Acta Astronautica Vol. 9. No. 3, pp. 147-154. 1982 0094-5765182/030147-08503.0010 Printed in Great Britain. Pergamon Press Ltd.

SOME ASPECTS RELATED TO THE SATELLITE APPLICATIONS IN NON-STATIONARY 24-HOUR ORBITSt

K. KUMAR Department of Aeronautical Engineering, Indian Institute of Technology, I.I.T. Post Office Kanpur-208016, U.P.,

India.

(Received 13 November 1980; revised version received 18 August 1981)

Abstract--In view of the increasing crowding of the limited geosynchronous space, the inclined/elliptic 24-hr satellite orbits are likely to find greater acceptance by spacecraft designers in the future. The proposed quasi- synchronous orbits appear to present practically unlimited opportunities while retaining some of the essential features of geostationary systems. This paper examines some general aspects related to the application of these non-stationary orbits. The analysis suggests that their use enables considerable savings in the booster energy requirements. The disadvantages include the need for varying the communication power leading to increased radiated peak power requirements and angular satellite drift resulting in excessive demands on attitude control of the satellite and ground-based antennas. However, it is felt that the significant advantage of payload weight-saving may effectively compensate for the various disadvantages in several design situations, particularly for non- communication applications. Finally, some non-conventional applications of the quasi-stationary satellites are proposed.

I. INTRODUCTION

The circular, equatorial synchronous orbits enjoy a spe- cial status for numerous satellite applications, parti- cularly communications/l]. Since the success of SYN- COM in 1963, there has been a phenomenal growth in the field of communications via geosynchronous satellites (GSS). During 1963-80, about 90 GSS have been laun- ched of which over 70 are "comsats" of the various types/2, 3]. The corresponding figure for the GSS plan- ned or already launched during the first half of this decade alone is about 85. In view of the rapid worldwide growth in demand on satellite communications capacity as well as the extension of satellite applications to new areas, e.g. education, teleconferencing, broadcast, navigation of ships and airplanes, weather-forecasting, etc., even a faster rate of proliferation of the GSS[4-9] has been projected in years to follow. A conservative estimate of the communications demands expected at the turn of the century presents a somewhat alarming picture with excessive overcrowding of the geostationary space/10]. This overcrowding together with already visible signs of political/legal restrictions [11-14] on using it are

likely to lead to a situation of scarcity of this limited precious "commodity" for future exploitation.

The projected saturation of frequency allocation and the orbital space has led to several attempts towards efficient and equitable use of the GSO[15]. Vigorous efforts are on to meet the twin challenges of demand and conservation of spectrum and the orbit through new technological advancements [16-18]. This paper represents a modest effort in another direction whereby a fresh look into the alternative trajectories is undertaken in order to assess their suitability for diversification of

tBased on a paper presented at the XXXIst Congress of the International Astronautical Federation, Tokyo, Japan, 21-27 Sep- tember, 1980.

147

satellite operations for communications and other space applications. It is felt that in view of the significantly changed future world communications scenario since the mid-1960s the non-synchronous orbits may receiv~ more favourable attention from spacecraft designers in the near-future. Of these, the use of medium-altitude random orbits, with and without station-keeping, for com- munications applications is virtually ruled out by tradeoff studies including factors such as earth station tracking requirements, station-keeping-feasibility, radiated power requirements, the number, size and complexity of the earth stations needed, etc. [19-27]. Attention is therefore focused on the other alternatives of inclined/elliptic, 24--hr non-stationary or quasi-stationary orbits (QSO) for satellite applications.

A careful consideration of the potential advantages of the QSO reveals their several useful features. With satellites moving in such orbits, the problem of "rising" and "setting" of satellites and a consequent need for handing-over traffic between them can be totally avoided. These orbits can be quite helpful in relieving the possible future problem of satellite communication traffic con- gestion. A study by Rowe and Penzias[28] has shown that the best satellite packing schemes permitting the inclined circular orbits at the synchronous altitude yield an improvement factor of roughly six times over a purely equatorial system in the frequency range of probable interest. An extension to include the inclined-elliptic 24-hr orbits would further augment the available synch- ronous space. Akin [29] has argued that these generalized synchronous orbits present too broad a scope for effective international legislation and should therefore be always available to potential users.

This paper examines some important aspects related to the use of the non-stationary 24-hr satellite orbits for communications and other general non-communication purposes.

148 K. KUMAR

2. SIMPLIFIED ANALYSIS OF SOME ASPECTS OF MOTION RELATED TO ORBITAL GEOMETRY

The various aspects of satellite motion that are likely to have a significant effect on the choice of parameters such as orbital eccentricity and inclination with respect to the equatorial plane may be summarized as follows:

--visibility of satellite from the ground station --communication power and energy requirements --satellite drift and attitude control requirements --radiation hazards in space environment --booster energy requirements.

It is now proposed to examine each of these aspects in some detail.

2.1 Visibility of satellite .from the ground station An important condition affecting the tracking

requirements for satellites and their use as an instan- taneous communications relay is its visibility from the ground stations being used for the purpose. This imposes constraints on the maximum permissible eccentricities that can be used for satellites in the 24-hr orbits. An attempt has therefore been made to obtain a theoretical estimate of this upper limit. Using a rather simplified analysis of the geometry of satellite motion (Fig. 1), it can be shown that the visibility of these satellites from the ground station can be assured provided the following inequalityt is satisfied [30]:

cos fl > (rdr);

cos ~ = ~,~d(Irllrel). where

On evaluating the expressions for cos fl in terms of the orbital elements, this inequality takes the form:

rnI{cos u cos (~ - 8) - sin u cos i sin ( f l - 8)} cos ~b

+ sin u sin i sin ~b] > 1.

tNomenclature is given in Appendix.

It may be pointed out that normally an attempt is made to choose the initial satellite position relative to the ground station so as to achieve the "best" visibility conditions possible. However, for the sake of a sim- plified estimate, a sub-optimal situation is considered assuming 8 = 8o = w + 11 at the time of perigee passage. The above inequality then takes the form

rn [{cos ( 0 - wet)+ (1 - c o s i)sin u sin ( f l - 8o- wet)} cos ~b

+ sin u sin i sin ~b] > 1.

The visibility of the satellites is thus governed by the various orbital and ground station parameters. For a con- servative estimate of the visibility conditions, the above inequality can be considerably simplified:

(1 - 4e2) '/2 > (1 - cos i) + ]sin i tan ~b[ + sec ~b/{an(1 - e)}.

This analysis does not consider the effect of atmosphere on radiations which in turn imposes a further constraint on the requirement of a minimum satellite elevation relative to the ground station. However, it is felt that in view of the margins implicitly introduced in the above conservative estimate at the various stages, the final result obtained here may be quite useful for preliminary design purposes. A simple iteration procedure has now been used for numerical computation of this limit as a function of the orbital inclination (i) and the ground station latitude (&). The results thus obtained (Table 1) show that the use of relatively larger eccentricities is possible without the loss of visibility even for moderately large orbital inclinations and ground station latitudes.

Attention is now focused on the influence of orbital perturbations caused by Earth's oblateness, luni-solar gravitational field and the solar radiation pressure on the visibility. The two important effects peculiar to the QSO are nodal and apsidal precessions ( - 0.02 deg/day). However, these slow variations which diminish further with increase in inclination are unlikely to alter the visibility-picture significantly. Even in the most adverse

Fig. 1. Geometry of satellite motion.

Some aspects related to the satellite applications in non-stationary 24-hour orbits 149

Table 1. Maximum permissible eccentricities ensuring visibility

0 5 10 15 20 25 30 35 40

0 0.478 0.478 0.477 0.477 0.475 0.474 0.471 0.468 0.464 5 0.478 0.476 0.475 0.473 0.470 0.467 0.462 0.457 0.450

10 0.476 0.473 0.471 0.467 0.463 0.457 0.450 0.442 0.430 15 0.473 0.469 0.465 0.459 0.453 0.445 0.435 0.422 0.406 20 0.469 0.463 0.457 0.449 0.440 0.429 0.415 0.397 0.374 25 0.463 0.456 0.447 0.437 0.424 0.409 0.390 0.366 0.333 30 0.455 0.446 0.434 0.421 0.405 0.385 0.359 0.326 0.280 35 0.445 0.433 0.418 0.401 0.380 0.354 0.320 0.274 0.206 40 0.432 0.417 0.399 0.376 0.349 0.314 0.268 0.201 0.079

situations, where these drifts may have to be arrested, it is likely to result in merely a marginal increase in demands on fuel consumption for maneuvers normally needed for controlling the orbital inclination.

It may be pointed out, however, that the upper limit on permissible eccentricities is likely to be further con- strained by several other factors. Important among these appear to be considerations of simultaneous visibility from several ground stations and radiation and com- munication interference.

2.2 Communication power and energy requirements Recognizing that the communication power required

for transmission from or to the satellite is proportional to the square of the distance between the satellite and the ground station, it can be shown that:

(Pq . . . . . /P~,) = [1 + e/(1 - 1/an)] 2.

energy requirements for uninterrupted communications:

Ea forbit (r - r e ) 2 dt.

This relation can also be rewritten in the form:

r:(r- re) 2] .a,~ Ea Jo

On evaluating the integral appearing in this expression, it can be shown that the ratio of the energy requirements for communications through satellites in the elliptic and circular orbits is approximately given by:

(EqJE~s)=(1 - e 2) I[2 [1 + e2(1 +2~an + 5/2a, 2)

- e4(73/8 - 7~an + 35/4an2)].

On substituting for the value of an, the above ratio can be written as a function of eccentricity alone:

(Pq . . . . . /Pgs) ~- (1 + 1.177e) 2.

The numerical results obtained using this relation are shown in Table 2. It may be observed that the maximum radiated power requirement increases with increase in orbital eccentricity. An increase in peak power require- ment appears to be a significant disadvantage in the use of the QSO for the conventional satellite communi- cations, as it directly influences the associated hardware requirements and costs. This increase is, however, ac- companied by a corresponding reduction in the power required near the points of closest approach leaving a surplus which can be utilized for some alternative ap- plications. It is, proposed, therefore, to compare the total communications energy required for the various 24-hr orbits.

using the following approximate proportionality rela- tion, it is easy to compute and compare the radiated

For a better appreciation of this factor, these results have been computed for different eccentricities and tabulated (Table 2). It may be observed that the total energy requirement shows only a weak dependence on eccentricity. Here, it may be worthwhile to point out that the effect of small variations in orbital inclination on the communication power and energy requirements is likely to be still less significant.

2.3 Satellite dri[t and attitude control requirements A careful consideration of the satellite motion in the

elliptic orbits reveals several significant problems. Firstly, the attitude excitation induced by orbital eccen- tricity leads to rather large satellite attitude fluctuations. A simple linearized analysis of the equation of pitching librational motion of uncontrolled satellites in slightly elliptic orbits shows that its amplitude is approximately given by - 2 e / ( 3 K ~ - l ) radians. However, a more detailed nonlinear analysis carried out by Brereton and Modi[31] suggests that the librational amplitude may in general be higher for relatively larger eccentricities. Fur-

Table 2. Effect of eccentricity on radiated beam power and energy requirements

Eccentricity 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

(Pq,.r*,,,/Ps,) I 1.12 1.25 1.38 1.53 1.68 1.83 1.99 2.16 2.34 2.52 (Eq,IE v) I 1.01 1.02 1.04 1.06 1.08 1.09 1.08 1.04 0.95 0.80

150

thermore, a stable operation of the gravity gradient sys- tems is not possible for eccentricities exceeding a limit- ing value (-0.35). This in turn would lead to a con- siderable increase in demands on the attitude control sub-systems resulting in significant payload weight and space penalties.

Furthermore, the satellites in the proposed orbits suffer a periodic angular drift with respect to the ground station. The non-stationary nature of the satellites results in periodic oscillations of the line-of-sight (i.e. the line joining the ground station and the satellite) with respect to the local vertical. An analysis is undertaken, therefore, to assess the effects of the periodic angular satellite drift associated with eUipticity. The results of this analysis are presented in Fig. 2. It may be observed that increasing the orbital eccentricity has a significant adverse influence on the misalignment of the ground and space systems. This in turn necessitates the use of some suitable control devices for achieving a properly synchronized variation in the orientation of the satellite and ground-based antenna. A non-zero inclination of the orbit with the equatorial plane is expected to add further to these complications.

3. RADIATION HAZARDS IN SPACE ENVIRONMENT

The highly energetic particles of the corpuscular radiations in the space environment[32, 33] have been a concern from the very early days of space flight. Their hazardous influence on human life, degrading and damaging effects on material and interference with scientific measurements and observations are well recognized[M]. Here, the objective is to compare the effect of the radiation hazards on usability of the various QSO for space applications with that for the GSO.

In view of the near-uniform distribution of the solar wind and solar flare particles at the altitudes of (4re) and above [35], their influence on satellites in the 24-hr orbits of interest (i.e. e -< 0.3) would remain virtually the same,

O0

70--

60- -

5O

o ~max/-,0

o

~mox 3C-

2(?

0 0.10 0.20 030 040 0.50 e

Fig. 2. Plots showing the effect of eccentricity on ama~ and Ym,x

K. KUMAR

thus, suggesting no particular difficulty or advantage in using the QSO. The inner Van Allen belt is confined to lower altitudes (-< 1.8re) and has therefore practically no effect on satellites in the 24-hr orbits under con- sideration. However, the outer Van Allen belt charac- terized by heavily populated high energy (i.e. ene rgy - 1.5 Mev) particles, essentially electrons, is of primary concern in choice of the orbits. The intensity of these electrons which depends on altitude, longitude and lati- tude is further influenced by the solar wind and occurence of the solar flares. It is important to recognize that the significant parameter here is the total electron energy flux dose received by the satellites per orbit. Attention is therefore focused on estimating this parameter for the various 24-hr orbits from relevant satellite data[35-38]. The averages thus obtained and presented in Table 3 clearly show that increasing the orbital eccentricity may provide a slight advantage from the view-point of total energy flux dose encountered by the satellites.

Furthermore, the radiation intensity of Van Allen belts decreases on either side of the geomagnetic equa- tor, almost completely vanishing at 450 S or 45°N to it. This implies the existence of a rather large useful range of orbital inclinations with associated daily energy dose nearly equal to or below that for the GSO.

Thus, from the viewpoint of radiation hazards alone, the satellites in the QSO cannot be any less efficient than the commonly used GSO.

4. BOOSTER ENERGY REQUIREMENTS

Here, it is proposed to examine the effect of orbital eccentricity and inclination on the booster energy requirements for the various 24-hr orbits. Since injection of the satellite into the final desired orbit is generally preceded by establishing a circular parking orbit first, the total impulse required in transfer of the satellite from a typical parking orbit to the final desired trajectory has been computed and compared. Hohmann transfer has been assumed in the analysis. Furthermore, in the situa- tion where the perfect geostationary system is desired, the final impulse at the apogee of the transfer orbit is also assumed to provide for the change in the inclination of the orbital plane. It is then easy to show that the non-dimensionalized expressions as obtained for the total velocity increments required for the satellite trans- fer from the parking orbit to the final stationary and non-stationary orbits can be written as

AVg~ = [2/(1 + n)] "2. n - n "2

+ [l + 2/(1 + n) - 2{2/(! + n)} "2 cos i],2

A~?qs = [2(1 + e)/{! + n(1 + e)}] ~/2' n - n '/2

+ [(1 - e)/(l + e)] '/2

- [2/{(1 + e ) . (1 + n(1 + e)))] ~/2.

Using these expressions, it is easy to compute the net saving obtained by the choice of the proposed in- clined/elliptic orbits over the perfect, equatorial cir- cular orbit. From the results thus obtained (Table 4), it is

Some aspects related to the satellite applications in non-stationary 24-hour orbits

Table 3. Effect of eccentricity on daily energy flux dose on satellites in 24-hr orbits

Eccentricity 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Daily dose ×10 -4(rads) 1.21 1.21 1.20 1.19 1.17 1.14 1.09 0.99 0.85 0.79 0.68

151

Table 4. Impulse savingst as affected by eccentricity and inclination of the quasi-synch- ronous orbit

eX•o 0 5 10 15 20 25 30 35 40

0 0 0.004 0.016 0.035 0.061 0.092 0.127 0.166 0.207 0.05 0.015 0.019 0.031 0.050 0.076 0.107 0.142 0.181 0.222 0.10 0.031 0.035 0.047 0.066 0.092 0.123 0.158 0.196 0.237 0.15 0.047 0.051 0.063 0.082 0.108 0.139 0.174 0.213 0.254 0.20 0.064 0.068 0.080 0.099 0.125 0.156 0.191 0.230 0.271 0.25 0.082 0.086 0.098 0.117 0.143 0.173 0.209 0.247 0.288 0.30 0.100 0.104 0.116 0.135 0.161 0.192 0.227 0.266 0.307 0.35 0.119 0.123 0.135 0.154 0.180 0.211 0.246 0.285 0.326 0.40 0.139 0.143 0.155 0.174 0.200 0.231 0.266 0.304 0.346 0.45 0.159 0.164 0.175 0.195 0.220 0.251 0.286 0.325 0.366 0.50 0.181 0.185 0.197 0.2t6 0.242 0.273 0.308 0.346 0.388

apparent that the use of the non-stationary orbits enables significant savings in the booster power requirements, particularly for larger orbital eccentricities (e) and in- clinations (i). Thus on the basis of booster energy requirements alone, the QSO appear to be quite attrac- tive. Dial and Cooley [39] have shown that by placing the International Ultraviolet Explorer (IUE) scientific mis- sion payload in the inclined-elliptic 24-hr orbits instead of the perfect GSO as proposed earlier, the net on- station weight capability of the delta 2914 launch vehicle can be significantly enhanced. In fact, it has been con- cluded that a net payload weight advantage of 23 kg can be achieved which leads to an overall greater cost- effectiveness of the space mission. The use of the elec- trically powered orbital transfer vehicles/space trans- portation system being proposed for future missions, however, would lead to some reduction in the net savings associated with the QSO, particularly for large and mas- sive satellites.

It may be pointed out that the choice of the non- stationary orbits provides a unique mission analysis problem and a challenge to meet all the constraints dictated by science, thermal, communications and other requirements.

5. GENERAL COST CONSIDERATIONS

The spacecraft cost, the cost of its launch into the final orbit and the cost of the associated ground segment are the most important components constituting the total cost of a space mission[39, 40]. A review of the relative costs due to the various factors appears to show con- siderable variation depending upon the nature of the mission. That makes it rather difficult to analyze the relative economics associated with the use of the satel- lites in the stationary and the non-stationary orbits, in

general terms, without reference to the specific objec- tives of the mission design. However, it is interesting to note that it has been possible to achieve a higher cost efficiency with the non-stationary 24-hr satellite orbits in certain specific situations involving limited mission objectives such as scientific space exploration.

It is felt that, in general, in missions involving mini- mal interaction with the ground segment (i.e. where the role of the ground segment is somewhat limited and involves relatively small amount of up-and-down-link communication including command, telemetry, tracking and reception of other useful data), the advantage of reduction in the booster power capability requirement may often be sufficient to justify the selection of the elliptic mission orbits. On the other hand, in commercial applications involving space communications as a major objective, the ground segment costs become a significant factor. These costs exhibit a strong dependence on the choice of orbits and are substantially lower for the perfect geosynchronous systems requiring the use of much simpler earth stations. With a large influx of small ground stations permitting the use of smaller antennas, the geostationary satellites have further gained ground [27, 41].

In case of inclined/elliptic 24-hr satellite orbits, several additional problems creep in. Relatively more sophisti- cated and expensive ground stations are needed for tracking and communicating with the visible but "mov- ing" satellites. However, such ground stations may enable the system to withstand larger periodic and secu- lar perturbations in the orbital inclination before an appreciable degradation in its performacne occurs. This may in turn lead to a significant reduction in N-S station- keeping requirements with a probable increase in the useful satellite life-span. These gains may partially corn-

152 K.

pensate for the otherwise generally adverse effect of the large increase in ground segment costs associated with the non-stationary satellites.

Furthermore, to maintain the constant levels of signal power being received at the satellite and at the ground station would require continually varying the transmitter power. Fortunately, however, with the present state of technology, this would not pose a serious problem. Per- haps, a much greater difficulty may lie in the problem of satellite drift relative to the ground station which in turn leads to a considerable increase in demand on the track- ing and attitude control subsystems. These factors are likely to almost entirely offset the advantages of the increased payload with the QSO for communications missions. However, the attitude control problem may be partially overcome by the use of the on-board elec- tronically steerable phased array antenna capable of following the line-of-sight to the cooperative ground station[42]. Recently, Kumar and Joshi[43] have pro- posed the use of solar radiation pressure for varying the spacecraft orientation in order to achieve its fixed ap- parent attitude with respect to the ground-station. The proposed technique may prove to be quite helpful in rendering the use of the non-stationary communications satellites more economical and hence more acceptable.

Finally, it may be worthwhile to point out that the additional factors such as the new developments in microprocessor technology leading to probable reduction in size, weight and costs of electronic components together with the recent inflationary trends in the cost of rocket fuel are likely to have a major impact on the relative cost-effectiveness of the stationary and the non- stationary systems in the future.

6. SOME OTHER APPLICATIONS OF THE

NON-STATIONARY ORBITS

The geosynchronous systems fail to provide direct telecommunications in the polar regions[44]. It is pos- sible, however, to extend the satellite coverage to the higher latitudes by placing the spacecrafts into inclined circular/elliptic orbits. The quasi-stationary nature of these satellites, enabling the use of relatively simpler ground stations, is likely to make them quite competitive with the highly elliptic sub-synchronous orbits used for Molniya type of satellite missions.

In view of the possible overcrowding of the geosynchronous space in the future, an international ban on its use for military purposes cannot be ruled out. In such an eventuality, the proposed QSO may find ready acceptance, as an alternative to the GSO now used, along with random medium altitude orbits [45-48] for military communication purposes. In fact, for strategic/tactical reasons, the QSO may even be preferred in certain situations.

The space-nations with limited launch capability may sometimes find it rather attractive to begin with the quasi-stationary satellites for an indigenous experimental communication mission. In this context, the cases of Communications Technology Satellite (CTS) launched for Canada and small domestic satellite HS-333 built for NASA and INTELSAT may be cited where marginal

KUMAR

reduction in payload weight achieved through a minimal electronic redundancy and various other weight saving techniques made it possible to use the smaller inexpen- sive and highly reliable Thor-Delta launch vehicles [44, 49, 50] . Such an experimental communi- cation mission may also provide an opportunity for the collection of a vast amount of useful communication data at widely and continuously varying altitudes.

It is now proposed to examine the suitability of the inclined/elliptic 24-hr orbits as an alternative to the geostationary circular path for satellite solar power generation first proposed by Glaser[51]. The additional problems associated with this usage of the non-synch- ronous orbits do not appear to be significantly different from those involved in communications applications. So far as the question of attitude control for aligning the satellite with the line-of-sight is concerned, it may be possible to tackle it using nearly passive solar attitude control approach recently proposed by Kumar and Joshi[43]. Furthermore, as the ground antenna being considered for receiving the microwave beam transmit- ted from the satellite is based on the principle of half wave dipole rectification and does not have to be pointed precisely at the transmitting space antenna, controlling the huge ground antenna may not be necessary at least for low orbital ellipticity and/or inclination with respect to the equatorial plane. The periodic satellite drift towards or away from the ground station appears to pose a somewhat more serious problem, however, it may still be acceptable in some specific situations demanding avail- able output power patterns especially planned to meeting the excessive peak power requirements. At the current level of technological developments, the terrestrial power generation options are no doubt cheaper. But with numerous attempts on improving the overall efficiency in space power generation in progress, rapidly escalating costs of terrestrial fuels (some of which are getting depleted at an alarming rate) and growing constraints on permissible environmental pollution generated by these options, the balance may get altered in not too distant a future. This suggests that a flexible design approach together with some further related technological developments may make it possible to profitably exploit the power satellites in the QSO.

The usefulness of a space vehicle for gathering scientific and technological data has been well recog- nized. The data thus gathered using this elevated plat- form in space is then transmitted to an earth terminal via the down-communication-link. It is interesting to note that in several situations permitting delay in the trans- mission from the satellite to the ground station, it may be acceptable to unload the collected data once every orbit. Particularly, in view of some recent and likely future developments in the technology of data compression and storage, this scheme may appear to be quite attractive. In this approach, by limiting the data transmisson to short periods during the satellite excursions through the peri- gee, the on-board radiated power requirement can be substantially cut down, thus increasing the cost- effectiveness of the space mission.

From the earlier discussion, it is apparent that for the

Some aspects related to the satellite applications in non-stationary 24-hour orbits

elliptic 24-hour orbits, the ground and satellite trans- mitter power requirements would show considerable variation, being minimum at the perigee and maximum at the aopgee. This suggests that from the point of view of communication power requirements alone, the use of satellites in elliptic synchronous orbits would be economical in the vicinity of the perigee and un- economical near the apogee. The large economies of ground and satellite power may be possible if only the portion of the trajectory close to the perigee is employed for communication purposes. This concept may be exploited for augmenting the the country's total tele- communication capacity at "rush hours". Needless to say that its implementation requires careful positioning of the spacecraft in orbit so that the time of its perigee passage is nearly the same as that for the traffic peak load. However, this would leave a major portion of the trajectory unused and thus adversely affect the overall cost-effectiveness of the mission, unless the idle portion can be put to use for some other worthwhile space applications. This idea can be further generalized by suitably combining the brief communication periods with a large variety of other space applications in a mission. Thus it is felt that the QSO may be particularly suitable for multi-space missions.

7. CONCLUDING REMARKS

The important points of the present article may be summarized as follows:

(i) In view of the increasing crowding of equatorial space at a rapid rate and the associated legal/political problems, the proposed QSO are expected to play a greater role in future space missions.

(ii) The simplified visibility analysis carried out here should be quite useful for preliminary design purposes. The analysis shows that even for relatively larger eccen- tricities and with moderate orbital inclinations and ground station latitudes, the uninterrupted satellite visi- bility is possible.

(ii) The peak power requirements for communications show a continuous increase with increasing orbital eccentricity. However, this may not present a major limitation, particularly in non-communication space mis- sions.

(iv) A major problem associated with the use of the QSO and the resulting angular satellite drift relative to the ground station appears to be excessive demand on the attitude control subsystems. However, in view of a simple, nearly passive solar attitude control approach proposed by the author, it may be possible to overcome this difficulty to a large extent.

(v) The use of the proposed QSO enables considerable savings in the booster energy requirements. This ad- vantage is of rather special significance as it is likely to provide an effective counter to the various disadvantages in several design situations, particularly for non-com- munication applications.

(vi) In view of the changing pattern of costs asso- ciated with the various space mission components, the problem of overcrowding of the usable equatorial space, restriction on usin~ the frequencies, etc., a need for plac-

153

ing even the communications satellites into the QSO appears to be a distinct future possibility.

(vii) The QSO can be effectively used for several non-conventional satellite applications:

--Satellite solar power generation for increasing peak load capacity.

--Delayed transmission of a variety of data collected over each orbit.

--Multi-space missions including communication in the vicinity of the perigee where the communication power requirement would be rather low.

Acknowledgement--A part of the above work was carried out under a research project sponsored and funded by the Indian Space Research Organization (ISRO), Department of Space, Government of India.

REFERENCES

1. W. L. Morgan, Satellite characteristic summary. Acta Astronautica 5, 455--466 (1978).

2. W. L. Morgan, Satellite utilization of the geosynchronous orbit. J. Br. Interplanetary Soc. 28, 195-205 (1975).

3. S. K. Shrivastava, Orbital perturbations and station-keeping of communications satellites: a brief survey. J. Spacecraft and Rockets 15, 67--68 (1978).

4. H. Rosen, A satellite system for educational television. Astronaut. Aeronaut. 6, 58--63 (1%8).

5. E. Ehrlich, Satellite aids for aviation. Astronaut. Aeronaut. 6, 64-70 (1%8).

6. J. B. Lagrade, Setting up of a worldwide maritime satellite system. J. Br. Interplanetary Soc. 30, 123-126 (1977).

7. D. Jarret, Satellite Communications: Future systems--Pro- gress in Astronautics and Aeronautics 54, AIAA (1977).

8. W. H. Robbins and P. L. Dononghe, CTS United States Experiment--a progress report. Acta Astronautica 5, 369-383 (1978),

9. L. T. Seaman, H. R. Reicherl, G. Kuraishi and T. Ohtake, Japanese broadcast satelliete. Acta Astronautica 5, 437--454 (1978).

10. M. Astrain, Economic effects of communications satellites. Presented in forum discussion on Economic Effects of Space Developments, XXXI IAF Congress, Tokyo (1980).

11. S. H. Reiger, Commercial satellite systems. Astronaut. Aerospace Engng 1, 26-30 (1%3).

12. W. E. Bradley, Communication strategy of geostationary orbit. Astronaut. Aeronaut. 6, 34--41 (1968).

13. G. Beardsley. The impact of space. Astronaut. Aeronaut. 6, 71-73 (1%8).

14. G. E. Lavean and E. J. Martin, Communications satellites; the second decade. Astronaut. Aeronaut. 12, 54--61 (1974).

15. K. Miya, T. Muratani and H. Satoh, Towards efficient and equitable use of the geostationary orbit. Acta Astronautica 7, 1065-1073 (1980).

16. D. Jarret, Meeting the twin challenges of demand and con- servation of spectrum and orbit through technology. Paper 25-1, EASCON (1977).

17. L. Pollack, Technologies for future INTELSAT satellites. J. Spacecraft and Rockets 17, 4-8 (1980).

18. R. L. Harvey, The critical satellite technical issues of future pervasive broadband low-cost communications network. Acta Astronautica 7, 1191-1211 (1980).

19. S. G. Lutz, Twelve advantages of stationary satellite system for point to point communication. Proc. Hearings Presented at House of Representatives, U.S.A., pp. 50-59 (1%i).

20. F. P. Adler, Synchronous orbit communications satellites. Proc. 2nd Nat. Conf. on Peaceful Uses of Space, Seattle, U.S.A., pp. 187-191 (1%2).

21. L. Jaffe, Application satellites--communications and wea- ther. Proc. Conf. on Space Age Planning, Chicago, pp. 81-93 (1%3).

154 K. KUMAR

22. J. V. Charyk, Communication Satellite Corporation: Objec- tives and problems. Astronaut. Aerospace Engng 1, 45--48 (1%3).

23. S. Metzer, The commercial communications satellite sys- tems-1963-68. Astronaut. Aeronaut. 6, 42-51 (1%8).

24. B. I. Edelson and P. L. Bargellini, Progress and trends in satellite communication: a survey. Presented at the XXVIth Int. Astronautical Cong., Lisbon, Portugal (1975).

25. H. O. Ruppe, A history of communication satellites. J. Br. Interplanetary Soc. 30, 131-134 (1977).

26. P. L. Bargellini, Principles and evolution of satellite com- munications. Acta Astronautica 5, 135-149 (1978).

27. R. C. Davis, F. H. Esch, L. Palmer and L. Pollack, Future trends in communications satellite systems. Acta Astronau- tica 5, 275-298 (1978).

28. H. E. Rowe and A. A. Penzias, Efficient spacing of synch- ronous communication satellites. Bell Systems Tech. J. 47, 2379-2433 (1%8).

29. D. L. Akin, Some applications of non-stationary geosynch- ronous orbits. AIAA Paper No. 78-1407, presented at the AIAAIAAS Astrodynamics Conf., Palo Alto, California (1978).

30. V. K. Joshi, Feasibility of using satellites in non-equatorial, elliptic, 24-hour orbits for uninterrupted communications. M. Tech. Thesis, I.I.T. Kanpur, India (1979).

31. R. C. Brereton and V. J. Modi, On the stability of planar librations of a dumb-bell satellite in an elliptic orbit. Aeronaut. J. 70, Roy. Aeronaut. Soc., 1098-1102 (1%6).

32. R. F. Filipowsky and E. I. Muehldorf, Space Com- munications Systems, pp. 60--74, Prentice Hall, London (1%5).

33. J. W. Haffner, Nuclear Science and Technology Series on Radiation and Shielding in Space. Academic Press, New York (1%7).

34. S. L. Russal, Radiation shielding considerations in manned spacecraft design. J. Spacecraft and Rockets 1, 311-315 (1%4).

35. E. G. Stassinopoulos, The geostationary radiation environ- ment. Z Spacecraft and Rockets 17, 145-152 (1980).

36. P. Rothwell and C. E. Mcllwain, Magnetic Storms and the Van Allen radiation belts---observations from satellite 1958E (Explorer VI). J. Geophysical Res. 65, 799-806 (1%0).

37. A. Rosen and T. A. Farley, Characteristics of Van Alien radiation zones as measured by the scintillation counter on Explorer VI. J. Geophysical Res. 66, 2013-2028 (1%1).

38. B. J. O. Brian, J. A. Van Allen, C. D. Laughlin and L. A. Frank, Absolute electron intensities in the heart of the earth's outer radiation zone. J. Geophysical Res. 67, 397--403 (1%2).

39. O. L. Dial and J. L. Cooley, Mission design implications of an inclined elliptical geosynchronous orbit (International Ultraviolet Explorer). J. Spacecraft and Rockets 14, 401-408 (1977).

40. L. B. Early, C. Rebers and P. Canghran, Economics of communications satellite systems--1976. Acta Astronautica 5, 261-273 (1978).

41. J. V. Charyk, Communications satellites. J. Spacecraft and Rockets 14, 385-394 (1977).

42. L. Jaffe, NASA communication satellite developments. Astronaut. Aerospace Engng 1, 48-51 (i%3).

43. K. Kumar and V. K. Joshi, An attitude control approach for compensation of satellite drift in elliptic synchronous orbits. Acta Astronautica 8, 719-731 (1981).

44. E. Sion, Hughes domestic communications satellite systems. Acta Astronautica 5, 189-218 (1978).

45. J. S. Dorsey, Defense communications satellite program. Astronaut. Aerospace Engng 1, 52-53 (1%3).

46. L. G. Fischer, Military satellite control, Astronaut. Aeros- pace Engng 1, 54-57 (i%3).

47. V. W. Wall, Military communication satellites, Astronaut. Aeronaut. 6, 52-57 (1%8).

48. F. E. Bond, Military satellite communication: an overview. Prog. Astronaut. Aeronaut. 41, 43-51 (1976).

49. H. R. Raine, The communications technology satellite flight performance. Acta Astronautica 5, 343-367 (1978).

50. J. F. Kleiger, RCA Satcom: an example of wight optimized satellite design for maximum communications capacity. Acta Astronautica 5, 21%242 (1978).

51. P. E. Glaser, Development of the satellite solar power sta- tion. Space Flight 18, 198-208 (1976).

APPENDIX

Nomenclature a~ radius of parking orbit, r, + h a2 radius of the geostationary orbit

a3, a4 perigee and apogee distances of the quasi-stationary orbit, a4 = 2a2 - a3 (Fig. 1)

an (a2/r,), 6.624 E communication energy required for the duration of

an orbit Es,, Eq, communication energy required for the geosynch-

ronous and quasi-stationary orbits, respectively e eccentricity of the orbit h altitude of the parking orbit i inclination of the plane of the parking or the quasi-

stationary orbits with respect to the equatorial plane

Ki mass-distribution parameter, 1 for dumb-bell satel- lite with its long axis aligned with the local ver- tical

n aJal P communication power as transmitted from satel-

lite/ground station Pq,.~,x maximum communication power required in the

case of quasi-stationary orbits P~s communication power required for the geosynch-

ronous orbit r distance between satellite and center of the earth,

Fig. 1 r, earth-radius r~ (r/r,) t time

u w+O w argument of perigee as measured from the line of

modes we spinning velocity of the Earth a the angle between satellite local vertical and the

line-of-sight, Fig. 1 amax amplitude of the angular satellite drift relative to the

ground station 3 the angular distance between the satellite and the

ground station as observed from the Earth center, Fig. I

~, the angle between the local vertical at the ground station and the line-of-sight, Fig. 1

3'm~x amplitude of the desired periodic changes in orien- tation of the ground-based antenna

8, 8o the instantaneous and initial celestial longitudes of the ground station as measured from the vernal equinox

0 satellite position angle, as measured from the peri- gee, Fig. 1

# Earth's gravitational field constant latitude of the ground station

l~ nodal angle as measured from the vernal equinox A Vg,,A Vqs total velocity increments required for transfer of

satellite from the parking orbit to the geosta- tionary and quasi-stationary orbits, respectively

A Vs,, A r~¢, dimensionless velocity increments; A Vgs = A V~s(a2/~)" 2, A ~q, = A Vq, (a2/~F 2