing in. It is also recommended to fill fields Constrain Plate Scale (it is your rough plate scale) and Constrain Sky Location (it is approximate coordinates of frame center), so software will resolve your image quicker.
When plate solve process is finished you will see rulers with angular scale (instead of pixel scale) at the image. Then you need to turn Aperture Photometry Tool mode in main AstroImageJ window, and in the image window you select Edit->Aperture settings and set aperture in such way, so it will fit star size at our image (don’t worry about background annulus setting – it is not relevant for astrometry). Then you click with mouse at our targets. After each click new star should be added to Measurements window data. Star centroid is determined automatically, but it is worth to click as close star center as possible, so zoom image in.
Last step is to import this data to spread sheet. You can export Measurements data directly to XLS file, or select, copy and paste to already opened sheet. When you have data in the sheet you need to add four more columns at the end. Call them dRa, dDec, Separation, Position Angle. You can find these cells formulas below, assuming that:
- A and B stars data are in the rows 2 and 3
- RA coordinate is in the column O
- Dec coordinate is in the column P
column dRA (S in the sheet): =15*(O3-O2)*COS(RADIANS(P3)) column dDec (T in the sheet): =P3-P2 column Sep. (U in the sheet): =SQRT(S9^2+T9^2)*3600 column Pos. angle (V in the sheet): =DEGREES(ATAN(S9/T9))
For testing I used Trapezium stars, because I already have a few short exposed frames of this area. Calculated results from three different frames are below:
They are pretty consistent and agree to other data found in the net:
Second example I measured with Struve 484 in the NGC1502 open cluster:
According to WDS catalog data Struve 484 separation is 5.5″ and PA is 133 degrees.
As I mentioned before for astrometry you can use other software. Some of them (like MPO Canopus) calculate separation and position angle in the fly, so you do not need to use spread sheet anymore: