Included In propellent budget

'Sec. 632 if plane change also required.

'Sec. 632 if plane change also required.

relative to the body as when it approached, but in a different direction. This phenomenon is like the elastic collision between a baseball and a bat in which the velocity of the ball relative to the bat is nearly the same, but its velocity relative to the surrounding baseball park can change dramatically. We can use flybys to change direction, to provide increased heliocentric energy for solar system exploration, or to reduce the amount of energy the satellite has in inertial space. For example, one of the most energy-efficient ways to send a space probe near the Sun is to use a flyby of Jupiter to reduce the intrinsic heliocentric orbital velocity of Earth associated with any spacecraft launched from Earth.

A second way to produce a large AV without burning propellant is to use the atmosphere of the Earth or other planets to change the spacecraft's direction or reduce its energy relative to the planet. The manned flight program has used this method from the beginning to dissipate spacecraft energy for return to the Earth's surface. Mars Pathfinder used aerobraking for planetary exploration. It can also be used to produce a major plane change through an aeroassist trajectory [Austin, Cruz, and French, 1982; Mease, 1988].

The solar sail is a third way to avoid using propellant. The large, lightweight sail uses solar radiation to slowly push a satellite the way the wind pushes a sailboat Of course, the low-pressure sunlight produces very low acceleration.

The aerospace literature discusses many alternatives for providing spaceflight energy. But experimental techniques (those other than rocket propulsion and atmospheric braking) are risky and costly, so normal rocket propulsion will ordinarily be used to develop the needed AV, if this is at all feasible.

The AV budget described in Table 7-3 measures the energy we must give to the spacecraft's center of mass to meet mission conditions. When we transform this AV budget into a propellant budget (Chap. 10), we must consider other characteristics. These include, for example, inefficiencies from thrusters misaligned with the AV direction, and any propulsion diverted from AVto provide attitude control during orbit maneuvers. Chapters 10 and 17 describe propulsion requirements in detail.

For most circumstances, the A V budget does not include margin because it results from astrodynamic equations with little error. Instead, we maintain the margin in the propellant budget itself, where we can reflect such specific elements as residual propellant. An exception is the use of AVto overcome atmospheric drag. Here the AV depends upon the density of the atmosphere, which is both variable and difficult to predict Consequently, we must either conservatively estimate the atmospheric density or incorporate AV margin for low-Earth satellites to compensate for atmospheric variations.

7.4 Selecting Orbits for Earth-Referenced Spacecraft

The first step in finding the appropriate orbit for an Earth-referenced mission is to determine if a specialized orbit from Table 7-4 applies.* We should examine each of these orbits individually to see if its characteristics will meet the mission requirements at reasonable cost. Space missions need not be in specialized orbits, but these orbits have come into common use because of their valuable characteristics. Because they do constrain such orbit parameters as altitude and inclination, we must determine whether or not to use them before doing the more detailed design trades described below.

It is frequently the existence of specialized orbits which yields very different solutions for a given space mission problem. Thus, a geosynchronous orbit may provide the best coverage characteristics, but may demand too much propellant, instrument resolution, or power. This trade of value versus cost can lead to dramatically different solutions, depending on mission needs. For a traditional communications system, the value of providing continuous communications coverage outweighs the cost and performance loss associated with the distance to geostationary orbit Some communications systems provide continuous coverage with a low-Earth orbit constellation as described in Sec. 7.6. In the case of FireSat continuous coverage is not required and

TABLE 7-4. Specialized Orbits Used for Earth-Referenced Missions. For nearly circular low-Earth orbits, the eccentricity wfll undergo a low-amplitude oscillation. A frozen orbit is one which has a small eccentricity (-0.001) which does not oscillate due to a balancing of the J2 and J3 perturbations.




Where Discussed

Geosynchronous (GEO)

Maintains nearly fixed position over equator

Communications, weather

Sec. 6.1.4


Orbit rotates so as to maintain approximately constant orientation with respect to Sun

Earth resources, weather

Sea 622


Apogee/perigee do not rotate

High latitude communications

Sec. 622

Frozen Orbit

Minimizes changes in orbit parameters

Any orbit requiring stable conditions

See Chobotov [1996]

Repeating Ground Track

Subsatellite trace repeats

Any orbit where constant viewing angles are desirable

Sec. 6.5

the need for fine resolution on the ground for an IR detection system precluded a geosynchronous orbit, so its mission characteristics are dramatically different There is no a priori way of knowing how these trades will conclude, so we may need to cany more than one orbit into detailed design trades. In any case, we should reconsider specialized orbits from time to time to see whether or not their benefits are indeed worth their added constraints.

Orbit design is inherently iterative. We must evaluate the effects of orbit trades on the mission as a whole. In selecting the orbit, we need to evaluate a single satellite vs. a constellation, specialized orbits, and the choice of altitude and inclination. For example, alternative solutions to a communications problem include a single large satellite in geosynchronous equatorial orbit and a constellation of small satellites in low-Earth orbit at high inclination.

The first step in designing mission orbits is to determine the effect of orbit parameters on key mission requirements. Table 7-5 summarizes the mission requirements that ordinarily affect the orbit The table shows that altitude is the most important of orbit design parameter.

The easiest way to begin the orbit trade process is by assuming a circular orbit and then conducting altitude and inclination trades as described below and summarized in the table. This process establishes a range of altitudes and inclinations, from which we can select one or more alternatives. Documenting the reasons for these results is particularly important, so we can revisit the trade from time to time as mission requirements and conditions change.

Selecting the mission orbit is often highly complex, involving such choices as availability of launch vehicle, coverage, payload performance, communication links, and any political or technical constraints or restrictions. Thus, considerable effort may go into the process outlined in Table 7-1. Figure 3-1 in Sec. 3.23 shows the results of the altitude trade for the FireSat mission. Typically these trades do not result in specific values for altitude or inclination, but a range of acceptable values and an indication of those we would prefer. Ordinarily, low altitudes achieve better instru-

TABLE 7-5. Principal Mission Requirements That Normally Affect Earth-Referenced Orbit Design.

Mission Requirement

Parameter Affected

Where Discussed

Coverage Continuity Frequency Duration

Field of view (or swath width) Ground track Area coverage rate Viewing angles Earth locations of interest

Altitude Inclination

Node (only relevant for some orbits) Eccentricity

Sec. 7.2

Sensitivity or Performance

Exposure or dwell time




Chaps. 9,13

Environment and Survivability

Radiation environment Lighting conditions Hostile action


(Inclination usually secondary)

Chap. 8

Launch Capability

Launch cost On-orbit weight Launch site limitations

Altitude Inclination

Chap. 18

Ground Communications

Ground station locations Use of relay satellites Data timeliness




Chap. 13

Orbit Lifetime

Altitude Eccentricity

Sees. 6.2.3,8.1.5

Legal or Political Constraints


Launch safety restrictions International allocation

Altitude Inclination Longitude In GEO

Sec. 21.1

ment performance because they are closer to the Earth's surface. They also require less energy to reach orbit On die other hand, higher orbits have longer lifetimes and provide better Earth coverage. Higher orbits are also more survivable for satellites with military applications. Orbit selection factors usually compete with each other with some factors favoring higher orbits and some lower.

Often, a key factor in altitude selection is the satellite's radiation environment As described in Sec. 8.1, the radiation environment undergoes a substantial change at approximately 1,000 km. Below this altitude the atmosphere will quickly clear out charged particles, so the radiation density is low. Above this altitude are the Van Allen belts, whose high level of trapped radiation can greatly reduce the lifetime of spacecraft components. Most mission orbits therefore separate naturally into either low-Earth orbits (LEO), below 1,000 to 5,000 km, and geosynchronous orbits (GEO), which are well above the Van Allen belts. Mid-range altitudes may have coverage characteristics which make them particularly valuable for some missions. However, the additional shielding or reduced life stemming from this region's increased radiation environment also makes them more costly.

Having worked the problem assuming a circular orbit, we should also assess the potential advantages of using eccentric orbits. These orbits have a greater peak altitude for a given amount of energy, lower perigee than is possible with a circular orbit, and lower velocity at apogee, which makes more time available there. Unfortunately, eccentric orbits also give us non-uniform coverage and variable range and speed.

Eccentric orbits have an additional difficulty because the oblateness of the Earth causes perturbations which make perigee rotate rapidly. This rotation leads to rapid changes in the apogee's position relative to the Earth's surface. Thus, with most orbits, we cannot maintain apogee for long over a given latitude. As Sec. 6.2 describes, the first-order rotation of perigee is proportional to (2 - 2.5 sin2¿) which equals zero at an inclination, i = 63.4 deg. At this critical inclination the perigee will not rotate, so we can maintain both apogee and perigee over fixed latitudes. Because this orientation can provide coverage at high northern latitudes, the Soviet Union has used such a Molniya orbit for communications satellites for many years. Geosynchronous orbits do not provide good coverage in high latitude regions.

Eccentric orbits help us sample either a range of altitudes or higher or lower altitudes than would otherwise be possible. That is why scientific monitoring missions often use high eccentricity orbits. As discussed in Sec. 7.6, Draim [1985, 1987a, 1987b] has done an extensive evaluation of the use of elliptical orbits and concluded that they can have significant advantages in optimizing coverage and reducing the number of satellites required.

FireSat Mission Orbit Our first step for the FireSat mission orbit is to look at the appropriateness of the specialized orbits from Table 7-4. This is done for FireSat in Table 7-6. As is frequency the case, the results provide two distinct regimes. One possibility is a single geosynchronous FireSat In this case, coverage of North America will be continuous but coverage will not be available for most of the rest of the world. Resolution will probably be the driving requirement

TABLE 7-6. FireSat Specialized Orbit Trade. The conclusion is that in low-Earth orbit we do not need a specialized orbit for FireSat Thé frozen orbit can be used with any of the low-Earth orbit solutions.




Good for FireSat


Continuous view of continental U.S.

High energy requirement No world-wide coverage Coverage of Alaska not good




High energy requirement



Good Alaska coverage Acceptable view of continental U.S.

High energy requirement Strongly varying range

No, unless Alaska Is critical

Frozen Orbit

Minimizes propellant usage



Repeating Ground Track

Repeating viewing angle (marginal advantage)

Restricts choice of altitude Some perturbations stronger

Probably not

The alternative is a low-Earth orbit constellation. Resolution is Iks of a problem than for geosynchronous. Coverage will not be continuous and will depend on the number of satellites. None of the specialized low-Earth orbits is needed for FireSat (A frozen orbit can be used with essentially any low-Earth orbit) Thus, for the low-Earth constellation option, there will be a broad trade between coverage, launchability, altitude maintenance, and the radiation environment

For low-Earth orbit, coverage will be the principal driving requirement. Figure 3-1 in Sec. 3-2.3 summarized the FireSat altitude trades and resulted in selecting an altitude rangé of 600 to 800 km with a preliminary value of700 km. This may be affected by further coverage, weight, and launch selection trades. FireSat will need to cover high northern latitudes, but coverage of the polar regions is not needed. Therefore, we select a preliminary inclination of 55 deg which will provide coverage to about 65 deg latitude. This will be refined by later performance trades, but is not likely to change by much.

Zero eccentricity should be selected unless there is a compelling reason to do otherwise. There is not in this case, so the FireSat orbit should be circular. Thus, the preliminary FireSat low-Earth orbit constellation has a = 700 km, i = 55 deg, e = 0, and the number of satellites selected to meet minimum coverage requirements.

13 Selecting Transfer, Parking, and Space-Referenced Orbits

Selecting transfer, parking, and space-referenced orbits proceeds much the same as for Earth-referenced orbits, although their characteristics will be different Table 7-7 summarizes the main requirements. We still look first at specialized orbits and then at general orbit characteristics. Table 7-8 shows the most common specialized orbits. The orbits described in this section may be either the end goal of the whole mission or simply one portion, but the criteria for selection will be the same in either case.

TABLE 7-7. Principal Requirements that Normally Affect Design of Transfer, Parking, and Space-Referenced Orbits.


Where Discussed

Accessibility (AV required)

Orbit decay rate and long-term stability

Ground station communications, especially for maneuvers

Radiation environment

Thermal environment (Sun angle and eclipse constraints) Accessibility by Shuttle or transfer vehicles

Sees. 6.3,7.3 Sec. 6.2.3 Sees. 5.3,12. Sec. 8.1 Sees. 5.1,10.3 Sec. 18.2

7.5.1 Selecting a Transfer Orbit

A transfer orbit must get the spacecraft where it wants to be. For transfer orbits early in the mission, the launch vehicle or a separate upper stage was traditionally tasked with doing the work as described in Chap. 18. Because of the continuing drive to reduce cost integral propulsion upper stages have become substantially more common (see Chap. 17).

TABLE 7-8. Specialized Orbits Used for Transfer, Parking, or Space-Referenced Operations.





Lunar or Planetary Flyby

Same relative velocity approaching and leaving flyby body

Used to provide energy change or plane change

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