Gallery of the simulated photographs – In E.S. King's foot steps

In 1902 E.S. King published an article with a photographic plate of the globular cluster M 13. The specific property of this plate is how it was obtained namely without any human intervention. Neither the movement in the direction of the declination nor in that of the rightascension was corrected. E.S. King calculated based on the location in the sky (declination, local hour angle) and the latitude of the observatory the position of the hour axis and the drive rate. After that he let the telescope track the star field for one hour alone. The result is the above figure. If this plate is enlarged one sees that the stars are not completely point symmetric but almost. Think about that, he had only an adjustable mechanical clock and therefore I consider it is a real master piece.

Step by step to the photograph of M 13, the effect ...

To get an impression how E.S. King's photograph of M13 came into existence I will show you step by step the different effects. The parameters of the simulation are identical to those E.S. King published. The observing place is the Harvard College Observatory (geographical latitude j= 42.38o) and he started the exposure at the local hour angle t= 3h11m and it lasted for one hour. The diameter of the aperture of the Draper telescope was 279 Millimeter (11”) and the focal length 3350 millimeter.



... of the alignment of the hour axis


Figure 1: The hour axis points on the true celestial pole and the telescope rate is sidereal. The length of the scale in the lower left corner equals to 10 arc seconds in both directions. North is up and East to the left. The trails have been calculated for three wavelengths (450, 550 und 650 nm).

Figure 2: The hour axis points to the apparent (refracted) pole otherwise like fig. 1.




In fig.1 the hour axis points on the true celestial pole and the drive rate is sidereal and corresponds to the rotation velocity of the Earth. The nine stars placed on a quadratic grid with edge lengths of 20 arcseconds are at the beginning of the exposure centered an because the telescope is faster than the motion of the apparent sky the star trails point eastward. Because the local hour angle is increasing the effect of the refraction increases too and the apparent position of the star is moved in the direction of the zenith. The resulting star trails are longer than 10 arc seconds.

In fig, 2 the improvement due the position of the hour axis, it points now to the apparent (refracted) pole, is clearly visible. The movement in the direction of the declination is substantially reduced and a little bit over compensated.

... of the drive rate


Figure 3: The hour axis points to the apparent (refracted) pole and the drive rate is equal to the so called King's rate, otherwise like fig. 1.

Figure 4: The actual drive rate corresponds to E.S. King's equation (see article).


Often telescopes can be operated at different drive rates, e.g. lunar or solar rates. In recent years another possibility was added, the so called King's rate. This drive rate is in principle not constant and varies with declination, the local hour angle and further depends on the meteorological data on the ground. The socalled King's drive rate has only a meaning for the declination of 0o in the meridian and only if the hour axis points on the celestial pole. In other cases it is not better or worse than the sidereal rate, because the differences will be adjusted by guiding correction systems.

In fig. 3 one can estimate the effect of the King's rate compared to the sidereal rate (fig. 1 and 2). The star trails are now compressed in the direction of the rightascension. In the direction perpendicular nothing happened, because the position of the hour axis is still the same as it was previously (see fig. 2). The situation changes in case where the drive rate equals the formula E.S. King gave in his article. The movement in the direction of the rightascension is zero. That means, in case the mechanical setup of the drive works perfectly, one can omit a tracking correction system. Like in the previous case nothing changes in the direction of the declination. The length of the star trails are now only about 2.5 arc seconds.

The fine adjustment of the hour axis


Figure 5: The hour axis is setup according to E.S. King's equation depending on the declination and the local hour angle during the exposure. The simulation took place during calm air (seeing equal to zero). The star at lower left is brightened in order that the finer detail around the center can be observed.

Figure 6: Same as fig. 5 but with a seeing of about 1.5 arc second.


The only possibility to compensate the movement in the direction of the declination is to vary the position of the hour axis depending on the local hour angle an the declination of the center of the star field in question. That was done in fig. 5 and the up to now used three color mode shows only three distinct points. That is the reason why the presentation mode has been changed to where the diffraction image has been simulated too. The effect of the dispersion is now clearly visible as a minute spectrum.

The difference between fig. 5 and fig. 6 is that the seeing is not zero it has a value of about 1.5 arc seconds. If one measures the deformation of the star trail resp. one determines the length of the seen spectrum in fig. 5 one obtains nearly the value given by E.S. King of 2 arcseconds. The spectrum has a length of about 1.5 arc second. It is very likely that E.S. King used a plate which was sensitive only at the blue end of the spectrum then in the panchromatic case the length would be something around 2.5 to 3 arc seconds. As I pointed out at the beginning E.S. King had no electronic equipment and I assume that he did not change the position of the hour axis during the exposure and one can conclude that the length of the star trails he published are absolutely realistic.

Comments, questions, corrections: markus.wildi@one-arcsec.org

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