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5th Responsive Space Conference April 23–26, 2007

Los Angeles, CA

Circular vs. Elliptical Orbits for Persistent Communications James R. Wertz Microcosm, Inc.

5th Responsive Space Conference RS5-2007-2005

AIAA RS5-2007-2005

1J. Wertz Microcosm — Orbits for Persistent Communications 4/24/07

5th Responsive Space Conference, Los Angeles, CA, April 23–26, 2007

Circular vs. Elliptical Orbitsfor Persistent Communications*

James R. Wertz, Microcosm, Inc.†

AbstractResponsive Communications missions typicallyrequire “persistent communications,” i.e., repeatcoverage that lasts for an extended period or theentire day. LEO orbits cannot provide thiscoverage without a large number of satellites andGEO satellites are typically large and expensive,with a long development time. The solution hastraditionally been thought of as moderate altitudeelliptical orbits, such as Magic or Cobra orbits.However, recent IR&D work by Microcosmsuggests that this may be the wrong answer.This paper compares moderate altitude ellipticaland circular orbits in terms of coverage,coverage flexibility, constellation size, ASATvulnerability, the environment, impact on space-craft design, and overall system cost. Theconclusion reached is that circular MEO orbitsare a better choice than elliptical MEO orbits forsupplementary or persistent communications.

BackgroundOne of the key missions for Responsive Space ispersistent supplemental communications. Thereis an ever-increasing demand for both voice andhigh bandwidth data communications in militaryapplications. This is an area with high potentialfor responsive systems because the need andlocation of the demand may change rapidly withthe changing world situation. Properly designed,low-cost, responsive communications systemscould greatly alleviate this problem.

The traditional choices have been either largegeosynchronous (GEO) communications satell-ites, such as MilStar, or low Earth orbit (LEO)communications constellations, such as Iridium.The GEO systems tend to be very expensive andhigh power with development and deploymentschedules that can run a decade or more.

LEO systems also tend to be expensive becauseof the large number of satellites required forglobal coverage. In addition, LEO globalcommunications systems have had majorfinancial problems in the past. The Iridiumconstellation of 66 satellites was built at a cost ofapproximately $5.5 billion and ultimately soldfor $25 million.

For responsive supplemental communications,we want focused coverage of a particular regionthat can be put in place rapidly and at low cost.24/7 coverage would be best, but intermittentcoverage could also have significant utility. Thegoal is to trade away global coverage and longlife for dramatically reduced cost and launch-on-demand.

At RS3 Microcosm presented a paper that, basedon our work and others, recommended thepotential use of an elliptical (Magic) orbit forsupplemental persistent communications [Hop-kins, undated; Wertz, 2005]. The generalcharacteristics of the Magic orbit are as follows:

• Elliptical orbit with a 3 hour period (525km x 7,800 km orbit).

• Critical inclination of 63.4 deg or 116.6deg.

• Argument of perigee adjusted so thatapogee covers the latitude of interest.

• Provides approximately 1 hour ofcoverage once/day or possibly twice/day.

• Constellation of 12 to 24 satellitesrequired to provide 24/7 coverage,although full coverage may be availablein some cases with smaller numbers ofsatellites.

A possible alternative to the Magic orbit is amedium Earth orbit (MEO) constellation usingcircular orbits at an altitude of 5,000 to 15,000km. The purpose of this paper is to compare theMEO circular orbit constellation with the Magic

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*Copyright, 2007, Microcosm, Inc.†Micrcosm, Inc., 4940 West 147th Street, Hawthorne, CA90250-6708.Email: [email protected]

AIAA RS5-2007-2005


orbit constellation in terms of the key parametersthat determine system cost, performance, andvulnerability.

CoveragePerhaps the most fundamental characteristic ofimportance to persistent communications is thecoverage per satellite, shown in Fig. 1 for bothelliptical and circular orbits. We compare orbitswith the same apogee altitude (rather than meanaltitude) because the Magic orbit system isintended to do most of its communications at ornear apogee and it is this altitude that sizes thecommunication and power systems. In addition,by comparing them at the same apogee altitude,the power and antenna size for the groundsystem will be the same.

Fig. 1. Coverage vs. Apogee Altitude forCircular and Elliptical Orbits. See text fordiscussion.

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The results in Figure 1 seem counterintuitive.For two satellites at the same altitude, one in acircular orbit and one at apogee of an ellipticalorbit, the elliptical orbit satellite will be travelingslower and, therefore, would appear to be inview of the ground for a longer period.However, the elliptical orbit drops quicklytoward perigee and the satellite soon disappearsfrom view. In the circular orbit, the satelliteremains at a high altitude and, therefore, can beseen over a longer arc.

Persistent communications requires both goodcoverage per satellite and an appropriateconstellation pattern. A typical ground track

pattern and coverage for the Magic orbit isshown in Fig. 2. Because the spacecraft do notremain fixed relative to each other, cross linkswill require a significant steering range.

Fig. 2. Ground Track (blue) and coveragecircles (red) for a Magic orbit.

With the MEO circular orbit constellation, wecreate a “street of coverage” pattern in whichmultiple satellites in a single plane provide aband of coverage around the world centered onthe orbit plane. (See, for example, Wertz[2001].) In this pattern, satellites remain fixedwith respect to each other over time, such thatcross links require only fine steering to take intoaccount attitude motion or the small variationsdue to higher order orbit perturbations.

A traditional MEO circular orbit pattern isshown in Fig. 3A. This pattern requires up to 3cross-links to get data 180 deg around the world.Above 7,000 km altitude, an alternativeinterlocking pattern is available as shown in Fig.3B. In this case, the same 6 satellites provide aredundant constellation and a single cross linkcan get data 180 deg around the world. Thisreduces the amount of hardware that is tied up inany individual data transmission and, therefore,increases by a factor of 2 to 3 the effective datathroughput available for a given set of hardware.The coverage circles for a 6-satelliteconstellation at 10,000 km altitude are shown inFig. 4. Note that the overlap will increasesubstantially as the altitude is increased or theeffective working elevation angle is decreased.

AIAA RS5-2007-2005


Fig. 3. A (top) Traditional “Street-of-Coverage” Pattern. B (bottom)Interlocking Pattern Available above7,000 km.

Fig. 4. Coverage Circles for an InterlockingPattern Equatorial Constellation at 10,000km altitude.

Depending on the altitude and minimum workingangle, the MEO circular orbit constellation canprovide a very wide swath or coverage band

centered on the orbit plane. Table 1 gives typicalvalues for the swath width for varying altitudesand numbers of satellites. Depending on thelatitude, we can provide continuous coveragewith 4 to 6 satellites at 8,000 km and 3 to 5satellites at 15,000 km. Under essentially allcircumstances, the circular orbit constellationprovides better coverage (i.e., uses fewer satel-lites and covers a larger area) than an ellipticalorbit constellation with the same apogee.

Table 1. Swath Width as a Function ofAltitude and Number of Satellites for aMEO circular orbit “Street-of-Coverage”pattern. The values given assume a 10 degminimum working elevation angle.

Altitude# ofSats

Swath Width

5,000 km 6 74.7 deg

5,000 km 5 63.4 deg

5,000 km 4 26.4 deg

8,000 km 6 94.5 deg

8,000 km 5 86.8 deg

8,000 km 4 67.5 deg

15,000 km 5 111.5 deg

15,000 km 4 99.8 deg

15,000 km 3 48.8 deg

VulnerabilityThe recent Chinese ASAT test clearlydemonstrates the vulnerability of low altitudesatellites. The intercept of a satellite in LEOrequires a launch delta V of somewhat more than3,500 m/s which can be provided by a singlestage, suborbital vehicle. A LEO communi-cations or surveillance satellite has to fly overthe area of interest and, therefore, is a potentialtarget. An intercept can occur in approximately5 to 8 minutes.

One of the best defenses against ASAT weaponsis altitude. A satellite in MEO does not need tofly over the target area and can communicatewith mid-latitude regions from over the equator(or over the poles). An intercept in MEO cantake 20 to 30 minutes, which may be sufficienttime to maneuver or deploy a decoy or chaff.

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Reaching MEO altitudes requires a launch deltaV in excess of 12,000 m/s, which is more delta Vthan is required to put a satellite into LEO andrequires a 3-stage or very high performance 2-stage launch vehicle. If the satellite is over theequator, then the ASAT launch must be movedto the vicinity of the equator or an even longertime and higher delta V will be required. Thus,while the MEO altitudes do not providecomplete safety, they are much less vulnerable toASATs than LEO satellites.

The elliptical Magic orbit is intermediate invulnerability between the LEO and MEO orbits.It generally flies over the area of interest nearapogee at high altitudes. It will be at vulnerableLEO altitudes over much of the orbit, but notnecessarily when it is over the target area.Unfortunately, if the satellite is, for example, atapogee over the target area on an ascending pass,then 12 hours later on a descending pass over thetarget, the satellite will be at a much loweraltitude, typically at or near perigee. Thus,depending on the specific conditions of thetarget/satellite geometry, it is likely that Magicorbit will have much of the same vulnerability asthe LEO orbit.

Orbit Flexibilityand Accessibility

The elliptical Magic orbit must be at the criticalinclination of 63.4 deg or its complement of116.6 deg in order to avoid the rapid rotation ofperigee due to the Earth’s oblateness. (See, forexample, Wertz [2001] or Vallado [2001].)Within this orbit plane, apogee can bemaintained over any desired orientation aroundthe orbit so as to provide good coverage atvarying latitudes. However, this does provide apotential failure mode if the critical inclination isnot achieved.

In contrast, for the circular MEO constellationboth the altitude and inclination are essentially“free parameters” that can be adjusted as neededto meet the needs of a particular mission. Ingeneral, the specific values achieved will not becritical. Thus, the circular orbit eliminates thepotential failure mode and provides moreflexibility in meeting specific coverageobjectives.

In addition, there are two special cases of interestin the circular MEO orbits.

• Equatorial Ring. A single ring ofsatellites around the equator providescontinuous coverage for all latitudes thatfall within the width of the Street-of-Coverage band defined in Table 1.Depending on the number of satellites,altitude, and minimum working elevationangle, this can provide continuouscoverage for latitudes as far north andsouth as 50 deg to 60 deg.

• Polar Ring. Similarly, a single ring ofsatellites in a polar orbit can providecontinuous coverage for latitudes withinas much as 50 deg to 60 deg of the pole.

Both of the above rings have the addedadvantage of particularly simple cross-links sincethe relative positions of the satellites do notchange as they move in their orbit. A polar ringplus an equatorial ring could provide wholeEarth coverage, although the cross linkingbetween the two rings would be more complexbecause of their relative motion.

The accessibility of an orbit is the mass availablein that orbit relative to the mass available in a100 NMi circular orbit at an inclination equal tothe latitude of the launch site. (For a moreextended discussion of accessibility, includingnumerical techniques for evaluating it, see thesee the Orbit Cost Function discussion by Wertz[2001].) The actual mass available in any orbitwill depend on the launch vehicle, the launchsite, and the flight profile. However, if weassume a generic launch capability of 1000 lbs to100 NMi due east from KSC, then theapproximate masses to the orbits of interest are:

• Magic orbit 426 lbs

• MEO circular,20 deg inclination 326 lbs

• MEO circular,70 deg inclination 249 lbs

Thus, depending on the latitude of interest, theMagic orbit will allow a somewhat heaviersatellite that the MEO circular orbit at an altitudeequal to apogee of the Magic orbit.

Radiation Environment andSpacecraft Complexity

For both the Magic and MEO circular orbits theradiation environment is challenging. This is the

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primary reason that more MEO constellations arenot flying at present.

In low Earth orbit, below approximately 900 km,the radiation environment is relatively benign.However, at the inner edge of the Van Allenbelts the radiation environment risesdramatically. (See, for example, Tribble [2003]or Wertz and Larson [1999].) Therefore, boththe elliptical Magic orbit and the circular MEOorbits will be in a very high radiationenvironment, although it may be possible to putthe MEO constellation between the proton andelectron belts to mitigate the environmentproblem to some degree. Nonetheless, thefundamental trade for achieving persistentcommunications is whether the reduced numberof satellites and better coverage of the ellipticaland MEO orbits is worth the high cost ofradiation hardening the satellites. In this respectthe elliptical and MEO circular orbits will bevery similar. It may be that the shorter expectedlife for responsive missions will be a key factorin this regard.

The other major system-level trade is on the sizeand complexity of the spacecraft bus andpayload. The geometrical parameters that effectthese trades are summarized in Table 2. In LEOa communications spacecraft can be small andsimple. However, a single satellite is never inview of one location on the ground for more than10 to 14 minutes, depending on the altitude andminimum working elevation angle. This, in turnimplies the need for a large number of satellitesand potentially very high cost.

Table 2. Geometrical Parameters for theOrbits being considered. Assumes a 10deg minimum working elevation angle. (Forcomputations, see Wertz [2001].)

Parameter LEO Magic Units

Altitude 800 525 x 7,800 km

Range to Horizon 2,370 1,750 – 11,600 km

Earth Ang. Radius 62.7 67.5 – 26.7 deg

Orbit Ang. Vel. 3.8 1.0 – 4.4 deg/min

Ang. Vel. at Nadir 0.53 0.03 – 0.96 deg/sec

Low MEO High MEO

Altitude 8,000 15,000 km

Range to Horizon 11,800 19,300 km

Earth Ang. Radius 26.3 17.4 deg

Orbit Ang. Vel. 1.3 0.7 deg/min

Ang. Vel. at Nadir 0.04 0.02 deg/sec

In many respects the MEO circular constellationis similar to the LEO case. The angular size ofthe Earth, range to nadir, power requirements,and angular rates are all constant.

In contrast, as can be seen in the table, ellipticalorbits cover a wide range in terms of angular sizeof the Earth, range to nadir (and to the horizon),power requirements, and angular rates. All ofthese will tend to complicate the design of thepayload and spacecraft bus. This problem ismitigated to a degree because the payload doesnot have to operate in the vicinity of perigee.However, the more the operating range isconfined to a region near apogee, the lesscoverage that is available per satellite. Thus,substantial additional complexity is introducedby using elliptical, rather than circular, orbits.

ConclusionThe overall conclusions for the various aspectsof the comparison between elliptical Magic andcircular MEO orbits are summarized in Table 3.

Table 3. Conclusions of the Magic vs. MEOCircular Orbit Trade. See text fordiscussion.

Characteristic Elliptical (Magic)Orbit

MEO Circular Orbit

Coverage/Satellite

Similar Similar

ConstellationSize

12 - 24 satellites(may be less insome cases)

3 - 6 satellites

ASATVulnerability

Moderate – High Low

Satellite DesignComplexity

Complex Simple

RadiationEnvironment

High High (may be able toreduce)

CoverageFlexibility

Moderate (inc.fixed)

High (inc. andaltitude variable)

Accessibility Moderate Moderate(somewhat lesspayload mass thanMagic orbit withsame apogee)

Overall SystemCost

Moderate Low–Moderate

For a given launch vehicle, somewhat more massis available in the Magic orbit than in thecomparable MEO orbit. However, essentially allother aspects of the trades favor the MEO circular

AIAA RS5-2007-2005


orbits over the Magic elliptical orbits forpersistent communications. This is counter to the“traditional” solution of elliptical orbits aspreviously proposed by Microcosm and others.The preferred orbits for any particular missionmay well depend on a detailed design analysis.However, we strongly recommend evaluatingconstellations of satellites in MEO circular orbitsas the likely preferred choice for PersistentCommunications.

ReferencesHopkins, R.G. “Long-Access Orbits.” TheAerospace Corporation, briefing presentation.

Tribble, A., 2003. The Space Environment:Implications for Spacecraft Design. Princeton,NJ; Princeton U. Press.

Vallado, D., 2001. Fundamentals of Astro-dynamics and Applications. Dordrecht, theNetherlands and El Segundo, CA; KluwerAcademic and Microcosm Press.

Wertz, J.R., and Larson, W.J., 1999. SpaceMission Analysis and Design, 3rd ed. Dordrecht,the Netherlands and El Segundo, CA; KluwerAcademic and Microcosm Press.

Wertz, J.R., 2001. Mission Geometry; Orbit andConstellation Design and Management.Dordrecht, the Netherlands and El Segundo, CA;Kluwer Academic and Microcosm Press.

Wertz, J.R., 2005. “Coverage, Responsiveness,and Accessibility for Various ‘ResponsiveOrbits’.” Paper No. RS3-2005-2002, presented at3rd Responsive Space Conference, Los Angeles,CA, April 25–28, 2005.

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