Proc. Indian Acad. Sci. (Engg. Sci.), Vol. 3, Part I, March 1980, pp. 47-65. Printed in India. Attitude and orbit control for satellite broadcasting missions C A MARKLAND Attitude and Orbit Control Division, European Space Research and Technology Centre, Noordwijk, The Netherlands M S received 3 July 1978; revised 5 February 1979 Abstract. This paper gives a broad introduction to the problems of attitude and orbit control of geostationary communications satellites. It specifically discusses the relationships between the satellite user's requirements for a broadcasting mission and the design of the attitude and orbit control system. To put the subject in perspective, a brief review of past and present satellites is presented first. Then orbit control is described in terms of the forces that act on a satellite in geostation.~ orbit _and the necessary station-keeping strategies. The design of attitude control systems for tlaree-ax~sstabilised satellites is presented by considering the disturbance torques, attitude sensors and actuators and by identifying the various system problems and their solutions.. Sources of error in pointing the satellite towards the earth are discussed together with the formulation of error budgets. Finally, the design approach for missions that require extremely accurate pointing is considered, and some remarks are given regarding the achievable accuracy for this class of satellite missions. Keywords. Communication satellites; twenty-four hour orbits; orbit perturbations; station-keeping; attitude control; angular momentum; attitude indicators; accuracy; satellite broadcasting missions; broadcast satellite. 1. Introduction The purpose of this paper is to give a broad introduction to attitude and orbit control of geostationary satellites and, in particular, to discuss the connections between the mission requirements imposed upon a broadcast satellite and the design of the corresponding attitude and orbit control system (AOCS). Thus, while no funda- mentally new knowledge is presented here, the main objectives are to highlight system-level interface problems that are rarely discussed in the literature and to show people involved in the planning of future broadcast missions some of the impact of their requirements. In order to define the class of satellites under discussion and the modes of attitude control suitable for it, it is appropriate to make a brief review of past and present satellites taking the Intelsat family of communications satellites shown in figure 1 as a point of reference. Intelsats I and II were essentially cylindrical in shape and they were 'spin- stabilised'. This means that the orientation in space of only one axis of the body (i.e. the spin axis) is controlled. Provided that the required accuracy for this orientation is not better than 3- to i degree, which was the ease for Intelsats I and II since the antennabeam width was 17 degrees, this leads to very simple on-board attitude control hardware. For Intelsat III, the same attitude control system was employed for the main body, but an increase in communications capability was 47 48 C A Markland Figure 1. The developmentof INTELSAT satellites. obtained by mechanically despinning the antenna with respect to the body. Plainly, this requires an additional control loop for antenna pointing. The extension of the technique of spin-stabilisationto give more communications capacity (which implies larger antennas and more solar cells)was limited by a funda- mental law of physics. It follows from Newton's laws that the angular momentum of a body is constant unless torques are imposed upon it from outside. Internal torques cannot change the overall momentum, but they can affect the amount of kinetic energy in the body. Specifically, if they dissipate energy (e.g. in heat) then the body will move to the state of minimum energy. This minimum energy state for spin-stabilised satellites is the desired mode of spin only if the inertia about the desired spin axis is greater than the inertia about any other axis. That is, the body has to be roughly disc-shaped or ' oblate '. If any transverse axis has a greater inertia, then the body will br stable in spin only about this axis. Attitude and orbit control for satellite missions 49 Plainly, adding large despun antennas above the spinning body will contravene this condition, i.e., it will make the body prolate (pencil-shaped), so that it will spin- stably about a transverse axis and not about the axis of symmetry. Before Intelsat IV could be accepted, therefore, a solution to this stability problem had to be found. Hughes Aircraft Company found the solution and termed it the Gyrostat (Iorillo 1967) although now it is more generally referred to as the ' dual-spin' configuration. In this configuration, an energy dissipating device (e.g. a damped pendulum) is placed on the despun part, and this has the effect of stabilising the complete prolate satellite about the spin axis of its rotating section. Hughes exploited this principle very suc- cessfully in Intelsat IV and IVA in which 4~~ spot beams are employed, and a dual- spin configuration was one of the two winners selected by Comsat for Intelsat V in the first technical evaluation. From the point-of-view of AOCS design, it has proved to be a fine example of high performance with simple hardware. Now to consider the European side, dual-spin configurations received a great deal of attention at the time of the first broadcast satellite proposals in 1969. They were studied in some depth (Brewer et al 1970, 1974) but finally they were eliminated mainly on the basis of lack of growth capability due to the inefficiency of their cylind- rical solar arrays. The first European geostationary broadcast satellite was the Franco-German satellite Symphonie shown in figure 2. This satellite is not spin- stabilised but rather it has 'three-axis attitude stabilisation', i.e. the orientation in space of all three axes is controlled. In retrospect it does appear to have some similarity to spin-stabilised configurations (the body-fixed solar arrays and the general disc-shape) but from the control system point-of-view the major step has been made. ESA's first satellite in this field is the Orbital Test Satellite (OTS) illustrated in figure 3. In contrast to Symphonie, the solar arrays rotate to track the Sun while the body-fixed antennas track the Earth. This three-axis stabilised configuration has virtually become the ' classical' pattern for all present communication and broadcast satellites. Certainly, it is being adopted for most current missions including Intelsat V and the Indian communications satellite APPLE. The remainder of this paper is concerned solely with this configuration and refinements thereof. Figure 2. The Symphoniesatellite. Pro. C--4 50 C A Markland Figure 3. The'orbital test satellite (OTS). All the satellites mentioned above were designed for communications in the general sense and for telephone communications especially. Although this paper relates specifically to satellites used for broadcasting, its contents do apply to a very wide range of future communications satellites in which high power and high accuracy are requirements. The functions of attitude and orbit control are invariably combined in satellite design because they use the same on-board hardware. However, while they are closely related, they are also different in nature with orbit control being usually performed by commands from a ground station and attitude control being performed by closed-loop control systems on-board the satellite. Thus, for the moment, they will be considered separately. Attitude and orbit control for satellite missions 51 2. Orbit control 2.1. General This discussion of orbit control is restricted to near-geostationary orbits, since con- tinuous visibility of the satellite from the Earth stations and the absence of large rela- tive motions are desirable features for all communications missions and they are mandatory for economic broadcasting to many simple ground receivers. Nonetheless, it is worth remembering that other orbits have been used; for example, the highly elliptical, inclined orbits of the Russian Molniya series. The characteristics of the ideal geostationary orbit are: (i) it is perfectly circular (i.e. eccentricity = zero) (ii) it is in the plane of the Earth's equator (i.e. inclination : zero) (iii) the altitude is 35 786 km =5.611 Earth radii. When these three conditions are exactly satisfied, the orbital period is equal to the Earth's period of rotation (i.e., one sidereal day=23 hr 56 rain 4.09s) and the satellite is stationary when seen from the Earth. Deviations from these conditions cause relative motion. Specifically, a non-zero inclination causes the satellite to move daily in a narrow, North-South figure-of-eight, a non-zero eccentricity produces a daily East-West oscillation, and a different altitude produces a different orbital period and a constant drift eastward or westward. What are the environmental forces acting on a satellite that can disturb its ideal geostationary orbit? Of course, the principal force is that due to the gravitational attraction of the Earth. The Earth can be regarded as a point mass to a first order, which will not by itself disturb the orbit, but its second order effects are important. There are also important gravitational forces due to the Sun and the Moon, and solar radiation pressure gives a significant disturbance. Other forces, such as atmospheric drag, electric and magnetic fields, and meteorite impact, are negligible at geostationary altitude. A comprehensive survey of these phenomena has been given by Shrivastava (1978), and there is a detailed discussion in Michielsen & Webb (1970). 2.2. North-South control First let us consider the environmental forces that move the satellite out of the equa- torial plane and thereby produce a North-South relative motion. These forces are gravitational, and they result from the fact that the plane of the geostationary orbit (the equatorial plane) is tilted with respect to the plane of the Earth's orbit around the Sun (the ecliptic plane) and also with respect to the plane of the Moon's orbit around the Earth.