There have been a few postings recently about observing accuracy, so
here is my contribution.
Many (probably most) observers determine satellite positions as a
fraction between 2 stars. The error in position is partly due to the
accuracy of the star positions, partly due to the error in determining
the fraction.
In the pre-computer days star positions were measured by ruler on star
maps (error maybe 0.02deg with a good map); if you still do this then
check the accuracy by measuring a few stars whose true positions are known.
These days star catalogs are commonly used, so the error in star positions
is very small.
The major error is due to the fraction.
On 1968 October 16 an experiment was performed in which a simulated
satellite passed among a projected star field, and about 30 satellite
observers estimated the fraction (which was later measured accurately).
Here is a summary of the results collected by Gordon Taylor, all in %;
see below for column f2.
Test True Mean Standard f2
fraction error deviation
1 55 -1 4 5
2 34 1 6 4
3 157 -10 11 18
4 27 -1 4 4
5 53 -3 5 5
6 203 -4 20 42
7 85 0 4 3
8 -21 3 4 5
9 27 -2 4 4
10 73 1 5 4
11 -59 8 11 19
12 20 0 4 3
Note that tests 3 6 8 11 extrapolate beyond the stars, the others
are interpolations. As one might expect, the extrapolations are
generally less accurate. Unfortunately none of the tests went close
to either star. I believe that close to a star, the error would be
approximately proportional to the distance from that star.
In 1985 I started interpolating by computer, and I wanted a formula
to give me accuracy, depending on fraction and star separation. I chose:
error = e+(star separation)*abs(f*(1-f))*k
where e and k are constants.
The formula is symmetric about f=0.5 (=50%), and gives the desired
behaviour near either star (f near 0 or 1), and larger errors for
extrapolations (f<0 or f>1).
Column f2 above is this function with constant e=0 and k=0.2 (=20%),
which is a reasonable fit to the standard deviations except for the 3
biggest extrapolations.
Constant e allows for the resolution of your binoculars (plus star map
errors if used), and should be small, but not zero. Currently I use
a peculiar e=0.02+0.005*(star separation) deg and k=1/12 which gives
3.6% for separation 2deg and f=0.5, (similar to my personal results at
the meeting).
I probably should use e=0.01deg and k=0.12 which would usually give
similar results. Those with higher magnification than my 11* should use
smaller e.
Note that e is much larger than the nominal resolution of the binoculars,
since we are watching moving objects, often variable or faint.
Sometimes the accuracy from the formula has to be degraded, for example
if the visibility is bad, the satellite very faint, or only briefly
visible, or a cat has just jumped onto your lap.
You can get some idea of your accuracy by finding 3 stars in a line,
quickly estimating the fraction, and later calculating the exact
fraction from the star positions. Or estimate the ratio (separation
stars A & B)/(separation stars B & C). Or write a PC simulation of the
1968 experiment (I have a QBASIC program for this).
Mike Waterman mike.waterman@marconi.com
Site Yateley = COSPAR 2115 = 51.3286N 0.7950W 75m.
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