Methods for small telescopes

Introduction

Where to look?

Overview of methods at the telescope

Short is good

Stacking is the cheapest way to buy yourself better hardware...

(stacking techniques)

It's all in the timing...

Direct NEO Distance Determination by Parallax (added 30 Dec 2004)

Introduction

Performing NEO follow-up work often involves imaging fast moving (sometimes very fast moving) faint objects, so therefore to provide good astrometric positions:

• Exposures need to be short so that images are as near round as possible
• The total exposure needs to be as as long as possible to give a good S/N ratio (the stronger the better for measurement accuracy)
• The timing of the exposure needs to be good in absolute terms so that any error in the position introduced from the timing is negligible. For fast moving objects this means timing to better than one second.

These factors have led me to develop the following techniques to suit my equipment. Other observers with different equipment will no doubt have their own methods - these work for me.

Where to look?

Overview of methods at the telescope

A number of short exposures are taken and stacked together taking into account the object's motion. The pc clock is kept aligned with UT over the internet and software is used to ensure that exposures start as close as possible to an integer second.

Short is good

(Lots of) short exposures taken at sidereal rate have several advantages over longer exposures taken tracking the object:

• Often the original ephemeris prediction for a NEO is somewhat off, based on possibly a very short arc at discovery. Stacking short exposures means that if the original rate of motion gets revised significantly the images can be re-stacked with the correct motion allowing a more precise position to be measured. Taking a long exposure and tracking at the originally published rate does not have this advantage.
• When a NEO passes close to a field star the exposures where the object is at it's closest can be left out when stacking, allowing a measure to be made. If a long, single exposure had been taken the field star would have ruined the image permanently.
• If there are other objects in the field of view (e.g. main belt asteroids, moving at different rates) these can be stacked independently to obtain better S/N ratio and reduce trailing, allowing all objects to be measured with good sharp images.

As a general rule I try and keep exposures short enough to stop the object trailing more than about the size of 1 pixel (or 3 arcsec when I'm using 2x2 binning) during the exposure. e.g. if the object is travelling at 30 arcsec per minute then I would expose for 1/10th of a minute or 6 seconds, to keep the trailing to 3 arcsec. The brightness of the object will dictate how many exposures need to be taken, so that the total integration when stacked is enough to record the object well.

For faster moving objects I normally use 2x2 binning to speed up image download. Exposures in these cases can be very short, sometimes only 1-2 seconds, so getting as many images as possible as the object crosses the frame can be very important and the shorter download speed can be critical.

Accuracy limitations of the LX200 mount and the advantages of re-stacking mean I normally limit all my exposures to a maximum of 30 seconds duration. Exposing longer than 30 seconds cause a small percentage of images to be slightly trailed.

Stacking is the cheapest way to buy yourself better hardware...

As the accuracy of astrometry is so dependent on the strength of the image being measured, I use Astrometrica to stack multiple exposures together to increase the signal strength. For $25 you can get results as if you had a telescope or CCD several times larger or more sensitive than you actually have.

Astrometrica provides functionality to:

• Stack multiple images together
• reduce astrometric positions
• provide magnitude information
• create a report file in the correct format for sending to the MPC
• Provide an overlay for any moving objects in the field of view (as long as the orbital elements have been downloaded)
• detect moving objects in a set of three  or more images 
• preview images prior to stacking to discard any that may have defects 

I strongly recommend Astrometrica to get the best from your equipment.

Check out the Stacking Techniques pages for more information on how to get the most out of Track & Stack.

It's all in the timing...

A fundamental issue with measuring the exposure start time with the AP47p  (and many other commercial CCD's) is that the camera only records the exposure start time to whole seconds, but NEO work can demand time to be recorded significantly more accurately than this.

To get around this limitation the PC's clock is set to better than one second accuracy and then exposures are started at the moment the PC's clock changes from one second to the next. If both are done correctly then the actual exposure mid-time can be determined to significantly better than one second accuracy.

During an observing run the PC is connected to the Internet and the freeware utility Dimension4 is used to keep the PC accurately aligned to UT.

A Visual Basic program called CCDCamCtl is used to initiate one or more exposures. Before each one it waits for the PC clock to change from one integer second to the next. As soon as it does the program instructs Maxim DL/CCD to open the camera shutter. The number of milliseconds between this command and the program receiving control back again is measured. Generally just a few hundredths of a second elapse from the PC clock second changing and control returning to the program. The start time + the millisecond count is used to set the Exposure start time FITS header keyword with a value to three decimal places.

From the fastest NEOs measured at Great Shefford with this setup the timing error appears to be of the order of 1/3 second or better in absolute terms, the actual amount being masked by a combination of the real clock inaccuracy and all other components contributing errors (e.g. star catalogue positions, imperfect optics etc.)

As an example, click below to see a stack of images of 2003 DW10, taken during it's close approach to Earth on 2003 March 2.8 UT when it was moving at over 150 arcsec per minute:

Using a close approach like this is probably the easiest way to check in absolute terms the precision of time measurement, which can be rather difficult to determine otherwise.  

The residuals for 2003 DW10 published by the MPC for the 24 positions reported from J95 on 2003 March 2 were used to give some idea of the maximum timing error by assuming each residual was entirely due to errors in timing.

The standard deviation of this error works out to be equivalent to a timing error of +/- 0.34 seconds. Other errors not considered here (e.g. star catalogue errors) are likely to reduce the actual error solely due to timing to slightly less than this value.