Measurement of Double Stars

Using

"The Chronometric Micrometer"

by

William T Geertsen, Jr

izar@juno.com 2/20/99 izar@gateway.net

The most often asked question is; "What is a double star"?

The second most often asked question is; "What is there to measure"?

The third most often asked question is; "Why measure double stars"?

Less frequently asked; "How do you do it"?

This outline will attempt to answer these questions and to provide a method for measuring double stars with small telescopes and inexpensive instruments.

Definitions:

Star: a self-luminous object, which shines by virtue of radiation, derived from internal

nuclear reactions.

Binary or Double star: The term "Binary star" was first used by William Herschel in

1802. The true union of two stars to form an actual physical system that obeyed the laws of gravity.

We now know that there can be many more than two stars gravitationally bound in a star system.

Measurement: The two elements of a binary system which are routinely measured are

the Position Angle (PA or q) and the Separation (S or r).

PA is the angle formed between the brighter star and the dimmer star, measured

counterclockwise from celestial North. PA is expressed in degrees of arc.

Separation is the apparent distance between the two stars and is expressed as an

angular measure in seconds of arc.

Reasons for, and methods of measurement:

The reason for measurement of double stars is to compute the orbit and ultimately, the mass of the stellar system. To this day we have no other way to determine stellar mass.

Over the centuries many methods have been used to acquire the PA and Separation by visual observation at the telescope. The instruments have exotic and technical sounding names such as; The Bi-filar Micrometer (BFM), the Diffraction Grating Micrometer (DGM), the reticle micrometer, the bi-refringent micrometer and the Chronometric Micrometer, to name a few.

This outline will describe only the "Chronometric Micrometer". Descriptions of the other instruments can be found in "The Webb Society Handbook" vol.-1 and in the "Double Star Observers Handbook", ch.-5.

"Chronometric Micrometer" is a pretty scary sounding name for something you may spend hours with, alone, on a cold night. Another name for it is "The Transit Method", which is much friendlier sounding.

Chronometric refers to time and transit refers to the passage of a star across a line in the field of view. So, we measure the time it takes for both stars to cross the line. Think of it as a race with two horses, one will cross the finish line before the other. We will time the interval between the first crossing and the second crossing.

Micrometer refers to measuring very small values with a high degree of precision. The PA will be measured with a protractor and the time will be measured with a stopwatch.

Our Chronometric Micrometer is therefore composed of an eyepiece with crosshairs (illuminated or not), a protractor (circular, 360 degrees) for the PA dial and a stopwatch which can be read to 0.01 seconds. Not so scary anymore!

The February, 1999 issue of S&T has an article describing double star measurement with just such a PA dial. To make it work, the author glued the protractor to a piece of foam-core and taped a brass strip to the eyepiece to act as an indicator. The protractor is fixed tightly to the focuser and the eyepiece is rotated with the indicator to read the Position Angle.

All double star micrometers utilize a position angle dial of some sort. The differences between micrometers are in the means of measuring separation. The transit method described here uses a stopwatch and the natural drift of the star across the field of view when the drive motor is turned off (assuming you have a RA drive at all).

Telescope requirements are relatively simple. Any type of telescope is suitable; reflector, refractor, compound etc. Good optics are necessary, but there is no reason to spend thousands of dollars if you already have a good telescope. The 3.5" Questar in the S&T article demonstrates what can be done with a small scope. A 60-90mm refractor can be used if the mounting is sturdy enough. I use a 6" Newtonian for all of my measurements at this time. The mount and eyepiece are of equal importance to the objective lens. If the scope jiggles or the star cant be kept on the crosshair during measurement you will be frustrated and will not get good results.

It is my opinion that an equatorial mount is essential. You will need to track the star and make small adjustment during each session, either manually or electronically. Alt / Az mounts can be used but the star field will rotate in the field of view and can result in errors.

Materials:

The protractor can be purchased at an arts and crafts store, a college bookstore or produced with a computer. The larger the better. 4-6" is about average.

Eyepieces with crosshairs and illuminated reticles can be purchased from Celestron and University Optics among others. The Orion catalog always has a large selection.

Foam-core can be found in any school or office supply store.

The brass strip is sold in hardware stores and hobby shops catering to radio controlled boat, car and airplane modelers.

An electronic stopwatch with a large digital display. It must read to at least 0.01 seconds.

I would also recommend building your PA dial around a 2x Barlow. That will not only increase the magnification but will also retain good eye relief while observing.

Other miscellaneous stuff includes black tape, a small piece of clear plastic, double sided foam tape (use the kind that holds belt clips on portable phones).

A scientific pocket calculator with sin, cos, tan functions.

The Procedure:

Install the micrometer in the focuser tube. Locate a bright star and bring it to focus in the center of the field of view. Align your finder scope if necessary.

Reposition the scope on the star you want to measure. Turn off the drive and adjust the cross hairs until the star drifts across the field of view on the cross hair all the way. This is very important and must be done carefully. Without moving the eyepiece, rotate the PA dial until 90degrees is under the indicator line. The crosshairs and the PA dial are now oriented N/S/E/W. The star was drifting along the E/W crosshair. Remember this.

Without moving the PA dial, rotate the eyepiece until the N/S crosshair bisects the two stars exactly through their centers. You will probably need to reposition the scope slightly to keep the stars on the wire. This is where a steady mount and good slow motion controls or a drive corrector are needed. Record the PA dial setting. Without moving the PA dial, rotate the eyepiece 180degrees and take another reading. Repeat this process until you have at least six PA dial readings. Estimate as closely as you can. The plastic protractor will read directly to 0.5 degrees (30 minutes of arc). You should be able to easily estimate half that or 0.25 degrees (15 minutes of arc). With practice you should be able to estimate to half of that or 0.125 degrees (7.5 minutes of arc). The more repetitions you make the better your data will be.

Without moving the eyepiece or the PA dial, reposition the star so that is to the East of the E/W wire (that's the one I told you to remember). Make sure your stopwatch is set to zero, and turn off the drive motor. The pair will drift toward the wire. When the leading star makes contact, start the watch. When the trailing star makes contact, stop the watch. Record the time. Reposition the stars to the East of the wire and repeat the process at least six times.

Your work at the telescope is finished for this star. If you move to another star, repeat the drift step and adjust as needed. Follow the same procedure for every star and at every session to minimize errors.

Process the data:

In the warmth of your living room, convert the PA dial readings to decimal angles and average them. You will need to subtract 180degrees from half of your readings first. The data on the star list will tell you which value to use.

(30deg 30min = 30.50 deg; 30min/60min/deg = 0.5deg + 30deg = 30.50 deg)

Average the times also.

Using a scientific pocket calculator;

convert the declination of the star to a decimal value.

From the quadrant circle on the worksheet, compute the value for i.

Substitute your values into the separation equation on the worksheet and solve the

equation.

Congratulations! You have measured your first double star and computed the separation.

Don't worry about your data matching the published data. There are many reasons why it may not. With practice, over time, you will gain confidence in your method and a large number of measurements. The more measurements you make of a star, the better your data will be.

There is no instant gratification here. If you are interested in joining the ranks of the great double star observers like Struve, Von Biesbrock, Worley etc. and making a very significant contribution to the science of astronomy, this is the way to do it.

Let's get to work and update the Washington Double Star Survey and maybe the professional astronomical community will stop looking down their collective noses at amateur astronomers. There are a lot more 'us' than 'them' and we have unlimited access to telescope time around the world. If they won't do this work, we will.

Drift, Position angle and separation diagrams.

Alternate PA dial design

The PA dial shown below is a slightly different design from that described earlier. The vernier shown will allow direct reading to 5 arcminutes. If you decide to use this type of dial, copy it to whatever size is convenient for you and have it laminated in plastic to protect it from moisture. Then cut it out and fit it to your focuser or barlow as described for the plastic protractor PA dial. The vernier is attached to the end of the indicator arm (attached to the eyepiece) with the arrow (zero) lined up with the dial centerline.

Example

Note the correct location and orientation of the vernier for this type of PA dial.

You will probably need a magnifying glass to read the vernier.

First, note the nearest 10-degree value (10, 20, 30 etc.).

Second, count the 1-degree marks (add them to the 10-degree value, 10,11,12,13 etc.).

Third, locate the mark on the vernier which lines up the best with any degree mark.

The example shows a PA of 12-degrees, 30-minutes.