Mission analysis for the INTERBALL project. Pre-launch orbits selection and longterm experiments planning

V. Prokhorenko
Space Research Institute,
Russian Academy of Sciences, 117810, Moscow, Russia

Abstract. The paper describes the approaches to certain problem of the mission analysis, which appear at various stages of the project: starting from orbits selection and strategic planning of the mission up to the flight operations. These problems somewhat evolved during the project preparation and were dictated by the scientific goals and general scenario of the INTERBALL Project as described by Galeev et al. 1993.


1. Introduction
2. Requirements following from the scientific goals and technical restrictions
3. The models used and the identification of critical regions in the near-earth environment
4. Choice of the tail probe orbit and season for the nightside phase of the experiment
4.1. One-parameter family of TP orbits with a free parameter DTM, the date of passage through the midnight NSH
4.2. Seasonal limitation as a consequence of technical restrictions
4.3. Choice of the launch date, launch time, and emergency reserve time for the launch delay
4.4. The Tail probe orbit parameters and launch strategy
5.Auroral probe orbit and auroral region
6. AP and TP orbit coordination for magnetic conjugacy
7. Expected pattern of passages through particular geophysical regions: a search for conjugacy
8. Conclusion
The Figures captiopns

1. Introduction

The work consists of 2 parts. The first part describes possible ways to select and to coordinate the orbits of two probes: the TAIL PROBE (TP) and AURORAL PROBE (AP) in order to solve scientific goals of the mission with respect to technical constrains. The 2nd part suggests the way of the mission analysis result visualization to make decisions in the longterm planning and operation of the experiments.

On the basis the entire class of the PROGNOZ-type satellite orbits the optimum season for the experiment could be chosen and the orbits for the two probes could be selected and coordinated to achieve maximum of magnetic conjugacy between two probes during their passage trough the night magnetosphere.

The study was split into a number of simple tasks, the result of their solution enable to have the general picture of orbital choice. Following this way we managed to find the parameter defining the two orbits coordination, which enables to select the Tail Probe and the Auroral Probe orbits separately.

This parameter, DTM, is the date of the midnight conjunction of the TP and AP orbits, when the TP orbit crosses the midnight part of the tail neutral sheet and the high latitude part of the AP orbit passes through the midnight auroral region. The launch dates of each probe will be defined within a range of dates preceding DTM. Taking into account the fact that the TP orbit passes through the magnetotail for a period of approximately 6 months centered on DTM, the high latitude part of the Auroral probe passage through the nightside auroral region can easily be made to coincide with this period by an appropriate choice of orbit. In fact, if we take the daily and annual effects of the neutral sheet motion into account, and the fact that the TP crosses the neutral sheet at discrete intervals, caused by the probe motion along its orbit (~ 4 day period), we see, that the TP injection into midnight neutral sheet region at a fixed date DTM may not be technically feasible due to the possibility of the TP orbit scattering at launch. For this reason, we do not claim a strict statement of the problem, nor a unique solution. However, this is not required for this practical problem, since during the injection the orbit parameters are so scattered that all efforts to achieve a rigorous solution may be unsuccessful. Another, more general, reason is the approximate knowledge of the true neutral sheet position, since its flapping motions is not described by any model.

The results of the analysis are presented in the following order: the goals, the models of the geophysical regions used, the selection of the proper orbit family, the selection of the optimal season for the experiment based on the technical constraints related to the limitation imposed by the TP crossing of the Earth's shadow, and the strategy of the launch date and time selection, taking into account the possibility of unforeseen short delays. This work contains an example of the orbits selected. In the last section the way to present the mission analysis results both for the longterm planning of the mission and for the daily operation of the experiments is shown.

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2. Requirements following from the scientific goals and technical restrictions

The main requirements on orbits following from the scientific goals of the mission are (see Galeev et al., 1993):

- to assure the passage of the Tail probe apogee through the night part of the magnetosphere (MS) for the first six months of the mission and to achieve magnetotail neutral sheet (NSH) crossings at distances of about 70 000 - 100 000 km, where steady auroral structures, substorm phenomena onset, and plasmoid generation processes are assumed to be located;
- to provide simultaneous passage of the high latitude part of the Auroral probe through the nightside auroral oval field lines at geocentric distances of up to 2 - 3 Earth radii, where auroral particle acceleration processes are operating;
- to coordinate the AP and TP orbits to assure the simultaneous entry of the probes into common magnetic field tubes (magnetic conjugacy) during the TP passage through the NSH and the AP passage through the nightside auroral oval (AUR) field lines;
- to assure the simultaneously passage of the TP and AP through the cusp field lines during the dayside part of the mission;
- to assure the effective operation of the UVAI and UVSIPS auroral imagers aboard the AP. The optimal season to pass through the nightside auroral region is the time when the auroral oval in the northern hemisphere is less illuminated (as close as possible to the winter season).

AP and TP orbits are chosen from a class of orbits with fixed initial values of the following parameters:

- perigee height hp - for the TP 500 km and for the AP 700 km;
- inclination to the Earth's equatorial plane - 65;
- apogee height ha for the TP in the range 180000 - 250000 km and for AP 15000 - 20000 km .

There are three free parameters: the time of the transition from the intermediate orbit to the operating orbit, the launch date, and the launch time. The time of transition to the operating orbit corresponds to the value of the perigee argument . For each fixed launch date the launch time defines the value of the right ascension of the ascending node . Therefore parameters such as the right ascension of the ascending node , the argument of perigee and the launch date DTL can be considered as free.

One of the essential technical restrictions for the TP is that of the time of TP entry into the Earth's shadow (the maximum time that the TP may stay within the shadow during one orbital revolution should not exceed 5 hours, and a passage into the shadow with duration more than 4 hours is allowed only once per year).

The ballistic lifetime of the orbits should not be less than 5 years. The time interval between the AP and TP launch dates must not be less than one month.

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3. The models used and the identification of critical regions in the near-earth environment

During the initial orbit selection and various stages of the experiment planning, the following models of geophysical regions were used:

- Near-Earth bow-shock (BSH): Fairfield et al., 1971; - Magnetopause (MGP): Sibeck et al., 1991;
- Neutral sheet (NSH): Fairfield, 1980;
- Auroral oval (AOV): Feldstein et al. 1967.
- Solar wind (SOW): the region outside the BSH;
- Magnetosheath (MSH): the region between the BSH and MGP;
- Inner magnetosphere (IMS): the region inside the MGP, for geocentric distances less then 10 RE (RE is an earth radius, 6371.2 km );
- Boundary layer, including the low latitude boundary layer (LLBL) and mantle (MBL): the region inside the MGP at a distance (1 RE from the MGP;
- Neutral sheet (NSH): centered on the model NSH surface region with thickness 1RE ;
- Tail plasma sheet (PSH): the region centered on the model NSH surface with the thickness 6 RE in the central midnight part, and 14 RE near the tail magnetopause;
- Radiation belt (RBT): the cavity between surfaces L = 1.2 RE and L = 4.5 RE (L is the McIlwain parameter (1961));
- Auroral field line (AUR) region: the funnel-shaped cavity limited to geocentric distances of the order of 10 RE , between surfaces formed by magnetic field lines from the polar and equatorial AOV borders;
- Polar cap (CAP): the cavity, limited to geocentric distances of about 10 RE , outside the surface formed by field lines from the AOV polar boundary;
- Day side cusp (CSP): the cavity between surfaces formed by field lines which emerge from the geomagnetic latitude boundaries at 79 and at 81 , and geomagnetic local time MLT within the range 9h to 15h . The upper boundary of this region coincides with the MPA boundary in geocentric distance.

To trace the magnetic field lines in the magnetotail and to search for the satellite locations within common geomagnetic field tubes, the full magnetic field model of Tsyganenko (1987) was used, which takes into account extraterrestrial sources of the magnetic field and the seasonal tilt of the geomagnetic dipole. It is also possibility to use the options for various geomagnetic disturbance levels, identified by the Kp index. In most of the calculations for this paper the fixed (average) value Kp = 2 was used.

We now explain some concepts which are important for the forthcoming description.

Geomagnetic local time (MLT) at an arbitrary point is the difference between the geomagnetic longitude of this point and the sun's geomagnetic longitude plus 12h .

Dipole axis which position, according to IGRF90, is determined by 79 northern latitude, 70 western longitude during daily rotation of the earth formed conic surface. Geomagnetic equatorial plane is perpendicular to the dipole axis. The zero geomagnetic meridian coincide with the geographical meridian, which pass trough the northern pole of dipole axis and southern pole of the earth's rotation axis.

Universal geomagnetic time (MUT) is the geomagnetic local time of the zero geomagnetic meridian. MUT is equal to 12h when the sun passes zero geomagnetic meridian. This time correspond to the 12h LT (geographical local time) on the northern magnetic pole, this is about 16h 42m universal time UTC (accurate to within the equation of time, this correction varies within +/- 15 min throughout the year).

To simplify the description we shall designate by the "axis of the magnetotail neutral sheet" the crossing line of the model surface of the magnetotail neutral sheet with the plane of midnight geomagnetic meridian. According to Fairfield (1980) this axis is parallel to the sun-earth direction and crosses the geomagnetic equatorial plane at a geocentric distance ~10.5 RE in the plane of the midnight meridian (MLT = 0h ).

The cusp axis is a field line with geomagnetic latitude 80 in the plane of the noon geomagnetic meridian (MLT = 12h ).

Another concept used in orbit selection and visualization relative to the boundaries of the simulated geophysical regions determined in rotating coordinate frames, is the "orbital torus" (Prokhorenko, 1983). The orbital torus is a toroidal surface, formed by the orbit in the rotating coordinate system connected to the motion of the earth around the sun and to the daily rotation of the earth. The orbital torus in space so as the orbital ellipse in the orbital plane enable one to generalize a particular position of the satellite in the orbit and even a particular realization of the orbit, which forms a particular winding on the orbital torus. The torus itself contains all possible options of this orbit (i. e. for different injectio dates into the same orbit, orbit parameters scattered during injection, etc). To take the orbit's evolution into account it is possible to use an osculating torus similar to an osculating ellipse. To a first approximation, the orbital torus can be obtained by turning the orbital ellipse around the axis of the rotating coordinate system in the direction, opposite to the rotation of the coordinate system itself (in this case each point along the orbit preserves the value of its geocentric distance and latitude).

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4. Choice of the tail probe orbit and season for the nightside phase of the experiment

4.1. One-parameter family of TP orbits with a free parameter DTM, the date of passage through the midnight NSH

On the basis of the NSH model it is possible to construct a surface generated by the annual motion of the earth around the sun. It is formed by the NSH axis which is parallel to the earth - sun direction and originates at a point at geocentric distance of ~10.5 RE in the geomagnetic equatorial and midnight meridian planes (MLT = 0h ).

The surface which results is crossed by the ecliptic plane and by the Earth's equatorial plane. The line of intersection connects to the equinox points. It pass below the ecliptic plane during the winter season and above it during the summer season. The main part of this surface is between the ecliptic plane and the Earth's equatorial plane. The part which corresponds to the summer season is in the southern hemisphere, and the part which corresponds to the winter season is in the northern hemisphere.

There is a line on this surface corresponding to each date. If the orbital ellipse is drawn through the point on this line with geocentric distance 70000 km , in the resulting orbit the TP will pass the NSH axis on this date (to within the TP rotation period) and at the required geocentric distance.

On the basis of a similar geometrical construction for each DTM the values of the two orbital elements (with the fixed value ha) are determined: the right ascension of the ascending node and the argument of perigee , measured in the orbital plane from the orbit's ascending node on the plane of the Earth's equator (for the range of possible values is determined). More detailed this problem is considered in the preprint Prokhorenko (1985).

A one-parameter family of orbits is obtained with the orbit passing through the magnetotail axis on the date DTM as a free parameter. The orbits obtained should be analyzed for ballistic lifetime and also checked for technical restrictions. The following section describes these problems.

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4.2. Seasonal limitation as a consequence of technical restrictions

The main technical restriction is that of the TP entry into and duration within the earth shadow. The maximum duration of the shadow in orbit depends on the geocentric distance of the orbit's descending node on the ecliptic plane which is determined by the value of the perigee argument measured from the line of orbit nodes on the ecliptic plane. As the latter is a function of , and i, the restrictions from the shadow duration imposes a bound on these parameters.

On the basis of the one-parameter family of orbits obtained above, some subset of orbits is chosen. This subset corresponds to an interval of dates DTM approximately positioned between the equinoxes, and including the summer season. In these subsets of the orbits the main scientific goals of the project, as summarized above, are realized, and the technical restrictions on the earth shadow duration are respected.

The results of these studies for the family of TP orbits with a fixed apogee (about 200000 km ) are displayed in figure 1, which may be useful for selecting the season and the TP orbit parameters. In this figure DTM is shown on the X axis in day number from the beginning of the year, and the perigee argument () on the Y axis; it is measured from the orbit's ascending node on the Earth's equatorial plane.

Taking into account the annual and daily motions of the neutral sheet, with various assumptions about the position of the dipole axis, three lines (a solid one and two dashed ones) were obtained. These lines contain the values of the perigee argument for which the NSH axis will be crossed on a fixed date at a fixed geocentric distance. For the solid line (marked by crosses) it was assumed that north magnetic pole was in the midnight geographical meridian (0h LT, or 0h MUT). The dotted line corresponds to the passage of this pole across the noon (12h MUT). The dashed line corresponds to 6h or 18h MUT.

If we choose along to the dotted line (or lying above it) with any position of the dipole axis on the chosen date, we can obtain a remote crossing of the orbit with the neutral sheet axis (at geocentric distance > 70000 km ). If we choose along the solid line, the remote crossing of the neutral sheet axis is possible only for a single position of the dipole axis, which correspond to 0h MUT (once per day). The region filled with the small crosses shows the prohibited values of the parameter , when the NSH axis crossing is not remote enough for any position of the dipole axis.

The region filled with zeros shows the values of for which the maximum possible duration of the shadow is longer than 5 hours.

The shown right ascension of the node corresponds to the along the dashed line.

It can be seen from this figure that for DTM between March 1 and October 10 there are no problems with the selection of the TP orbit parameters. Out of this time interval the shadow restriction make it possible to identify the argument of the perigee which does not provide for the TP remote crossing of the NSH for an arbitrary position of the dipole axis. It leads to a decrease in the total crossing time with the neutral sheet in that class of orbits.

Each particular orbit option (with fixed value of DTM and value) correspond a single point in the figure 1. Four orbit options, marked V1,...,V4 in this figure, were considered. The sections by the horizontal lines define the sets of orbits with fixed value of and a small range of different dates for the NSH axis passage. We now turn to the particular option selection for the TP orbit.

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4.3. Choice of the launch date, launch time, and emergency reserve time for the launch delay

For each orbit chosen on the basis of a given date DTM of the intersection with the NSH axis, the launch date DTL can be chosen from a certain range of dates preceding DTM. From the scientific requirements of the project it is desirable that the DTL not be separated from DTM by more than six months. Then the initial position of the orbit is in the morning sector and the satellite's entry into the nightside region of the NSH occurs no later than six months after launch.

When choosing the launch date it should be taken into account that the high-apogee orbit considered has a rather low initial perigee height. During each month for these orbits there are launch windows which provide the essential growth of the perigee height immediately after launch by the effect of gravitational perturbations from the moon and sun. For some orbits these windows are only two or three days long, and for others, longer. The main launch date and reserve dates for emergency situations during pre-launch tests are chosen from these windows.

The universal time of the launch UTC is defined simply as a function of three parameters: the right ascension of the ascending node , the sidereal time S0 at Greenwich midnight on the launch date, and the constant geographical longitude Ln , which is determined by the coordinates of the launch site on the earth and by the injection orbit:

UTC = ( - Ln -S0)/E, (1)

where E is the mean solar angular rate of the earth's rotation.

The equatorial local time of the orbital ascending node during the launch is

LTn = UTC E + Ln. (2)

The right ascension of the ascending node can be given as the sum of the sidereal time S0 at Greenwich midnight on the launch date and the equatorial local time of the ascending node of orbit

= S0 + LTn. (3)

In case of pre-launch emergency a delay of the launch date is possible within the launch windows with a correction of the launch time by -4 minutes (per day). In this case the nominal orbit is required (with accuracy up to the scatter in the orbit injection parameters).

Since the launch windows are restricted, the emergency reserve time should be limited to allow launch on the same date. In this case the change in the launch time, for example by 2 hours, from equation (2), shifts the orbit relative to local time meridians by the same 2 hours to the dayside. As a result, is changed, and DTM, the date of the NSH axis crossing, shifts by a month ahead. Both the main parameter of the missions (DTM) and the orbit ballistic characteristics can change: lifetime, maximum duration of the shadow, and also the geocentric distances of the intersections with the NSH. All these aspects should be taken into account to choose the nominal orbit and launch dates.

Thus for orbits corresponding to DTM in spring and summer, the required launch time reserve can be found from the corresponding choice of the . At the autumn boundary of the DTM determined above, the required time reserve can be created by definition a new limit on the allowable DTM range, by moving the border closer to the summer season.

Figure 1 illustrates the four variants of the orbits, the horizontal lines segments show how the values of the orbit parameters change when the launch time shifts by one hour (due to this shift, the values of DTM and change).

The possible variants of the TP orbit which have passages trough the midnight tail region in the autumn, close to winter are problematic due to the emergency launch delay, because of the danger of the increase in the orbit parameters by the admissible duration of the earth shadow.

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4.4. The Tail probe orbit parameters and launch strategy

Consider the parameters of one an orbit similar to V4 in figure 1, corresponding to the autumn passage of the NSH axis. These parameters were chosen with a launch emergency delay not more 1 hour.

    Date of the MS midnight tail passage  DTM  September 17
    launch date                           DTL  24.03.94
    perigee height                        hp   371 km
    apogee height                         ha   193 000 km
    inclination                           i    65
    right ascension of the ascending node     173
    perigee argument                          332

Some remarks are called for concerning the nominal value chosen for the apogee height ha , which corresponds to a nominal initial value of the draconic period of the orbit of about 91 hours and differs by 5 hours from the nearest multiple of a sidereal day (a sidereal day is shorter than the mean solar day by 4 min). This nominal value ha is chosen to provide stability in the average time of TP entry into the NSH, taking into account the scatter in the orbit period during the injection and possible changes in the launch dates.

In figure 2 the TP orbit is shown in SGE coordinates (the Z SGE axis coincides with the rotation axis of the earth, and the XZ SGE plane contains the earth - sun direction).

The cross sections of the annual orbital torus are shown on the XZ plane, and the projections of the revolutions are shown on the XY plane . The broken lines correspond to the pre-apogee part of the orbit, the solid ones to the post-apogee part. Orbits are marked with step 6h . Figure 2 also shows the positions of the NSH axis (corresponding to DTM September 17) and the CSP axis positions for two positions of the dipole axis, when the north magnetic pole is (I) in the midnight (0h MUT) and (III) in the noon geographical meridian (12h MUT).

Figure 2b shows the projections of the orbital torus crossing lines with the NSH for various positions of the dipole axis corresponding to 0h MUT (I), 6h MUT (II), 12h MUT (III), and 18h MUT (IV). For each satellite revolution these lines show the parts (marked by solid lines) where the intersections with the NSH can occur. For every month only one orbit is shown (the numbers of the orbits are plotted). In this case the most remote crossings with the neutral sheet occur in the evening-midnight sector.

The TP orbit position relative to the BSH and MGP are shown in Galeev et al. (1993).

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5.Auroral probe orbit and auroral region

The AP orbit is chosen on the basis of the following principal requirements: a) to cause the AP to pass trough the AUR region at distances of 12000 - 19000 km from the earth's surface and b) to achieve conjugacy (magnetic field line mapping) with the TP orbit, i.e. to assure that both probes are in a common magnetic field tube in the tail phase of the mission. Auroural oval visibility for the AP auroral imagers and solar illumination of the northern auroral oval must also be taken into account.

For the AUR region simulation Feldstein's 1967 model of the auroral oval and the dipole approximation for tracing the field lines to AP altitudes are used. From this and the restrictions on the radiation dose, an apogee height of about 20000 km and an initial value of the perigee argument of about 285 were chosen. In this orbit a midnight region AUR passage is provided on the ascending and descending parts of the orbit (by passage these regions of the orbit on the nightside) and a cusp passage occurs near the apogee point, when the high latitude part of the orbit moves to the day side (in the second phase of mission).

To provide conjugacy in the first stage, it is necessary to select parts of the AP orbit which will insure a passage in the nightside AUR region, taking into account the orbital evolution and annual and daily effects which influence the relative positions of the AP orbit and the AUR region. The geometric construction in figure 3 allows a visualization of the process of the determining those regions of the orbit which will enter the midnight AUR region when the high latitude region of the orbit passes through the corresponding meridians of local time. Figures 3a, c, and e correspond to the nightside phase of the project, and figures 3b, d, and f - to the dayside phase. Orbits are marked with step 1h.

Figure 3a in the GM frame (where the Z axis coincides with earth's rotation axis and the XZ plane contains the dipole axis) shows AUR night region boundary cross sections and the cross section of the daily orbital torus in the XZ plane. The daily orbital torus is a surface, which in the coordinate system connected with the rotating earth, forms as a result of the relative (reverse) daily rotation of the orbit. It can be seen from Figure 3a that the entire high latitude region of the orbit (with values of geocentric latitude > 40 ) can enter the AUR nightside.

Figure 3c shows the projections onto the earth's surface the daily orbital torus and AUR night boundaries cross sections, and projections of the one daily set of revolutions (4 revolutions). The geographical longitude values are plotted on this figure. The longitudinal shift of an orbit during a revolution is about 90 . It can be seen from this figure that the most highest latitude region of the orbit (with the latitude > 63 ) can enter the AUR region only within a range of geographical longitudes from 80 to 140 (i.-e. above northern Siberia). Outside this longitude range this part of the AP orbit will be in the polar cap region. Taking into account that the orbit shift per revolution is 90 and the range of longitudes is 60 , the entry of the highest latitude region into the auroral region cannot be guaranteed even for one orbital revolution per day. In Figure 3e the corresponding region of the orbit is located between the two * symbols.

Taking into account a possible daily orbit longitudinal shift, where precise value depends on the actual orbital period (including possible launch dispersion), it is not possible to predict the longitude of the AP orbit at DTM. But it is possible to determine part of the orbit, which in any case dips into the AUR region. In figure 3e the borders of these parts are indicated by + and * . One of them belongs to the ascending branch (dotted line), and the other to the descending branch (solid line). The borders indicated by * correspond to the orbital torus and AUR polar border crossing at geographical longitude 155 (or 65 ) see Figure 3c. The points indicated by + correspond to the crossings of the equatorial AUR border at longitude about 245 (or -25 ). The high latitude region of the orbit is divided into 3 parts, shown in Figure 3e in the orbital plane, + and * symbols mark the boundaries of those parts of the orbit where the passage trough the AUR region is guaranteed. One of these regions, located on the ascending branch, corresponds to the range of geocentric latitudes from 50 to 62 ; the other, located on the descending branch, to latitudes 64 to 50 . These parts of the AP orbit will be used to determine the conjugacy of the AP and TP orbits.

In figures 3b, d, and f, in addition to the AP orbit crossings of the dayside AUR region, the crossings with the cusp region are included. It is interesting to note that the AP crossing of the cusp region is possible only in the range 240 - 340 longitude, i. e. in the western hemisphere. At the same time the size of this longitude interval assure a passage through the cusp region in at least one orbital revolution per day. The corresponding part of the orbit is marked by the rhombus in figure 3f.

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6. AP and TP orbit coordination for magnetic conjugacy

To coordinate the AP orbit with the TP orbit passage through the midnight region of the NSH at DTM, another free parameter of the AP orbit, the right ascension of the ascending node (), is used. This parameter is chosen so that the part of the AP orbit which is certain to enter the AUR midnight region, will be in the midnight meridian plane on the date DTM.

On the basis of two areas of the AP orbit obtained in section 5 for each date DTM, two values of the right ascension of the ascending node () can be chosen. One of them (ab) provides the passage through the midnight meridian plane of the ascending branch of the orbit region on the given date. The other one (db) provides the passage on the same date trough the midnight meridian plane of the other region of the orbit belonging to the descending branch. Figure 4 shows the dependence of ab and db on DTM.

There is one more important requirement which affects the choice of one of the two possible values of the right ascension of the ascending node. This is auroral oval visibility for the auroral imagers UVAI and UVSIPS aboard the AP. Taking into account the restrictions on the attitude control system of the satellite, whose spin axis is directed towards the sun, and the fields of view of the instruments relative to the satellite spin axis (see Cogger et al. 1993, and Kuzmin et al. 1993) the range of may be divided into three parts (see figure 4). For between 90 and 280 (marked by long dashed lines) the operation of these imaging instruments is possible during the entire night phase. For the second, narrower range (marked by short dashed broken lines), the UVAI may view the auroral oval during the day phase in addition. For the remaining values of the UVAI cannot to operated near midnight region (in the period of midnight conjunction with TP).

As a result, a specially restricted range of DTM emerges (from the beginning of March to the middle of November). For this range it is possible to choose the values which are favorable for the imagers. This range is indicated in figure 4 by the " o " marks. For a restricted range of DTM (from the end of May to the beginning of November), it is possible to develop a type of AP orbits in which the UVAI may be operated during the entire year (this DTM interval is denoted by square symbols).

From this, for various DTM, the optimal value of can be chosen from the two possibilities. For DTM, corresponding to spring passage through the middle of the magnetotail, and taking auroral visibility for the imagers into account , it is necessary to use the greater of the two possible values (ab). For DTM from the autumn range, the same problem can be solved using only the lower value (db).

DTL, the launch date for the AP orbit, can be chosen rather arbitrarily but not later than 2.5 months before DTM. The initial value (0 must be chosen taking into account the evolution of this parameter due to gravitational perturbation of the geopotential ( -0.34 per day) in the interval between the launch date DTL and DTM.

The method used for coordination of the TP and AP orbits provides local time synchronization of the high latitude part of the AP orbit passage through the AUR region with passage of the TP orbit through the NSH and PSH regions. Such a synchronization is a necessary but insufficient condition for obtaining location of the probes in common magnetic field tubes while passing through the corresponding magnetospheric regions. The sufficient condition for obtaining conjugacy in the magnetospheric tail is that the TP itself (not just its orbit) pass trough the NSH and PSH regions for longer than the period of the AP (i.e. more than 6 hours). Only this will provide conjugacy with any degree of accuracy. The parameters of the AP orbit, coordinated with the version of the TP orbit above, are given below.

    Date of passage through MT midnight   DTM  September 17
    launch date                           DTL  30.06.94
    perigee height                        hp   772 km
    apogee height                         ha   19 200 km
    inclination                           i    65
    right ascension of the ascending node     245
    perigee argument                          285

The launch date for this orbit is taken to be 2.5 months before DTM . The initial value of the local time of the apogee point is about 6h. Figure 5 shows a polar plot (geomagnetic latitude - geomagnetic local time of the footprints of the magnetic field lines) of the 4 revolutions during the first day after launch and day DTM 17.09.94. Various marks show the corresponding passage of the AP through the radiation belts, auroral region, and polar cap.

The launch time is a function of the launch date and . It is assumed that not more than a half hour emergency delay is reserved for the launch, which leads to increasing of the initial local time of the apogee by the same half hour, and increasing of the by 7.5, as a result, that portion of the AP orbit, which is coordinated with the TP orbit, is also shifted along the AP orbit, but this shift is not important for conjugacy, because there is a reserve for this case.

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7. Expected pattern of passages through particular geophysical regions: a search for conjugacy

For pre-launch mission analysis and longterm planning of the experiments the above models of the regions studied were used to characterize the average expected positions of the boundaries of various regions. During the operational phase of the mission (after the initial phase, when the orbit parameters have been determinate and preliminary analysis of the results has been carried out) the used geophysical models may be corrected taking into account solar and geophysical activity forecast, or improved "space weather" prediction capabilities.

In various stages of the mission, different forms of visualization may be more useful. Thus during the mission preparations phase and development of the general experiment strategy, as well as the longterm planning condensed summary graphics showing the passage through the regions studied , similar to those of figures 6 -10, will be made available.

Figure 6shows, for the Tail probe, the crossing times of the thin MGP and BSH boundaries and also the times of passage through the radiation belts, neutral sheet, plasma sheet and cusp region. The date is given on the X axis, and the time from the node (in hours) for each revolution (draconic period of the orbit) is given on the Y axis. It should be mentioned that such a pre-launch prediction is rather preliminary due to the possible scattering in the TP orbital period during injection; also, possible changes in the launch date can lead to a significant change in the distribution of passage times through the regions. Nevertheless the general type of the crossing pattern described here will not change (i.-e. the number of the satellite passage trough to the regions, their average durations, annual changes, etc.).

Figure 7 shows, for the AP, a summary of the AUR, CAP, and CSP geomagnetic local time passages; the annual trend is evident. The X axis on that figure is the same as on the previous one; the Y axis is geomagnetic local time. This figure is similar to figure 5, but covers the full year (for every half month the AP orbit "linear polar diagram" for one day is shown). From figure 7 one can determine the time of the AP passage through the night part of the magnetosphere (it starts in July and finishes at the end of December). The midnight passage through the AUR region starts in July and stops at the middle of November, with the possible interruption near beginning of August, when apogee passes through the midnight polar cap region. Thus the dayside phase (from 6h to 18h MLT) starts before night phase will finished, at the middle of September and goes through noon from the beginning of November 1994 to the end of February 1995.

In figures 8 and 9 the visibility windows of the auroral oval for the UVAI and UVSIPS cameras are shown for the full year in the same way. The difference is that Moscow time (UTC - 3 hours) is shown on the Y -axis. It can be seen from these figures how the time of the windows changes. There is an interruption in the UVSIPS windows from the beginning of December 1994 to the end of January 1995. There are no interruptions in UVAI windows; it is possible to use this camera even in the dayside phase of the project. However this forecast of the windows is very preliminary and more accurate calculations will be necessary during the flight where the motion of the satellite spin axis under the influence of gravitation perturbations can be taken into account .

Figure 10 can be used for a one month flight planning. It presents the TP geophysical region boundary passage times for September 1994 as an example. The date is plotted along the X axis, and Moscow time along the Y axis. On the same figure the summary of the passage through the AUR and CAP regions for the AP orbit is shown (small symbols). This figure can be used to select the time intervals for the coordination of the AP and TP operation. From this summary the time intervals can be chosen which provide possible conjugate location of the two satellite in common magnetic field tubes.

It should be mentioned, that any pre-flight predictions of the conjugacy can be considered as only very preliminary. This is because even a small change of the orbital period during the launch could made very significant changes of the real satellite position along its particular orbit, especially, after many orbits revolutions. For example, in case of the AP orbital period only 1 minute difference with the nominal one, the satellite position along its orbit after one and half month is changed for 3 hours. As a result, the apogee and perigee passage times exchange their places in the time table. It must also be remembered that the actual geophysical situation at any particular moment can very considerably from the average models used in these calculations and that this natural variability is outside the scope of this analysis.

Using the average models, particular conjugacy cases were subjected to a more detailed simulation using the full magnetospheric magnetic field model of Tsyganenko (1987). Detailed calculations of the magnetic field lines passing through both probes and of the footprints of those lines at the earth's surface were performed. The magnetic conjugacy achieved by the two probes can be graded depending on the proximity of their two footprints. Figure 11 shows an example of case, where their angular geocentric separation was less than 2 . The positions of the probes are shown (the circles corresponds to the TP, and the double triangle to the AP position) on their orbits and the corresponding magnetic field lines are shown in GSM coordinates. On the polar diagram (inset) the positions of the corresponding footprints are shown.

The analysis presented above was done using the MISVIS software package developed at IKI and run on an IBM PC AT using DOS.

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8. Conclusion

The choice of the TP and AP orbits for the Interball project is based on the results of this work. The launch dates can be changed during the preparation phase. In making the final choice of the orbit parameters and launch dates we tried to take into account such factors as dates of pre-flight tests, equipment availability, and various other restrictions on the possible launch dates, etc.

To achieve the above TP orbit (see section 4.4), the initial value of the right ascension of the ascending node must be chosen for each possible launch date in such a way that, taking into account the evolution of this parameter, its value will be 170.8 by 17.09.94.

The initial value of the for the corresponding AP orbit, a function of its launch date, must be chosen in such a way that, taking its evolution into account it will be 218.7 by 17.09.94.

The following events are expected in the TP and AP orbits. Tail probe passes through the tail region for 6 months staring in beginning of July 1994, and Auoral probe passes through the night region AUR exact the same time. During all this period joint operation of the two probes in the tail is possible.

The dayside phase of the project (inside of magnetosphere) starts before the nightside phase is finished (in the beginning of November 1994). Auroral Probe passes the noon cusp region from the middle of November 1994 to the beginning of March 1995. The Tail Probe orbit passes the dayside cusp region in the same time.

The Tail Probe passes through the solar wind and crosses the bow shock from the end of March to the end of June 1994 and from the middle of December 1994 to the end of June 1995. The magnetopause crossings stop between the middle of August and the end of November 1994.

These orbits pass trough the magnetotail during the autumn period when the neutral sheet transit from the southern to the northern hemisphere and the auroral oval is before (and during) polar night. This is a good condition for auroral imagers with respect to solar illumination of the oval. This option for the AP orbit also provides the best conditions for the UVAI camera, as it have possibility to operate all year without interruption; the viewing conditions for the UVSIPS camera is not so good, there are about 2 month interruption of visibility during dayside phase of mission.

The maximum time for the TP orbit in the earth's shadow is about 4,5 hours and can by reached at the middle of September (but it is possible to perform two passage through the shadow with less duration, about 3 - 3.5 hours, it depend from the launch date and the orbital period scattering during the launch).

Thus these TP and AP orbits meet all scientific requirements and technical constraints for the INERBALL mission.

Acknowledgements. This work was carried out in the Software Department of the Russian Academy Space Research Institute. The author expresses her gratitude to department head Dr. R. Nazirov for his constant and benevolent attention to this work. The author also thanks Professor L. Zeleny and many other colleagues, participants in the project, for their advice during numerous discussions of the project goals and constraints.

The author considers it her pleasant debt to express gratitude to Professor Yu. Galperin who read this paper and made a number of useful remarks.

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The Figures captiopns

Fig. 1. To the choice of the TP orbit parameters and the season of the magnetotail passing. The region of the possible perigee argument values depending of the date DTM (date of the midnight neutral sheet crossing), obtained in accordance with the requirements concerning to the range of the NSH crossings and restrictions by the Earth shadow occultation. V1-V4 - considered versions of the orbit.

Fig. 2. The distance range of the possible neutral sheet crossings for the Tail probe orbit with the launch date in March and date of passing through the midnight NSH region at the middle of September

Fig. 3. To the choice of the AP orbit parts which enter into the night AUR region taking into cosideration annual and daily effects of the AP orbit and AUR region relative motion.

Fig. 4. To the definition of the right ascension of the AP orbits ascending node values depending on the DTM (date of the Midnight Conjunction with the Tail probe) and the choice of the most favorable orbits which provide the auroral oval visibility for two auroral imagers onboard.
To provide the UVAI operation during whole nightside phase it is necesary to select the AP orbits corresponding to the DTM, belonging to the time inerval within the borders marked by circles.
The AP orbits corresponding to DTM interval within the borders, marked by squares, provide the operation of UVAI also during the dayside phase.

Fig. 5. A polar diagram of the AP magnetic field line footprints for two particular dates: soon after launch and at the DTM date. The corresponding geophysical regions are marked by different symbols.

Fig. 6. The annual distribution of the Tail probe crossing times of the thin magnetopause (MGP) and Bowshock (BSH) boundaries, and also of the times passage trough the radiation belts (RBT), neutral sheet (NSH), plasma sheet (PSH) & cusp (CSP) regions for the TP orbit, which cross the midnight magnetotail at the middle of September.

Fig. 7. The geomagnetic local time of the Aauroral probe passage through the AUR, CAP & CSP regions annual trend

Fig. 8. The annual distribution of the UVAI camera visibility windows onboard the Auroral probe.

Fig. 9. The annual distribution of the UVSIPS camera visibility windows onboard the Auroral probe

Fig. 10. A combined picture of the the Tail and Auroral Probes geophysical regions passage times.

Fig. 11. An example of two probes magnetic conjugacy. Circles show the Tail probe positions, double triangles - the Aauroral probe positions in the GSM frame. The corresponding footprints projections along the magnetic field lines are shown in the polar diagram.

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