ON OBSERVATION OF LOW-MASS AND SMALL-SIZE SPACE OBJECTS USING THE GROUND-BASED OPTOELECTRONIC MEANS

S.E. Zdor, V.I. Kolinko, V.V. Titenko

The existing general trend to reduce the mass, the size and the power consumption of technical devices and systems is also applicable to space systems in full measure. At the 3rd International Conference on small-scale satellites it was noted [1]: “…the strategy of research and exploitation of the outer space using low-mass and small-size space vehicles (SV) is taking on special actuality. The share of low-mass and small-size SV in the orbital groups of spacecraft, that are launched now, increases continually. The forecasting evaluations show that this trend will grow in future”.

In view of the fact that minor space vehicles are now becoming the key element of the perspective space programs a lot of leading space companies of the USA, Russia, the UK, Germany, France and China carry on active works in developing new generation of space systems using micro- and nanotechnologies to solve problems related to the science, economics, defense and the state security.

The more active policy in the field of small-scale space vehicles is due to the fact that the developing potential of micro- and nanotechnology allows to greatly improve the performance characteristics of the conventional space vehicles.

At the same time it should be admitted that the use of small-size space vehicles at the contemporary level cannot completely replace or displace the conventional space vehicles which are multi-purpose and multi-functional in most cases and are designed to solve problems that cannot be “covered” by minor SV. Therefore, the transition to the use of small- size space vehicles should be gradual and successive based on the well-grounded scientific and technical policy according to the principle of “wherever it is necessary and advantageous”.

The given lengthy quotation from [1] defines the general trend of the small-size SV development. Table 1 gives the concrete information on small-size SVs that were launched in 1981–2001.

SV type	Years																	Total
	up to 90	90	91	92	93	94	95	96	97	98	99	00	01	02	03	04	05
Mini SV 100-500 kg	33	13	19	17	16	14	3	10	14	19	49	15	2	6	7	8	2	247
Micro SV 10-100 kg	144	22	25	11	9	5	8	5	9	29	15	9	10	8	5	8	3	325
Nano SV 1-10 kg	-	-	-	-	-	-	-	-	1	3	1	7	1	-	-	1	1	15
Pico SV 0.1-1 kg	-	-	-	-	-	-	-	-	-	-	-	-	2	-	2	-	-	4
Femto SV up to 0.1kg	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Total	177	35	44	26	25	19	11	15	24	51	65	31	15	18	23	19	6	606

By the minor SV classification adopted by space vehicle designers the account of their mass is taken first of all. The size characteristics are not considered to be the principal ones, since the cost of launching into an orbit is usually estimated in «dollars per kilogram». When SVs are observed by the optoelectronics means quite other characteristics, however, begin to play the decisive part, and first of all the dimensions of space vehicles, their configuration, and the optical properties of their surfaces.

Fig. 1.

It is necessary, therefore, to determine the dependence between the mass of a SV and its characteristics affecting its brilliance, and first of all its dimensions. If it is assumed that a space object of any virtual configuration can be approximated by a certain equivalent sphere with the radius r_eq, then it is expedient to set this dependence as r_eq = r_eq (M_SV) where M_SV is the mass of the SV. Unfortunately for a great many of SVs such dependence can be obtained only approximately. The diagram on Fig. 1 actually shows the dependence r_eq = r_eq (M_SV) for minor space vehicles beginning from «Sputnik-1» and «Avangard-1» and ending with some vehicles that are in the design stage now. Though this diagram is not at all complete, it still allows to clarify the situation arising in the outer space. The obtained statistics show that for «mini-SV» the radius r_eq lies within the range of 0.3 through 0.9 m and for «pico-SV» it is within the range of 0.05-0.1 m.

The above consideration concerns for the most part with the space vehicle observation. The important component of the general problem of minor space objects (SO) is also the observation of space refuse fragments [3]. The operation of passive optoelectronic means for observation of both space vehicles and space refuse fragments, while being practically identical, still presents some difference. This difference is due to the fact that for the space vehicles it is necessary to obtain the «catalogue» data, while for the space refuse fragments it is possible to statistically estimate the space contamination at certain altitudes without running a catalogue for concrete minor SOs. This difference should be taken into account in further consideration.

It is known that for SO detection by a passive optoelectronic means the following conditions should be met:

• the SO must fall into the field of view;
• the SO brilliance must be not weaker than the penetrability of the optoelectronic means;
• the SO velocity must be within the range of velocities recordable by the means.

For small-size SO the second condition is the most difficult to be fulfilled. For the quantitative estimation of the SO brilliance in the stellar magnitudes in the V (visual) system the following expression can be used:

         (1)

where m_Θ is the visible Sun's magnitude in V system behind the atmosphere, m_Θ = – 26.78; α is the SO integral reflectance (the albedo) of the visible object surface averaged over it; r_eq is the radius of the equivalent sphere; ψ is the phase angle which defines the quantity of the sunlight reflected in the direction of the optoelectronics means and depends on the mutual location of the SO, the Sun, and the observer; L is the slant range to the SO; τ_atm(0) is the integral atmospheric transmittance in the visible at zenith; z is the zenith angle at which the SO is observed from the optoelectronic means site; M(z) is the ratio of the air column mass at z angle to the air column mass at zenith.

In its turn

         (2)

where: R_e = 6371·10³ m is the Earth mean radius, H is the SO flight altitude.

We can assume with sufficient degree of accuracy that

         (3)

The SO albedo depends on the SO surface optical properties. In practice diffuse reflection is typical for most cases of the SO observation. As a rule the value of α is in the range of 0.1 through 0.4.

By use of the method exposed above the estimation of brilliance for some typical SOs of different radii r_eq and located at different altitudes H has been performed. While calculating, it was assumed that α = 0.3; τ_atm = 0.7. The calculation results are given in Table 2.

SV characteristics		SV brilliance, magnitude
SV type	req, m	Н=400 km		Н=4000 km		Н=40000 km
		z=70° ψ=8,2°	z=45° ψ=28°	z=70° ψ=3°	z=45° ψ=12°	z=70° ψ=0,5°	z=45° ψ=2,3°
Mini SV 100-500 kg	0,3-0,9	8,7-6,3	6,9-4,5	12,7-10,3	11,6-9,2	16,9-14,5	16,2-13,8
Micro SV 10-100 kg	0,15-0,5	10,2-7,6	8,5-5,8	14,2-11,6	13,1-10,5	18,4-15,8	17,7-15,1
Nano SV 1-10 kg	0,1-0,2	11,1-9,6	9,3-7,8	15,1-13,6	14,0-12.5	19,3-17,8	18,6-17,1
Pico SV 0,1-1 kg	0.07	11,9	10,1	15,9	14,7	20,1	19,4
Femto SV up to 0,1 kg	-	-	-	-	-	-	-

Another unfavorable factor affecting minor low-orbit SOs is their great apparent angular velocities ω_SO that reach 1.12 °/s at the altitude of 400 km and 0.089 °/s at the altitude of 4000 km. Such angular velocities impair the conditions for the SO recording, because, due to the lack of data related to their motion direction, the capability of the signal accumulation in photodetectors is reduced sharply.

The information about the SO average apparent angular velocities is given in Table 3. The velocities are given for the case of SO observation accounting for the Earth rotation. In the Table are given also the linear velocities of the SO image on the sensitive surface of the photodetector and the signal accumulation duration assuming that the focal length of the optical system is 2 m and the pixel size is 20 μm.

SO flight altitude, km	400	4000	40000
SO apparent angular velocity, °/с	0,72	0,074	0,0041
SO image linear velocity, mm/s	25	2,58	0,143
Signal accumulation duration, s	0,0012	0,011	0,21

If the movement direction of a minor SO is unknown, the way out can be found by introduction of the special search and detection mode described in [5]. The basis for this mode is the approach used by astronomers while photographing the meteors. The mode is as follows. The optoelectronic device field of view is adjusted to the reference point of thecelestial sphere, and then it is put in motion at a fixed velocity and in a fixed direction. The motion velocity is chosen to be equal to the SO velocity at the altitude to be monitored. During the motion the detection events occur repeatedly. When the area is examined the field of view is shifted to a new point and put in motion at the same velocity but in another direction.

In this mode the immobility or the low-mobility of a minor SO against the moving stars is used as a character by which they are automatically detected. As a result only those SOs are detected that move in the monitored direction at the monitored altitude and have the brilliance of m_SO ≤ m_p where m_p is the device penetrability. In this mode there is almost no loss in the penetrability at low altitudes, but it has to be paid for by sharp reduction of searching capabilities.

The above consideration is based on the supposition that the sunlight reflection by a SO obeys the diffusive law, and the mirror reflectivity component is not taken into account. Such behavior is true for the most part of the monitored area. When operating near the Earth shadow boundary the mirror component increases significantly and can exceed the diffusive one by several times. This fact should be taken into account when planning the operations on small-size SO.

1. The passive optoelectronic means working in the standard mode can detect small-size SO of the radius r_eq = 0.3 - 0.9 m located on the geostationary orbits and also objects of r_eq = 0.1 - 0.5 m located at middle and low orbits. All these objects fall into the «mini-SV» and «micro-SV» classes and make up more than 90% of the small-size vehicles. This group includes also a part of low-orbit objects of the «nano-SV» class.
2. As a matter of principle the optoelectronic means are capable to detect «micro-SV» on high orbits as well as «nano-SV», «pico-SV» and even «femto-SV» on low and middle orbits, but the special searching modes must be introduced that would direct efforts toward recording the mirror component of the reflected sunlight (mainly in the field adjacent to the Earth shadow boundary), and also modes that allow to increase signal accumulation time by tracing the supposed velocity vector. In the last case the search capabilities of devices are somewhat reduced.
3. For valid observation of all classes of low-mass and small-size SVs thoroughgoing measures are required to improve the optoelectronic means characteristics and first of all to increase their penetrability for 2^m – 3^m.

1. Анфимов Н.А. Тенденции развития космической техники на современном этапе. 3rd International Conference & Exhibition. «Small Satellites: new Technologies, Miniaturization Efficient Applications in 21st Century», vol. 1, May 2002, Korolev, Russia, p. 5-10.
2. Кузнецов А.Н., Осадченко А.С., Ромашкин А.М. Анализ сектора рынка малых спутников (наноспутников) и возможных схем их размещения в отсеках полезного груза средств выведения. 3rd International Conference & Exhibition. «Small Satellites: new Technologies, Miniaturization efficient Applications in 21st Century», vol. 1, May 2002, Korolev, Russia, p. 396-403.
3. Рыхлова Л.В. Проблемы околоземной астрономии. В кн.: «Околоземная астрономия (космический мусор)», М., Институт астрономии РАН, 1998, стр. 8-16.
4. Мартынов Д.Я. Курс практической астрофизики. – М.: «Наука», 1977.
5. Zdor S.E., Chernov V.S. Potentialities of Passive Opto-Electronic Means for Space Monitoring. «Orbital Debris Monitor», vol. 5(2), April, 1992., p. 13-14.

Размещен 7 декабря 2006.