EAON circular # 6


Unduly Precision

What do we measure when observing an occultation ? We are measuring the time when a shadow is passing over.

Passing over where ? There where is the entrance aperture of the detecting system : usually a frontal lens or a primary mirror, seldom an eye pupil or a naked photodetector.

The other parts of apparatus are only used to concentrate and record the information (formation of an image, detection of light flux, comparison with a timekeeping source, etc).

To reduce the observation, it is necessary to know the place where it has been made : that is to say the place of the entrance aperture.

How much precision is necessary ?

An asteroidal shadow usually runs in the range of 10km/s (a lunar one is around ten times slower, I do not consider this case here). The main errors come from timing and locating. An error of 1km about the place amounts to an error of 0.1s in timing.

Since the accuracy of the best visual observations reaches reliably 0.1s, the error introduced by geographical coordinates rounded to 1 arcsec is negligible. It is still the case if you master the problems of timing in videocording, thus reaching a range of at least 0.03s (an equivalency of a few hundred meters). The difference in coordinates between various geodetic systems is no more than that, and is not yet taken into account in asteroidal reductions (it is in lunar ones).

When there are many observations of the same body (as it is the case for the Moon), the mean accuracy increases as the square root of the number of observations. As ILOC collects thousands of lunar observations every year, the utmost precision is desirable.

We are not yet in this range for asteroids ; nevertheless, to measure within hundred meters the position and shape of a body hundreds MILLIONS of kilometers away gives a relative precision of one part per billion (a laboratory feat).

It can make no harm if you measure your location within 0.1 milliarcsec and 1cm in height. Just explain what you measured. Don't forget that when tracking a celestial body, your scope is moving. So 1 cm accuracy could be an unduly precision.

Raymond DUSSER, 2003.04.01