The mentioned period difference corresponds only 11 km difference in semimajor axis. It means taking into account rather small differences in other orbital parameters that the both s/c are moving approximately at the same orbit.
So the distance between them along orbit can be easily calculated multiplying the main s/c delay in arriving into some point of the orbit with respect to the subsatellite by velocity of the spacecraft.
For the coordinated experiments onboard two s/c it was planned to reach the relative distance between them about 5000 km when the main s/c would be at 100 000 km distance from the Earth center. During attitude maneuvers aimed to keep the Sun direction along spin axis the orbital parameters has been also changed as side effect. But their influence was relatively small. So at January the 9th the subsatellite was 43 minutes ahead the main s/c when reaching the fixed point of the orbit.
The trajectory measurements for the subsatellite were the measurements of the signal level produced by the telemetry transmitter onboard the subsatellite. Ten meter dish antenna has been used and the frequency of the signal was 1533.5 MHz. Antenna axis was targeted to the some fixed in a quasi interval reference system point of orbit; this point was followed during time interval when the s/c with operating transmitter went through antenna diagram. Maximum of the signal corresponds the time when the s/c comes through the antenna axis.
The mentioned point on the orbit was supposed to coincide with with the point of the main s/c orbit. And to calculate coordinates of this point parameters of the main s/c orbit has been taken.
Using described measurements one can calculate the period of the subsatellite orbit and the time when it crosses the equator. Following the experiments demands it was planned after reaching mentioned above 5000 km distance between s/c to apply the velocity impulse to the subsatellite in order to begin its relative motion with respect to the main s/c into its nearest vicinity i.e. several dozen km distance. It was intended to be achieved in the middle of April 1996. So in January the 9th the orbital maneuver has been executed.
But it was impossible to use the standard fulfillment of this maneuver because of nonstandard position of main inertia axes. The thrust of jets for the orbital maneuvering goes along construction axis Z which in standard situation is to be main inertia axis and consequently the spin axis. Actually as a result of failing to deploy one boom and one solar panel the main inertia axis took the rotated position at the 40 degrees angle with respect towards Z construction axis. It means that instead of to be constant in space Z axis and consequently the thrust direction describes the cone with the axis going along inertia axis (coinciding with spin axis if enough time passed after attitude maneuver). So for orbital maneuvering one needs to know and to predict the the attitude of the s/c.
The other feature complicating the orbital maneuvering is center of mass bias due to the same reason i.e. undeployment of boom. It causes the generation of moment by thrust and as a result the deviation of angular momentum (spin axis) during maneuver execution.
To meet the experiments demand (which is to reach ideally zero distance in the middle of April) it was necessary to increase the MAGION orbital period by approximately 140 seconds.
The optimal point to apply the impulse is the point of orbit where the projection of s/c velocity onto thrust direction is maximum. But the choice of this point is limited by demand to execute the maneuver in visibility region of the ground station.
For our particular case the point of maneuver could be chosen in the perigee vicinity on the ascending part of the orbit. To calculate the possible maneuver points the next procedure has been chosen.
Immediately after appearance of the s/c in the visibility zone the Sun the Earth sensors measurements are to be done in order to determine the attitude motion parameters for predicting ahead the s/c attitude. In this prediction the moments of local maximums of velocity projection onto Z axis direction (thrust direction) are to be calculated.
Following this approach two impulses, each 16 seconds long has been
applied. Between these impulses the attitude parameters were updated by
the new sensors measurements processing.
Then two additional 10 seconds impulses have been applied with interval
between them only 1 second.
The main difficulty here was the deficit of time for attitude
parameters determination. It meant the decreasing of the propellant
consumption efficiency.
So the execution of the maneuver was done with some delay. It caused
diminishing of the planned planned period increase. As a result this
increase was only 57 seconds.
This value has been determined by described above level of telemetry
signal measurements done in January the 9th (Fig.1 )and in January the
13th (Fig.2 ).
From these figures one can see that after orbital maneuver the periods
of the main s/c and MAGION have become approximately equal: according to
Fig.1 MAGION is ahead of the main s/c by 43 minutes and Fig.2 shows the
same value after one orbit. (Clearly visible modulation of the signal
is caused by the spin of the s/c with the rate about one revolution per
two minutes.)
Thus the presented measurements lead to the conclusion about necessity
of additional orbital maneuver.
Orbital maneuvering operations and trajectory measurements have been done
by J.Smilauer, V.Truhlik (Institute of Atmospheric Physics, Czehia)
and N.Eismont, E.Ryazanova (Space Reseach Instituite, Russia).
The head of the team is P.Triska.
neismont@esoc1.iki.rssi.ru
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