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ISSN 0010 9525, Cosmic Research, 2015, Vol. 53, No. 3, pp. 216­225. © Pleiades Publishing, Ltd., 2015. Original Russian Text © V.I. Zhuravlev, 2015, published in Kosmicheskie Issledovaniya, 2015, Vol. 53, No. 3, pp. 232­241.

Fakerat Software in the International Interferometric RadioAstron Project with Very Long Ground­Space Bases
V. I. Zhuravlev
Astro Space Center of the Lebedev Physical Institute, Russian Academy of Sciences (FIAN ASC), Leninskii pr. 53, Moscow 117924, Russia e mail: zhur@asc.rssi.ru
Received December 16, 2013

Abstarct--We present the description of Fakerat software developed for scheduling Very Long Baseline Inter ferometry (VLBI) observations on ground­space bases exceeding the size of the Earth. The results of sched uled observations using the Fakerat package, carried out during the first two years after launching the space radio telescope (SRT) in the space­ground interferometer mode, are reported in the paper. DOI: 10.1134/S0010952515030090

INTRODUCTION The RadioAstron space radio telescope (SRT) with a 10 meter reflector antenna onboard the "Navigator" base space platform was put into a high elliptical orbit in July of 2011. The period of its revolution around the Earth was about 8.5 days. Detailed information on the spacecraft (SC) can be found in the RadioAstron User Handbook (2012) on the FIAN ASC website http://www.asc.rssi.ru/radiastron/documents/rauh/en/ rauh.pdf, as well as in papers [1, 2]. In the first two years after SRT launching the tests of the space radio observatory have been performed according to the "Early Science Program (ESP) of the RadioAstron project. At this stage, along with testing of the SRT onboard set of instruments, Fakerat software tests have been also performed. Fakerat software is designed for mod eling the position of SRT pointed to the object, with regard to the design constraints on the SC orientation, the angle of SC visibility by the tracking ground station (TGS), as well as the angles of visibility of a source tracked by the ground based radio telescopes. After modeling the decision was made on the possibility of performing interferometric sessions for each particu lar object taking into account its scientific objectives, the duration of observation, the observation date, the wavelength range, the interferometer base projection, the filling of UV coverage, the tracking ground sta tion1 and ground based radio telescopes.
1

For data transmission in the interferometry mode at the ESP stage, only one high informative radio channel (HIRC) of the tracking ground station was used, which was prepared in Pushchino on the RT 22 telescope basis. At the moment of paper writing, the second HIRC was prepared on the basis of the equatorial installation of the Green Bank 43 m radio tele scope in the western hemisphere.

The Fakerat package is based on the programs contained in the "Caltech VLBI Analysis Program" package [3] and designed for scheduling and analysis of interferometric observations in the experiments with ground bases. Later on, in 1983, D.L. Meier (Jet Propulsion Laboratory) [4], while working on the "QUASAT" space project, added into the package the possibility of modeling the orbital radio telescope operation. The software has been further developed in D.W. Murphy's work on the "VSOP" project [5, 6]. Murphy introduced into the package the constraints for the first "VSOP" space radio telescope specifi cally designed for interferometry, and added the graphical interface, which has provided customers with friendly support in the study of research per spectives of interferometric observations. This sup port greatly facilitated the work related to scheduling the experiment. Just at this stage of software develop ment the Fakerat package appeared. Fakerat software was written in the Fortran language and implemented on SUN and HP working stations with the Unix operation system. In the spring of 2011, six months before the Radio Astron launching, we have modified the Fakerat pack age with regard to the necessary constraints and some other features imposed on the SC in the RadioAstron project. The modification consisted primarily in full replacement of the orbital unit of the package. In the new orbital unit we took into account the disturbances of the RadioAstron orbital elements; we also intro duced new functional constraints on the specified SC orientation, on the ground based means of providing the RadioAstron functioning, and made some changes in the graphical interface for more convenient use of the software. Currently, the modified version exists under the name Fakerat and is freely available on the FIAN ASC

216


FAKERAT SOFTWARE Table 1 Date, time x y km 155 550.653 150 064.383 144 743.696 ­30 793.986 ­30 247.683 ­29 702.761 0.435776 0.462246 0.489042 z v
x

217

v

y

v

z

km/s ­1.292218 ­1.328900 ­1.365355 0.126814 0.134241 0.141747

Jun. 1, 2014 00.17.06:574 ­110 773.371 Jun. 1, 2014 01.26.53:287 ­108 894.142 Jun. 1, 2014 02.32.43:403 ­107 015.913

website. Each user can acquire a compiled version of the Fakerat package along with the source code by the address: http://www.asc.rssi.ru/radioasron/software/ soft.html. There one can also find the instructions for the Fakerat package installation on the IBM PC under the guidance of the Linux operation system, the pack age description, some techniques of working with the package, and some useful tips are given. 2. THE ORBITAL MOTION OF THE SPACECRAFT The orbital motion of SC depends on the external forces acting on the vehicle. When considering the SC motion in the close vicinity of the Earth, i.e., at dis tances from a few hundred to thousands kilometers, the gravitational effect of other celestial bodies can be ignored [7]. However, when considering the SC motion at high altitudes, one should take into account the accelerations caused by the Moon and the Sun. The "VSOP" SRT orbit reached the altitude of 21400 km at the apogee and 560 km--at the perigee. The period of revolution around the Earth was equal to 6.3 hours. According to the model accepted in the Fakerat, due to relatively low orbital altitudes, the "VSOP" SRT motion was calculated in the Newtonian central gravi tational field as an undisturbed one. The value of the orbital altitude at the apogee for the RadioAstron SRT, when it entered the orbit after launching, was more than 15 times higher, than the value of the orbital altitude at the apogee for the "VSOP" SRT. The apogee altitude of the RadioAstron orbit was equal to 333.5 thousand km, the perigee alti tude was 578 km, and the period of revolution was 8.32 days. This distinction in the orbital parameters was motivated by a desire to obtain an ultra high angular resolution of objects. Here, the decrease in the degree of filling the UV coverage was supposed to be compen sated by the orbit evolution under an effect of distur bance from the Moon and the Sun. On the other hand, the RadioAstron motion is dis turbed by some other factors as well. Even relatively small forces, acting over a long period of time, can noticeably affect the orbit. During the flight over the high elliptic orbit the SC is affected by the complexity of the gravitational field configuration near the Earth, by the solar radiation pressure, by the aerodynamic forces arisen at SC passage through the atmosphere at altitudes up to 1000 km, etc. These disturbances sig
COSMIC RESEARCH Vol. 53 No. 3 2015

nificantly affect the SC orbit; so, the determination of the RadioAstron orbital elements requires another approach, which differs from that of the "VSOP" project. In the Fakerat model the motion over the elliptical orbit is specified by tabular values of coordinates x, y, z and components of the velocity vector vx, vy, vz of the SC center of masses in the geocentric coordinate sys tem. Coordinates and velocity vector components are attributed to some time instant t. As an example, Table 1 gives the values of these coordinates and velocities as a function of time. The geocentric coor dinates and velocities for the orbit as functions of time are calculated at the Keldysh Institute of Applied Mathematics (IAM) of the Russian Academy of Sci ences (RAS). To obtain the response of the interferometer, it is necessary to have the maximum possible accuracy of determination of SC coordinates and velocities. This is a rather time consuming task; so, as a rule, the orbit calculation for a correlator is limited by the duration of observations. The accuracy of the reconstructed orbit at data processing in a correlator is, for the position in space, not worse than ±500 m, and for the velocity, not worse than ±2 cm/s. More detailed information regarding the orbit reconstruction can be found in [2]. The requirements for the accuracy of orbital elements in the Fakerat package are one and a half to two orders of magnitude lower. This makes it possible to predict the orbit 5 to 6 years in advance, which is espe cially important for scheduling the future observations. Figure 1 presents the elements of the spatial motion of SC over the elliptical orbit: a is the semimajor axis of the orbit, e is the orbit eccentricity (0 e < 1); i is the orbital inclination, i.e., the angle between the orbital plane and the equatorial plane; is the ascend ing node longitude of the orbit; is the angle between the pericenter and the ascending node of the orbit; is the time of satellite passage through the pericenter of the orbit. The calculated evolution of six orbital elements up to the middle of the year 2019 is shown in Fig. 2. It shows that, under an effect of disturbances, the semi major axis changes from 170 up to 200 thousand km, the eccentricity, from 0.57 to 0.97, and the orbital inclination changes from 0.4° to 84°. There exist also several derived parameters: a(1 + e) is the apocenter of the orbit, a(1 ­ e) is the pericenter of


218
a(1 +e )

ZHURAVLEV Z

A

a(1 ­e )

u 0 i P X Y

Fig. 1. The elements of the orbit is elliptical. is the ascending node of the orbit, A is the apocenter and P is the pericenter of the orbit.

the orbit, and P is the SC period of revolution (or the orbital period). The SC orbital period is related with the size of the semimajor axis a as follows: P = 2 a

(

32

,

)

(1)

where = 3.9875 105 km3s­2 is the coefficient equal to the product of the gravitational constant by the mass of the Earth. The quantity µ a 3 2 is the mean angular velocity of SC motion over the orbit. The change of the orbital period is associated with the change of the semimajor axis of the orbit, the orbital period being increased with growing semimajor axis. According to expression (1) and the calculated model of evolution of orbital elements, shown in Fig. 2, up to the year 2017 the orbital period will remain in the range from 8.3 to 9.2 days, and after 2017 the maximum value of the orbital period will increase up to 10.2 days. On the other hand, the SC orbit is influenced by some disturbances, which are not determined a priori to a high accuracy. For example, these disturbances are associated with the action of reactive forces of the SC stabilization system's engines during unloading of gyroscopes. So, once every two to three months, on average, the IAM RAS provides the new updated tab ular values of coordinates and velocities for the Fak erat. It is also important to update the orbit after its correction. So, for example, in late 2011, a few months

after SC launch, perigee altitude increased. Fortu nately, such manipulations with SC happen rarely. For Fakerat functioning it is necessary to know the values of SC coordinates and velocities at the interme diate time instants. To obtain these values, we approxi mate the orbit by an ellipse with Earth's center of gravity at one of ellipse's foci. Here we take into account that the values of quantities x, y, z, vx, vy, vz at any point of the orbit are unambiguously related with the solution of Kepler's equations. Each new row of the table gives a new, updated approximation of the orbit. The semima jor axes of the ellipse, the ellipse orientation in space, as well as the SC localization in orbit were determined by six aforementioned elements. The plane of the orbit in space is specified by the orbit inclination and by the ascending node longitude. The pericenter of the orbit is determined by the angular distance from the ascending node to the orbit pericenter in the direction of SC motion. The time attribution is specified by the instant of SC passage through the pericenter. The pericenter determines the angular distance of an arbitrary point of the orbit: u = + , where is the true anomaly of this arbitrary point. And, finally, the shape and size of the orbit are specified by the semimajor axis and eccentricity. The values of orbital elements largely determine the fill ing of the UV coverage. Here, one should keep in mind that the highest angular resolution is achieved in the direction normal to the SRT orbit. The coor dinates of normals (, ) for the northern and south ern celestial hemispheres are defined by the following expressions: ( ­ 90°, 90° ­ i) and ( + 90°, i ­ 90°), respectively. In the RadioAstron project the monitor ing of sources in the regions located near the normal to the orbit on the southern celestial hemisphere is rarely implemented due to functional constraints (see Section 3). In Fig. 3 the normals to the orbit are designated as N . In observations of radio sources in the areas close to the normal, the UV coverage tracks are formed that have elliptic structure. This structure has large gaps. They will decrease when sources are moved from the normal to orbit projection in the celestial sphere. Their decrease is associated with simultaneous decrease of the angular resolution of a source. In the extreme case, when the source lies in the orbital plane, i.e., when it is located at the distance of 90° from the normal, the tracks of the UV coverage form a linear structure. A more detailed description of Fig. 3 will be given below. The sequence of operations at source observations, at adjusting and at laser location is determined by the Research program of works specified for the month ahead. This work is carried out by the operative SRT research group (FIAN ASC) [2]. The program takes into account scientific objectives, the current ballistic parameters of the orbit, the current constraints on the actuated ground based radio telescopes and constraints
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FAKERAT SOFTWARE 200 360

219

a, 106 m

190 , deg

240

180

120 170 2012 13 14 15 16 17 18 0 0.9 0.8 e 0.7 0.6 240 90 60 30 0 2012 13 14 15 16 17 18 Date, year
Fig. 2. Predicted values of changes of the orbital elements in time.

360

, deg 120 0 2012 13 14 15 16 17 18

i, deg

on the duration of observation modes for particular ori entations of SC and positions of the HIRK antenna. 3. FUNCTIONAL CONSTRAINTS OF THE SPACECRAFT There exist some constraints for the SC, which make it technically impossible for the SC to be point ing to any radio source, or make it impossible its effec tive monitoring. Below we describe only those con straints, which are incorporated in the Fakerat. 3.1. Constraints on the thermal regime. The obser vations cannot be performed: (1) if the angle between the SRT electric axis and the direction to the Sun cen ter is less than 90°; (2) if the angle between the SRT electric axis and the direction to the Sun center is larger than 165°; (3) when the distance from the Earth center to the SC is less than 20 thousand km, and the
COSMIC RESEARCH Vol. 53 No. 3 2015

radio source is located at an angular distance from the Earth disc's center less than 30°. 3.2. Constraints for the power supply system. The angle between the direction to the Sun center and the normal to the plane of power supply system's panels should not exceed 10°. 3.3. Constraints for monitoring radio sources located closely from the edges of the Earth and the Moon. The observations cannot be performed when the radio source is located at the distance less than 5° from the closest edge of the Earth, and when the radio source is located at the distance less than 5° from the center of the disc of the Moon. 3.4. Constraints imposed on the star sensors. The onboard control complex includes three star sensors: AX1, AX2, and AX3. Only two of them operate in the normal mode. The axes of two sensors AX1 and AX2


220 ()
N

ZHURAVLEV

GP

Declination, deg

50
P A
SUN

0

­50
N

25

20

15 10 5 Right ascension, hours (b)

0

GP

Declination, deg

50
SUN

N

0

P A

­50

N

25

20

15 10 5 Right ascension, hours

0

Fig. 3. Two examples of UV coverage for the whole sky.

are located in the half plane perpendicular to the elec tric axis X of the SRT and are turned around the axis parallel to the axis Y of rotation of the solar batteries' panel by the angle of 15° in the direction of axis ­X, and at the angle of 45° to the axes Y and ­Y, respectively. The axis of the third sensor AX3 is also located in the plane perpendicular to the SRT electric axis, but it is turned relative to axis ­X by 30° to the side of the third axis ­Z. The coordinate system defined above is right hand and orthogonal. According to the measurements performed by the Lavochkin Research and Production Association (Lavochkin RPA) in July 2012, the values of directing cosines of the star sensors are as follows: AX1: ­0.86640913, ­0.00055799, ­0.499933447 AX2: ­0.18425467, ­0.70842875, ­0.68130677 AX3: ­0.18282000, 0.70791153, ­0.68223024. The angle between the axis of each of two working sensors and interfering celestial body (the Sun, the Moon, and the Earth) must exceed the following: for the Sun, 40° (from the center of the Sun), for the Moon, 30° (from the center of the Moon), and for the Earth, 30° (from the nearest edge of the Earth).

3.5. Constraints for the high gain communication antenna (HGCA) "Board­Ground". This antenna provides communication with the ground tracking antenna for transmitting the scientific and service information, and also provides frequency synchroni zation. The observation of a radio source is possible only when this communication really exists. The ini tial angular position of the HGCA drive relative to the base coordinate system of SRT, defined above, is spec ified by directing cosines: axis X: ­0.95585102, ­0.00818895, 0.29373758 axis Y: ­0.00960202, 0.99994823, ­0.00336890 axis Z: ­0.29369479, ­0.00604064, ­0.95588015. The algorithm for calculating the angles of a drive of the HGCA for pointing its electrical axis to the sci ence data receiving station is as follows. When calcu lating the angles and it is necessary to take into account the angles 1 and 2 of the actual position of HGCA's electrical axis on the output flange of the HGCA drive. For zero drive angles ( = 0 and = 0) the angles 1 and 2 are determined as follows. 1--the angular deviation of the HGCA electric axis from the plane XOY. The positive direction of measuring is performed to the side of the ­OZ axis. 2--the angular deviation of the HGCA electric axis projection on the plane XOY from the OX axis. The positive direction is that to the side of the OY axis. At the initial position 1 = 15.03° and 2 = 0.32°. For the unit radius­vector r of the science data receiving station in the instrumental coordinate system the fulfillment of the following condition is checked: ry < cos (1 + n ), where n is the value of a safety threshold. In the first approximation = 1° The drive turning angles and , under the assumption that 1 = 0 and 2 = 0, are as follows:

= atan 2 -rz

(

1 - ry2 , rx

1 - ry2

- ar csi n si n 1

(

2 1 - ry ,
1

)

)

= arcsin ( ry c o s

)

- 2.

Then the values of calculated angles and are checked for belonging to the working range: min max , min max . The permissible range of turning angles is: for the angle --from ­73° to +90°, for the angle --from ­90° to +90°. The positive direction of rotation of the HGCA drive is accepted to be defined by the right hand coordinate system. 3.6. Constraints for the ground station of tracking and science data acquisition. The reception of research and service information in the RadioAstron project is performed on the ground based 22 m radio telescope of the Pushchino Radio Astronomy Observatory (PRAO). The radio telescope should provide SRT tracking during the communication session. As men
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FAKERAT SOFTWARE Table 2 X Y Z dA/dt dh/dt

221

GTS km Pushchino RT 22 Green Bank
2916.9559 882.8799 2248.6500 ­4924.4823 5190.0927 3944.1307 1.5 ­

ang. min / s
1.5 ­

tioned above, currently it is possible to use the Green station in the X Window system. The Fakerat package Bank tracking ground station there (TGS) with a mir shell is initiated after running the C Shell run script, ror size of 43 m. which sets the medium of variables needed for running The geocentric coordinates and maximum rates of the libraries of the graphic PGPLOT package. If the tracking in the azimuth dA dt and in the elevation package is set correctly, then the interactive menu of user interaction with the software from the Fakerat dh dt of the TGS are listed in Table 2. The permissible package should appear in the X Window. As men range of TGS turning angles in Pushchino was tioned above, the instruction for installing the package updated in the course of performing the ESP: in the is located on the of the FIAN ASC site with the Fak azimuth A it is from 6° to 354°, and in the height h it is erat software. Saving all introduced parameters via the from 10° to 84°. The permissible range of turning graphical interface and transmitting them to the other angles for the 43 m NRAO radio telescope is limited programs is accomplished via the menu_defaults file, a in the hour angle from ­6.5 hour to 6.5 hour, and in copy of which is contained in the file menu_defaults.1. the declination from 37° to 77°. After the Fakerat start, a series of possibilities opens 3.7. How does the sky area allowable for observa for the user for modeling the ground­space VLBI tions, change during a year? Figure 4 shows, in the (, observations. As the work with the Fakerat has shown, ) coordinates, the celestial sphere's areas allowable at the ESP stage the most popular options occurred to for observations during one year. These areas are aver be the following ones: (1) the review of the possibility of aged with a step of one month in accordance with UV coverage of the grid nodes ( = 2 hours, = 20°) functional constraints for SC (given in this Section 3) for the whole celestial sphere all sky uvplot, (2) the time and for the orbit (described in Section 2). The areas in evolution of the UV coverage for a particular chosen Fig. 4, allowable for observations, are darkened. In source time uvplot, (3) the image of the UV coverage of order to get this picture, we have scanned the celestial a particular source in an enlarged scale for a particular sphere in the right ascension with a step of 30 min and observation date uvplot, and (4) the test for violation of in the declination with a step of 4°. In so doing, we the constraints (see Section 3) when scheduling the have checked the possibility of performing SRT obser observation constraints. vation jointly with the ground based radio telescopes, involved in the RadioAstron project, for each node of the grid. The signal accumulation time was not less I than one hour. II As it is seen from Fig. 4, as the Sun moves from the southern hemisphere to the northern one, the area III allowable for observations decreases. This is mainly IV due to the functional constraints, ensuring the normal V thermal mode, and due to the possibility of HGCA pointing to the tracking ground antenna. VI Another interesting phenomenon can be seen in VII Fig. 4. This is the motion of the areas allowable for VIII observations to the side of increasing during a year. IX Here, one may note that some particular sources can X be observed at a certain time of the year only. The XI repeated observations are possible after a year only. Usually, the northern sources can be observed during 3 80 40 XII to 4 months within one year, and the southern ones, Declin 0 ­40 24 20 16 12 8 4 0 ation, deg during 2 months or less.
Right ascension, hours

4. THE FAKERAT PACKAGE USE STRATEGY Currently the Fakerat with the graphical interface is running under the guidance of the Linux working
COSMIC RESEARCH Vol. 53 No. 3 2015

Fig. 4. The areas accessible (dark) and inaccessible (light) for observation.


222

ZHURAVLEV

The basic operations that must be accomplished before proceeding to modeling the UV coverage are as follows: to incorporate the orbit into the package; for this purpose in the ~fakerat/orbit directory of the deployed Fakerat package, it is necessary to give a symbolic ref erence to the orbit with the name ra_orbit, to select the tracking station for transmitting the tracking station data: PUSCHINO and/or GBANK 5, to specify the observation date obs year, obs month obs day, to specify the observation starting time star hh:mm:ss, to specify the observation stopping time stop hh:mm:ss, to specify the receiver frequency observing band, to specify the signal accumulation time (s), to indicate the radio source source name, to specify the angle of right ascension of a radio source RA hh:mm:ss.ss, to specify the angle of declination of a radio source Dec dd:mm:ss.ss, to choose ground based radio telescopes intended to be used telescopes. We have already mentioned in Sections 2 and 3 some features occurring during the formation of the UV coverage and which should be taken into consideration in scheduling the observa tions. At the beginning of work on a new source it is necessary, first of all, to determine the time interval when the observations are possible. This study can be performed with using two options: (1) UV coverage of grid nodes throughout the celestial sphere, and (2) clarifying how the UV coverage of a considered source changes with time. If the observation is impos sible, then one can clear up the reasons of this by using the option called "the test for violation of the con straints." Figure 3 shows, as a comparison, the typical UV coverage of grids' nodes for the whole celestial sphere for two opposite observation epochs: when the Sun is located in the southern part of the celestial sphere (the upper figure) and in the northern part of the celes tial sphere (the lower figure). The C range (4.8 GHz) was used and the tracking station in Pushchino was running in this example. The following ground based telescopes were used in this example: Arecibo, VLA27, GBT, Jodrell Bank, Evpatoria, Parkes, Kalyazin, Usuda, Noto, Shanghai, and Badary. The figure indi cates the celestial sphere areas, which are inaccessible for observation due to constraints caused by the Sun. The projections of the Galaxy plane and SC orbital plane on the celestial sphere are presented. The apo center, pericenter, and SC's orbit normals are marked as A , P and N . Again, it is clearly seen from the comparison of two UV coverages, that in the summer period there exist considerable constraints caused both by the Sun, and by the possibilities of HGCA pointing to the tracking station.

Ground based radio telescopes participating in ground­space VLBI experiments at the ESP stage, are listed in Table 3. The sensitivity of a pair of radio tele scopes in the interferometric mode can be estimated as follows:



i, j

= 1 SEFDi SEFD j 2B ,

where is the coefficient of efficiency in relation to the non quantized case. For the combination of lev els with a single bit clipped signal (the space based radio telescope) and double bit clipped signal (the ground based radio telescope) = 0.675, and for the double bit clipped signals (ground based radio tele scopes) = 0.881. Here it is assumed that signal recording was performed with the Nyquist frequency; SEFDi,j is the effective radiation flux density for the i and j radio telescope in Jy, respectively, is the signal accumulation time in sec and B is the receiver band width in Hz. SEFD values are given in Table 3. 4.1. Frequency specification of the onboard complex of receivers. The RadioAstron carries the onboard complex consisting of four receivers, which allow the reception of a signal in four wavelength ranges. Each receiver (except the C band) has two independent channels, the inputs of which receive the signals pos sessing left (LCP) or right (RCP) circular polarization. In the C range (see below) the work with a single polar ization only is possible. The band from the intermedi ate frequency (IF) output of receivers is formed in the Formator and equals 16 MHz for the upper (USB) and lower (LSB) bands. In the P range (see below) the sig nal transfer from the receiver output from the IF range into the range of video frequencies is accomplished only for the upper or lower bands. Additional informa tion on the functioning of the onboard research com plex can be found in paper [2]. In each frequency channel the signal reception is possible in one of two central bands separated from each other by 8 MHz. The receivers provide signal reception: in the P range with central frequencies of 308 or 316 MHz and radiometric path of 16 MHz; in the L band with the central frequencies of 1660 or 1668 MHz and radiometric path of 60 MHz; in the C range with central frequencies of 4828 or 4836 MHz and radio metric path of 110 MHz; in the K band with central frequencies of 22 228 or 22 236 MHz, with eight sub ranges for a multi frequency synthesis, with four sub ranges for spectral observations of narrow radio lines and radiometric path of 150 MHz. The central frequencies of the eight sub ranges of the K range for a multi frequency synthesis are sepa rated from each other at 960 MHz: F­4 = 18388 or 18396 MHz, F­3 = 19348 or 19356 MHz, F­2 = 20308 or 20316 MHz, F­1 = 21268 or 21276 MHz, F0 = 22228 or 22236 MHz, F1 = 23188 or 23196 MHz, F2 = 24148 or 24156 MHz and F3 = 25108 or 25116 MHz.
COSMIC RESEARCH Vol. 53 No. 3 2015


FAKERAT SOFTWARE Table 3. Ground based radio telescopes and networks of radio telescopes in the RadioAstron project SEFD Ground based radio telescopes Diameter P m EVNa: Arecibo (Ar) Effelsberg (Eb/Ef) Hartebeesthoek (Hh) Jodrell Bank (Jb1) Jodrell Bank (Jb2) Medicina (Mc) Metsaehovi (Mh) Nanshan (Urumqi, Ur) Noto (Nt) Onsala (On) Sheshan (Shanghai, Sh) Torun (Tr) Westerbork (Wb) Yebes (Ys) Badary (Bd) Svetloe (Sv) Zelenchuk (Zc) Robledo (Ro, DSS63) Narrabri, ATCA (At) Ceduna (Cd) Hobart (Ho) Mopra (Mp) Parkes (Pa) Tidbinbilla (Ti, DSS43) VLBA_SC, VLBA_FD, VLBA_PT, VLBA_OV ASKAP (Ak) GBTd (Gb) PT 70 (Ev) Usuda (Us) VLA27e (Y) Warkworth (Ww) Ooty (Oo) RadioAstron SRT
a b c d e

223

Time L Jy C K %

305 100 26 76 25 32 14 25 32 25 25 32 14 â 25 40 32 32 32 70 1 â 22 30 26 22 64 70 25 1 â 12 100 70 64 1 â 25 12 530 â 30 10

12 600 132

3 19 450 65 320 700 300 784 320 670 300 40 330 360 300 35 LBAb: 340 420 340 42 23 VLBAc:

2 20 795 80 320 170 250 260 600 720 220 60 160 200 250 400

90 3000 910 700 2608 850 800 1700 500 200 710 710 710 83

980

150

11 51 6 6 2 31 3 5 29 5 4 21 26 50 20 20