1.  Introduction to artificial Earth satellites' observations

Optical observations of Earth-orbiting objects require specific equipment and non-standard observational strategies, differing from those typically used for astronomical purposes. The basic difference is extraordinarily fast movement of the objects in question on the celestial sphere, exceeding not only the velocity used for star observing (15"/s), but even the motion of the fastest Near-Earth Asteroids (typically several "/s with reference to background stars). In the case of LEO (Low Earth Orbit) objects the required telescope tracking speed may reach several thousands of arc seconds per second, which exceeds the capability of most typical astronomical telescopes. Thanks to the use of gear-less direct-drive motors, which have become more common in the last years, it has become possible to reach high motion speed maintaining high precision, which enables artificial satellite observations with relatively cheap telescopes from e.g. Planewave or ASA, despite the fact that they have not been designed specifically for this kind of observations.

Standard astronomical software requires that the images of reference stars and the target object should have regular, circular shapes to derive precise astrometry. In the case of artificial Earth satellites' observations this condition is hard or even impossible to fulfill, as it would require ultra-short exposure times, typically 0.1-0.001s. Such short exposure would only allow to image the brightest satellites and comparison stars, which would limit observational capability to very few targets. Since it is necessary to use longer exposure times, the result is either the image of the target as a point source and comparison stars in the form of parallel streaks (in the case of satellite tracking), or the images of stars as point sources and the satellite as a long streak (in the case of star tracking). The standard astrometric procedures must therefore be modified, supplemented with automatic detection and calculation of geometrical centers of streaks in the images, which is not trivial. No standard, widely accepted astronomical algorithms of this kind exist so far.

A crucial problem in Earth-orbiting objects' observations is the observation time, which should be recorded as accurately as possible. In the case of objects moving with angular velocity of over 1 degree per second the error in shutter opening and closing time should not exceed 1 millisecond. The error of the satellite's coordinates calculated from observations would otherwise be much larger than the error of its position in the recorded image. Astronomical CCD cameras are equipped with mechanical shutters, which opening/closing times are of the order of 10 milliseconds, while the moments of shutter opening/closing are determined with the errors of ~100 milliseconds. It is possible to improve these results by registering the shutter's opening/closing electronic signals independently from camera's driver. The errors in this approach may, however, still be substantial. The only method that guarantees proper time recording is to directly measure the position of diaphragm or shutter. Since none of the astronomical cameras has such a function, it is necessary to build a dedicated external shutter. This problem mainly applies to LEO and MEO objects (see Fig. 1), but needs to be solved in order to extend observation capabilities to these highly populated regions around the Earth.

Fig. 1. Position error of the optical measurement of a satellite in the celestial sphere with respect to the accuracy of time measurement of camera shutter opening and closing (all other error sources excluded). Area A shows the accuracy range available with a dedicated, accurate camera shutter. Areas B and C characterize the accuracies available with independent registering shutter opening/closing electronic signals (B) or a standard camera's driver (C).

In order to ensure good accuracy of satellite's astrometry it is important to use appropriate telescope's optical system. Larger telescopes (> 0.5m) provide higher observing range and better image scale per pixel, but this also smaller field of view (FOV) and larger price (not only the price of the telescope, but also of the CCD camera, which needs a large detector to utilize the telescope's FOV). On the other hand, small-diameter telescopes (< 0.3m) enables larger FOV, which is a great advantage for sky surveys and search for objects, which orbits are not accurately known. Their observing range is, however, limited, and the image scale per pixel is less favorable, so the position measurement is less accurate (see Fig. 2). Therefore it seems an optimal instrument should consist of two telescopes: one with larger, the other with smaller diameter, placed on a common mount. Such system would allow unique observing mode: the object would first be observed with wide-field, smaller telescope, which would enable the calculation of preliminary orbit, which in turn would be used to continue observations with the larger telescope. This approach would allow obtaining high precision of position measurements (provided by the larger telescope) for every object observed with the smaller one.

Fig. 2. Relative costs and basic parameters of a satellite telescope with respect to its aperture. Two areas have been marked, one optimal for lower accuracy surveys (A), the other optimal for higher accuracy observations of objects on known orbits (B).

2.  Artificial Earth satellites' observations with RBT/PST2 telescope

In the spring of 2015, the RBT/PST2 telescope in Arizona performed remotely controlled and fully automatic observations of artificial Earth satellites. Thanks to high flexibility of RBT controlling modules it was possible within only several days to program and put into operation procedures dedicated to automatic satellite tracking. These procedures enabled satellite observations in standard star tracking mode, as well as high speed satellite tracking mode. Images taken during these satellite tracking tests have been used for astrometry and orbit determination of the observed objects. The results have proved that a telescope of the same class as RBT is capable of measuring satellite positions with the accuracy of 0.5" or better.

The RBT telescope, used during the satellite observations described above, was initially designed for different purposes, which is why it is equipped with a CCD camera providing a small field of view (9' x 9') due to the small size of its detector. Unfortunately, the available TLE catalogs and standard calculation algorithms (such as SGP4) do not guarantee the predicted position accuracy to be good enough to spot the objects within the small FOV. This is why the instrument dedicated to satellite observations should provide as wide field of view as possible. In the case of RBT, which is based on Planewave CDK700, it is possible to extend the effective field of view up to 40' x 40' by changing the CCD camera to a model with larger detector and adding a focal reducer. Such change would substantially increase the rate of success of satellite detection in the obtained images, as well as the chance to record enough reference stars, which are crucial for astrometric measurements.

Despite RBT's limits, related to its original design goals, multiple successful observations have been performed of various Earth-orbiting objects, followed with the determination of their orbital parameters.

Fig. 3. An all-sky timelapse, presenting one night of RBT's robotic observations. At 8:50 UT the telescope begins the observations of 13 Earth-orbiting satellites.

3.  The results of artificial Earth satellite observations with RBT/PST2

Early in 2015 RBT/PST2 telescope has been used to conduct an observing campaign of Earth's satellites in LEO, MEO, GEO and HEO orbits. The campaign consisted of 12 nights during which 50 different targets have been observed. Some of the satellites were only observed once, others multiple times during different passages over Winer Observatory. Among the observed targets were:

  • geostationary satellites (Directv 8),
  • space telescopes (CXO, HST),
  • navigation satellites (GLONASS),
  • inactive satellites (Envisat),
  • geodynamic satellites (LAGEOS-I),
  • rocket stages (Ariane, Delta 1B),
  • International Space Station (ISS),
  • space debris (Fengyun1-C, Thor ablestar, midas 4, pageos 1, sl-6).
Fig. 4: Sample images of satellites and space debris:

a) Fengyun-1C (29782) - LEO, b) Lageos-I (08820) - MEO, c) Galaxy 12 (27715) - GEO, d) CXO (25867) - HEO

The artificial Earth's satellites and space debris were observed in two different modes: the star-tracking mode and satellite-tracking mode. Each of these strategies has both advantages and disadvantages.

The star-tracking mode, used most commonly in the beginning of the campaign, allows to reduce the influence of catalogue errors, especially regarding the satellite's mean motion. Also, star tracking mode requires the knowledge of satellite's position in the sky for a given moment, not the exact knowledge of its motion during whole observations. For fast-moving targets, however, this approach limits the number of images possible to obtain during a single observation to several at most.

The satellite-tracking mode allows to take many more images of the same satellite during its passage, but requires calculation of the satellite's velocity in the celestial sphere and appropriate modification of telescope controlling software.

Fig. 5. Goostationary satellite Directv 8 (28659) observed in different modes

a) star-tracking, b) satellite-tracking.

The artificial Earth's satellite images obtained during our campaign have been reduced and used for further astrometric analysis. Astrometric measurements of the satellites' positions were only possible in those images, which contained enough reference stars of known positions. As a result, we have obtained over 200 satellite positions from observations in both star-tracking mode and satellite-tracking mode. The uncertainties of the measured positions were less than 0.5", in many cases reaching even 0.1".

Residual distributions of all test observations are presented in figures 4 and 5. The targets' position residual scatter in right ascension is greater than the one in declination. This is an expected behavior due to fast movement of Earth's artificial satellites and the fact that in most cases the velocity component in right ascension dominates over the one in declination.

Our analysis included inspection of precise star catalogues (e.g. USNO, UCAC, NOMAD) regarding their usefulness for satellite astrometric analysis, as well as development of optimal observing strategies.

Fig. 6: Distribution of measured coordinates relatively to determined orbits in right ascension and declination for all astrometrical observations performed from April to June 2015.

The resulting Earth satellites' equatorial coordinates were then used to fit osculating orbits and determine the satellites' temporary orbital parameters. The differences between calculated orbits and satellite positions derived from observations were very small, reaching at most several arc seconds, which is a very good result, proving high quality of our observational data.

Examples of targets for which we calculated orbits from observations are listed below:

1. From 186 1-second exposures taken during 12 minutes of observations, we have derived spherical coordinates of the geostationary satellite nr 28659 with the accuracy of ~0.1". Based on these observations, we have calculated the orbit, which mean error is of the order of 3.9". The obtained orbital parameters are consistent with those derived from the catalogue.

2. For Chandra space telescope, localised in a highly elongated orbit, with the eccentricity e=0.75 and apogee distance of 135 000 km, we have measured 31 positions during less than 4 minutes. Despite such short observing time span, the coordinates measured with ~0.2" accuracy allowed to fit the orbit with the mean error of 3.3".

3. We have measured 45 positions of the upper stage of Ariane rocket (32295) within 2.5h. This satellite is located in a 9.5h HEO orbit. The uncertainty of the orbit calculated from our observations is of the order of 1.27", which proves the perfect inner consistency of the measurements. The calculated osculating orbit was compared with the mean orbit provided in TLE catalogue (see table 1). The calculated orbital parameters reveal the expected level of consistency with catalogue data.

Tab 1. Comparison of determined and catalogued orbital elements of object 32295.
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