Computer Programs

The accompanying suite of programs implement the equations discussed in chapter 7 (The Orbital Elements of a Visual Binary Star), chapter 12 (Simple Techniques of Measurement), chapter 15 (The Filar Micrometer) and chapter 22 (Some Useful Formulae).

The file ‘location.txt’ is created by the program Geographical Location.exe and written to the root directory of the hard disk (i.e. the C drive) from where it is read by the programs Julian Date and Epochs, Differential Refraction and Micrometer Reduction. The purpose of writing these text files to the root directory of the hard drive is so they can be read by the various programs regardless of which directories, or folders, in which the programs are placed. (Without the location.txt file the programs Differential Refraction and Micrometer Reduction will not return any results. Julian date and Epochs, on the other hand, will return the results (after displaying an error message), but the results will be for the Greenwich meridian.)

General Program Notes

It might be worth discussing some of the features common to all the programs before discussing each program in turn. Some of the points will be familiar to most users.

Double click on the program icon to launch the program. The cursor will be placed in the upper-left most box for entering the data. After entering the data in one box press the tab key to move to the next box in sequence. The final press of the tab key will highlight the button to execute the calculations. Just press the return key at this point. Pressing the tab key afterwards will highlight the quit button, which if then pressed will close the program.

The alternative method of moving through the sequence is to use the mouse and click on each box in turn, and eventually on the button to execute the calculations, however the tab key method would be quicker.

When the program has produced the results a new value can be found by changing the data in only those boxes for which a new result is required, e.g. in the program Julian date and Epochs, if the Besselian epoch for another day of the month is required click on the day box enter the new day value and then click on the ‘Find JD & Epoch’ button, i.e. the whole set of date and time data does not have to be re-entered.

Geographical Location

This should be the first program to run. It will ask for the observer’s latitude, longitude (in degrees, minutes and seconds), time zone (in hours) and whether or not daylight saving is in effect. The program then creates a file, location.txt, containing these details and displays the latitude and longitude in degrees (decimal form). As mentioned above, the programs Julian date and Epochs, Differential Refraction and Micrometer Reduction read the location file.

The purpose of this program is to obviate the need to enter the latitude and longitude each time the program is run, and to obviate the need to convert the local time to universal time for the time and date. The program will not need to be run until the observer changes location, or until there is a need to change the setting for daylight saving time.

Julian date and Epochs

This program is concerned chiefly with converting local time to the Besselian epoch for dating double star observations. The program also returns the Julian epoch, which was introduced with the 1976 IAU revision of astronomical constants. It is not used by double star observers but is included in case there should be any future developments in that direction.

The epochs are derived from the Julian date and consequently the JD is calculated as a matter of course. It is not used in visual binary observations, but would be used by those making observations of variable stars, such as eclipsing binaries.

The local apparent sidereal time (accurate to about a tenth of a second) and the day of the year (January 1 being day 1) are also provided.

If the location.txt file has the longitude, time zone and daylight saving values set to zero then the program will assume universal time. The program will indicate, beneath the date and time, whether local or universal time is used.

The Julian date and epochs are found from the (Gregorian) calendar date and time by clicking on the ‘Find JD & Epoch’ button. Conversely, the calendar date and time can be found from the Julian date by clicking on the ‘Find Calendar Date’ button. The time returned, however, is universal time not local time. This enables the local time to be converted to universal time by entering the local date and time, clicking on the ‘Find JD & Epoch’ button and then clicking on the ‘Find Calendar Date’ button. (The local sidereal time, however, remains that of the observer’s location, i.e. it is not converted to Greenwich sidereal time.) A note of caution here: pressing these two buttons back and forth a number of times will cause the date and time to change by an amount equal to the value of the time zone. Further discrepancies might arise because the Julian date might have been rounded for display, as the program reads the displayed Julian date when calculating the calendar date and time.

Differential Refraction

The corrections to the position angle and the separation are carried out using Chauvenet’s equations. No correction is made if the zenith distance is greater than 75 degrees because the equations become unreliable so close to the horizon. At such times the corrected vales for the position angle and the separation just state that the zenith distance is greater than 75 degrees.

The parallactic angle, which is necessary to calculate the effects of atmospheric refraction on the position angle and separation, is shown for those who observe double stars with altazimuth mounted telescopes and who therefore measure the zenithal, rather than the polar, position angle. The conversion from zenithal to polar position angle is made by adding the parallactic angle, Q, to the zenithal position angle, i.e. pPA = zPA + Q. The rate of the field rotation is also given to show how fast the parallactic angle was changing at the time.

The Besselian epoch is also given to date the observation, as the information required to calculate the parallactic angle is also used to calculate the epoch. This saves on having to run the JD&Epoch program subsequently.

Position Angle and Separation

Measurements of double stars are used to determine the orbital elements of the binary system. These elements can then be used to determine the position angle and separation of the binary for some given date. The program Position Angle and Separation

carries out the calculations involved in producing such an ephemeris from the orbital elements.

The program requires the orbital elements and the date of observation to be given and then returns the position angle and separation for the given date. The order of the orbital elements corresponds to that of the Sixth Catalog of Orbits of Visual Binary Stars. The catalogue is available online at http://ad.usno.navy.mil/wds/orb6.html

The output enables the position angle and separation for up to four different stars to be shown. (If any more are entered the top one, i.e. the first one entered, will scroll off the top of the output box.) The name of the star, which is optional, would be advisable for such uses so as to keep track of which values belong to which star.

The alternative use for the mutli-value display is to show the position angle and separation for a number of dates for the one star. This provides an indication of the speed of orbital motion around the date of observation if the dates close to each other, say a year or even half a year apart.

Position Angle Precession

The position angle given by the program Position Angle and Separation refers to same equinox as that of the position angle of the ascending node, i.e. no correction is made for the effects of precession and proper motion on the position angle. Such corrections are carried out using this program.

The program requires the right ascension, declination and proper motion in right ascension, along with the position angle. Note that the proper motion that is required in milliarcseconds per year, i.e. not in units of time.

The position angle can be found first, using Position Angle and Separation, and then precession applied, or the precession applied to the PA of the ascending node and the resulting position angle used as the PA of the ascending node to find the position angle. The two programs, Position Angle and Separation and Position Angle Precession, can be opened and set beside each other and the results of one then being transferred across to the other (manually).

Magnitudes

Magnitudes calculates the individual magnitudes of two stars whose combined magnitude and magnitude difference are known. The combined magnitude and magnitude difference are entered on the right hand side and the button ‘Individual Magnitudes’ is clicked and the individual magnitudes appear on the left hand side. However, if the individual magnitudes are entered on the left hand side and the button ‘Combined & Differences’ is clicked then the combined magnitude and magnitude difference appears on the right hand side. The brightness ratio of the two stars is found in each case.

Triple Star

The position angle and separation of star B with respect to star A are entered, along with the same values for star C, although with respect to the mid-point of the distance AB. The position angle and separation of star C with respect to star A is the result.

If star C can be seen in the field of view with the same power eyepiece as is used to measure AB it would follow that AC be measured in the same way as AB. This program should be used when star C lies outside the field of view a lower power eyepiece is required to see all three stars in the field of view at once.

Recommended Focal Ratio

This program carries out the simple division required to calculate a suitable focal ratio for observing double stars. The results give the recommended minimum focal ratios for a telescope without any Barlow lens, one with a 2x Barlow, one with a 3x Barlow and one with a 5x Barlow lens.

Rectangular to Polar conversion

This program is the spherical equivalent of the rectangular to polar co-ordinates of plane trigonometry. Specifically, it is for converting differences in right ascension and declination to position angle and separation.

The right ascension and declination of each of the two stars is to be given and the program returns the differences in right ascension and declination and the position angle and separation calculated from these differences.

Micrometer Calibration

It is necessary to obtain values for the orientation of the micrometer and the image scale of the telescope before any useful information can be derived from the micrometer. The program Micrometer Calibration can be used to obtain these values.

First enter the position angles and separations of the two calibration stars and then the number of measurements made of the stars. Measurements should be made at the beginning of the observing session and then again at the end of the session. The number of measurements made at the start of the observing session does not have to be the same necessarily as those made at the end of it. The same calibration star can be used both times, although different stars are more often used. The mean values of the measurements are then used for the position angle correction and image scale in the reduction of the observations.

When all of these initial values have been entered click on the ‘Calibrate’ button. A message box will appear to request the position angle readings made at the star of the observing session. Press enter, or click on the ‘OK’ button, and a series of input boxes will ask for the position angle readings.

Once the position angle readings have been entered another message box will appear requesting the double distance values. Press enter and a series of input boxes will appear asking for the double distance measurements. They will ask for the double distance measurements in pairs, i.e. the first double distance setting and when that is entered the second one will be asked for, the difference between the two being the double distance. The input value is expected to be in millimetres.

When the position angle and double distance measurements for the first star have been made the program will then ask for the same for the second star.

Each reading for the position angle and the two double distance measurements will show in the columns on the right under the respective headings of PA, Sep1 and Sep2. Each column can accommodate six entries for each star. If more than six entries are made only the last six will show.

The results will give the orientation correction, i.e. the correction to be applied to the position angle, and the image scale, i.e. the figure that converts the separation value in millimetres to seconds of arc. The standard deviation for the orientation and scale are also given. These values are written to a text file, micrometer.txt, which is placed in the root directory of the hard disk drive from where it is read by the program Micrometer Reduction.

Micrometer Reduction

The reduction of filar micrometer observations of double stars can be carried out with this program. The date and time are asked for as a single entry, namely year, month, day and hour of the day (24 hour format). The date and time should be entered as local time. The program uses the geographical location file, location.txt. If the measurements were taken over several days then the mean date would be the date to use (in which case the hour of the day would have little meaning and zero hours would suffice).

It is not necessary to enter anything in the position angle correction and image scale input boxes if the values for the correction and the scale were derived using the program Micrometer Calibration. Micrometer Calibration writes the scale and orientation values to a text file which is read by Micrometer Reduction. If this text file is not present then the position angle correction and the image scale values will have to be entered manually.

When all of these values have been entered click on the ‘Reduce’ button. A series of input boxes will then follow asking for the position angle readings. Once these have been completed another series of input boxes will appear asking for the double distance measurements. They will ask for the double distance measurements in pairs, i.e. the first double distance setting and when that is entered the second one will be asked for, the difference between the two being the double distance.

As each reading for the position angle and the two double distance measurements is entered it will show in the Data group under the respective headings of PA, Sep1 and Sep2. When the data has been entered each column of figures will be underlined with the mean value for each column being shown under the line. Each column can accommodate six entries (plus the mean values). If more than six entries are made only the last six will show.

The results of the program give the mean position angle, separation and their standard deviations. The Besselian epoch is also given to date the observations.

Ring Micrometer Calibration

Ring Micrometer Calibration is used to convert the transit times of a star across a ring micrometer to seconds of arc, being the scale of the ring micrometer.

The declination of the star whose transits were timed is entered along with the number of timings made for that star. The button ‘Calibrate’ is then clicked and a sequence of input boxes pops up into which the timings are entered.

If the resulting radius of the ring has a negative value it will be because the more southerly of the two stars was entered as the northern star.

Ring Micrometer Reduction

This program handles the complexities of reducing the observations of double stars to their position angles and separations.

The date and time are asked for as a single entry, namely year, month, day and hour of the day (24 hour format). The date and time should be entered as local time. The program uses the geographical location file, location.txt, which must be in the same directory as this program. If the measurements were taken over several days then the mean date would be the date to use (in which case the hour of the day would have little meaning and zero hours would suffice).

The declination of the primary star is entered along with those of the companion star. If the declination of the companion is not know, as will be the case more often than not, then enter ‘x’ for the degrees of declination for the companion. The radius (note: radius, not diameter) of the ring is entered and also the number of timings made of the star. When the ‘Reduce’ button is clicked a sequence of input boxes will appear into which the timings are to be entered (as with the calibration program). The results will be the difference in the right ascension of the two stars and their difference in declination, along with the position angle and separation.

Precession

Many double stars have not been measured in many years, sometimes in over a century. During that time they will have changed their positions due to the effects of precession and proper motion. An online program to calculate the effects of precession can be found at http://fuse.pha.jhu.edu/support/tools/precess.html