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Technical Constraints Impact on Mission Design to the Collinear Sun-Earth Libration Points

N. Eismont, A. Sukhanov, V. Khrapchenkov Space Research Institute, Russian Academy of Sciences

ABSTRACT

For the practical realization of the mission to the collinear Sun-Earth libration points technical constraints play a significant role. In the paper the influence of the constraints generated by the use of piggi-back mode of the delivering spacecraft to the vicinity of libration points are studied. High elliptical parking orbit of Molniya is taken as initial orbit for start to the L1, L2 libration points. The parameters of this orbit are supposed to be fixed and determined by the main payload demands. The duration of the passenger payload keeping on the mentioned 12 hours period orbit is limited for the case when launcher upper stage is used for the velocity impulse applying to put spacecraft onto transfer orbit to the libration point. The possibility to use one axis attitude control of the spacecraft for the executing correction maneuvers are investigated, supposing that spacecraft is spin stabilized with the spin axis directed to the Sun and maneuver impulse goes along this axis. The cost of constraints is presented in terms of characteristic velocity and time of transfer to the libration point vicinity. The goal of the paper is to understand the possibility of using regular launches of Molniya communication satellite by Soyuz-Fregat launch vehicle for sending low cost scientific spacecraft to Sun-Earth libration points.

INTRODUCTION

The mission to the vicinity of Sun-Earth collinear libration points are fulfilled and planned for the scientific experiments gaining big advantages from use of this region of space for optimal measurement conditions. Some of these experiments demand to keep spacecraft comparatively close to the libration points, for example the ones intended for microwave background and infrared radiation studies.

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The other experiments such as ones for solar wind exploration allow high values of amplitude in spacecraft motion relative to the libration points.

So it is a matter of scientific interest to explore feasibility to put spacecraft into orbits around collinear libration points supposing that deviation of the spacecraft from these points in the limits inside 1400 thousands km in transversal towards Sun-Earth line direction is acceptable. Such approach is dictated by the impact of technical constraints on the possibilities to put s/c onto orbit around libration points. These constraints are generated by the necessity to decrease the cost of launch and mission at large.

1. LIST AND NATURE OF TECHNICAL CONSTRAINTS

In our further consideration we accept assumption that possible libration points missions are restricted by possibilities of passenger launches by Russian launch vehicles, which are used for putting payload onto high elliptical orbits. Now in use are the following launch vehicles for these purposes: - Proton with DM on Breeze-M upper stage; - Molniya; - Soyuz with Fregat upper stage. Proton is used for the launches onto geostationary orbit, Molniya and Soyuz launch Molniya communication satellites and Oko military s/c onto high elliptical 12 hours period orbit.

During launch onto geostationary orbit s/c is put onto geostationary transfer high elliptical orbit (GTO).

It is important to underline that parameters of the orbit for the mentioned payload are fully determined by the payload demands including date and time of launch. The initial parameters of these payloads are close the following [1]:

Molniya: • period 0.5 star days, • perigee height ~ 640 km, • inclination ~ 63°, 3

• perigee argument 288°, • ascending node longitude is determined by demands of constellation configuration.

Oko: the similar parameters besides perigee argument what is about 320°.

For Proton GTO is quite typical with inclination about 47.5°, perigee height 200 km and apogee height 35920 km, perigee argument ~0° [2].

In case of Proton use for passenger payload launch the main obstacle is necessity to modify upper stage in order to mount additional payload.

Quite obviously this payload is to be mounted between upper stage and main spacecraft to be launched on GTO what is not so easy to do taking into account a broad variety of possible s/c to be put at the GTO to GSO by Proton. In case if upper stage to be used for maneuver to further transfer to Halo-orbit time delay for the appropriate additional engine burn is sufficient technical constraint (now the upper limit for this delay is several hours). It means that the s/c for the Halo-orbit mission is to be equipped by its own engine or Proton upper stage is to be significantly modified.

Use of Molniya launch vehicle excludes fully additional burn of the upper stage for our purposes because it can be started only once.

The most convenient option is the use of Soyuz-Fregat launch vehicle because Fregat upper stage equipped by multistarted engine. But even in this case there are restriction on the time interval between start of the launcher and last engine burn of the upper stage engine.

Given above can be summarized as constraint on the time interval between launch of the main s/c and the last maneuver to put onto Hallo-orbit passenger payload.

In addition in many cases it means that nominal transfer from initial high elliptical orbit to the Halo-orbit is to be executed by one impulse maneuver.

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To decrease the cost of the s/c the simplest attitude control is to be considered such as the case of spin stabilization. Example of such stabilization is Russian Prognoz series s/c with the spin axis periodically targeted towards Sun.

One of the s/c of this series was planned to be used in so-called "Relict-2" project with the main goal of investigation of microwave background radiation. Due to possibility to target the spin axis only in Sun direction the correction maneuvers of this s/c were to be fulfilled in Sun (or opposite to the Sun) direction, what is to be added to the list of possible technical constraints.

The other example of the attitude constraint is related to the libration point mission with the use of Solar Electric Propulsion (SEP) [3]. As it is well known SEP demands rather high electrical power. In optimal case solar panels are to be kept in position orthogonal to the Sun direction and thruster axes are to be directed along velocity vector, what can be achieved only with rotating panels or thrusters. To avoid this difficulty and to simplify attitude control it was proposed to use spin stabilization with spin axis being orthogonal towards Sun direction and being in orbit plane. Thrust is applied along spin axis. Solar panels form cylinder surface with the axis along spin axis. Thrusters are on when the angle between velocity vector and spin axis is less then 60°.

So the technical constraints listed above look rather strong to explore very possibility of mission to collinear libration points.

2. LAUNCH DATE IMPACT ON HALO-ORBIT IF ASCENDING NODE IS FIXED

Figures 1,2 present trajectories to the vicinity of L2 libration point and around it supposing one impulse transfer from GTO having inclination 62° and argument of perigee 0° with respect to equator and ascending node longitude 0°. The trajectories are given in solar-ecliptic coordinate system with tics interval equal 4 days. Four launch dates are checked: 15.01.98, 15.02.98, 27.02.98 and 22.03.98.

One can see from these figures that for dates from 15.02 to 22.03 the resulting Halo-orbit are rather similar with Y-axis amplitude within 800 000 km, X-coordinate changing within limits 5 from 1 150 000 km to 1 750 000 km and Z-axis amplitude 150 000 km. For the launch date 15.01 Y-axis amplitude is increased to 1 300 000 km with similar rise at motion amplitudes along other axes.

But in any case Figure 2 illustrate feasibility of broad enough launch window to put s/c onto Halo-orbit, more then two months, at least for the initial orbits with perigee argument close to zero.

3. ASCENDING NODE LONGITUDE INFLUENCE ON HALO-ORBIT CHARACTERISTICS

Most regular launches onto high elliptical orbit are planned for Molniya communication satellites. The main source of concern for using these launchers for putting passenger s/c onto Halo-orbit is value of the argument of perigee (288°) what means too big angle between ecliptic and line of apsides.

Figures 3,4 illustrate the feasibility to put s/c onto Halo-orbit under so strong constraints. Three trajectories are presented for different values of ascending node longitude of initial (parking) orbit: 0 deg., 90 deg. and 180 deg. First case corresponds to minimum angle between apogee-perigee line and elliptic plane and the last one – maximum angle. Consequently in the first case Halo-orbit looks the most "normal" and the last case present the trajectory with quite visible deviations from the libration point: up to 1 850 000 km in Y direction, and with approaching to the Earth in X-axis direction to 340 000 km.

The trajectories presented on the Figures 3,4 are related to the different launch dates, depending on ascending node longitude: 0 deg. – 12.12.98, 90 deg. – 22.02.98, 180 deg. – 10.07.98.

Values of osculating eccentricity e and semimajor axis a are respectively the following: e = 0.98, 0.99, 0.995; a = 652 154 km, 915 990 km, 1 525 700 km. 6

Fig. 1. 7

Fig. 2. 8

Fig. 3. 9

Fig. 4. 10

Similar calculations have been done for perigee argument 320° (case of Oko s/c as a main payload) which conformed the feasibility to put s/c onto trajectory in vicinity of L2 point using mentioned orbit as initial one (parking orbit).

4. PARKING ORBITS

Despite broad window of dates for launching s/c onto Halo-orbit it may happen that the waiting time on the orbit of the main payload will be more than 8 months. It leads to the necessity to optimize parking orbit parameters.

In the case when upper stage allows to put passenger payload onto higher orbit than GTO or Molniya orbit, the necessary propellent mass onboard s/c itself may be significantly reduced. But low orbit is more influenced by Moon and Sun perturbation. The most critical here is perigee height evolution.

To analyze evolution of the parking orbit the following formulae can be used [4]:

δa = 0, 3 15 µ1  a  2 2 δe = π   e 1 − e sin i sin 2ω , 4 µ0  r1  3 3 µ  a  cosi δΩ = − π 1   ()1 − e2 + 5e2 sin2 ω ,   2 2 µ0  r1  1 − e 3 15 µ  a  e2 δi = − π 1   sin 2i sin 2ω ,   2 8 µ0  r1  1 − e 3 3 µ  a  1 δω = π 1   []5cos2 i sin2 ω + ()1 − e2 (2 − 5sin2 ω),   2 2 µ0  r1  1 − e 3 15 µ  a  δh = − π 1   ae 1 − e2 sin2 i sin 2ω , P 4 µ  r  0  1  given secular evolution of the osculating parameters per orbit.

Here a, e, Ω, i, ω, hP are osculating semimajor axis, eccentricity, ascending node longitude, perigee argument, height of perigee with respect to the perturbing body orbit plane, in our case ecliptic plane (approximately), µ0 is Earth gravitational constant, µ1 is perturbing body gravitational constant (Moon and Sun in our case). 11

From these formulas one can see that perigee height increases if perigee lies in the second or fourth quarter of the orbit counted from ascending node on ecliptic and rate (per day) of perigee height change is proportional a5/2.

It means that parking orbit with perigee argument coinciding with Molniya orbit one for some positions of ascending node values (with respect to equator) does not satisfy this requirement and perigee height will decrease for these values of node longitude.

So to exclude additional constraint on initial orbit parameters the parking orbit is proposed to be chosen with Molniya orbit parameters as a baseline option.

For this option for transfer onto libration point orbit delta-V impulse about 700 m/s is necessary. Taking into account possible nominal and correction maneuvers, additional 400m/s delta-V capacity is to be reserved onboard s/c (about 300 m/s in case if amplitude of Halo- orbit is to be deceased from maximum to zero [5], and 100 m/s for correction maneuvers).

As to the case of Oko as a main payload (argument of perigee 320°)perigee heught rises for any longitude of ascending node, so it is safe to transfer our s/c to the orbit with higher apogee using upper stage engine, for example onto orbit with 100 000 km semimajor axis applying ~540 m/s delta-V with corresponding decreasing propellant onboard s/c.

5. FEASIBILITY OF MANEUVERS WITH DIRECTION OF THRUST CONSTRAINTS

As it was mentioned above constraints in engines thrust direction may be imposed as a low cost attitude control concept. It was shown in [6] that for correction maneuvers in order to keep s/c on Halo-orbit, Sun-directed delta-V impulses are enough for solving this problem. The propellant loses in this case do not exceed 18 percent. It gives the possibility to use for Halo-orbit mission spin stabilized s/c with spin axis periodically targeted to Sun.

Mission to libration point with the use of SEP and spin stabilized s/c was analyzed in [3]. It was supposed that thrust is applied when the angle between thrust and velocity vectors is inside 60° limits. 12

Results of this work have confirmed the possibility of such approach. Propellant consumption in this case will increase by 17 percent and time of transfer will be longer with factor 1.7 time comparing with case when thrusts directed along velocity vector.

CONCLUSIONS

Technical constraints influence on feasibility and principal characteristics of Halo-orbit mission have been studied. The main source of these constraints are demands to decrease the cost of mission.

It was shown that under constraints generated by requirements to launch s/c as a passenger together with the most regular mission such as Molniya, Oko and putting satellites onto geostationary transfer orbit, the mission to the collinear libration points are feasible. In the worst case spacecraft is to be rquipped by engine unit with delta-V capacity up to 1100 m/s.

Also it was concluded that use of spin-stabilized s/c with engine thrust along spin axis is possible. It is true for the case when spin axis is targeted to Sun and also for the solar electric propulsion when spin axis is orthogonal to the Sun direction and lies in orbit plane.

REFERENCES

1. Another Molniya-3. Novosti Kosmonavtiki, #12 (227), 2001, pp. 45-46. 2. Raduga-1: Military Comsat System Replenished. Novosti Kosmonavtiki, #12 (227), 2001, pp. 37-38. 3. A. Sukhanov, N. Eismont, A. Prudkoglyad. Trajectory Design for Experimantal

Mission to Sun-Earth L1 and L2 Points Using SEP. Paper presented to this Conference. 4. Introduction to the Theory of Flight of Artifical Earth Satellites (in Russian), p. 491. Moscow, Nauka, 1965. 5. N. Eismont, D. Dunham, S.-C. Jen, R. Farquhar. Lunar Swingby as a Tool for Halo- Orbit Optimization in Relict-2 Project. Proceeding of the ESA Symposium on Spacecraft Flight Dynamic, Germany, 30-4 October, 1991 (ESA SP-326, December 1991), pp.435-439. 13

6. P. Eliasbeng, T. Timokhova. Orbital Correction of Spacecraft in Vicinity of Collinear Center of Libration (in Russian). Space Research Institute Preprint 1003, Moscow, 1985.