Spacecraft Power Systems: Chapter 1. Satellite Overview

Part A

Power System Fundamentals

[10:12 27/10/04 T:/4382 PATEL.751 (2786)/4382-Text 01-07.3d] Ref: 4382 PATEL Ch01-07 Page: 1 1-132

Chapter 1Satellite Overview

1.1 Introduction

A satellite consists of various systems designed to meet the mission specificrequirements. All but the simplest satellites require a common set ofsystems shown by the solid lines in Figure 1.1. Complex satellites requireadditional systems shown by the dotted lines. The systems are classifiedinto two groups, the payload and the bus. The payload consists of thecommunications equipment in commercial satellites or science instrumentsin research satellites. The bus consists of all remaining equipment groupedinto several functional systems that support the payload. The power systemis one of the bus systems that consist of the solar array, battery, powerelectronics, distribution harness, and controls. Other essential bus systemsare the communications and data handling system to receive commandsand return information, telemetry sensors to gage the satellite state, and a


FIGURE 1.1 Satellite systems.

4 Spacecraft Power Systems

central computer to coordinate and control activities of all the systems.Satellites with complex missions also require systems to determine thespacecraft attitude and orbit orientation, and propulsion to control both.

Satellite design is generally optimized to the fullest extent such that anychange would result in a higher cost. The total mission cost, however, is acomplex function of many variables, and so is the power system cost. Thecost, C, in dollars per watt of power generated can be expressed as afunction of four major variables as follows:

C ¼ fðX1;X2;X3;X4Þ ð1:1Þ

where X1 ¼ cost per kg of the power system mass launched,

X2 ¼ cost per liter of the power system volume launched,

X3 ¼ cost per watt of the power system generation capacity, and

X4 ¼ cost of altitude control related with power system components.

1.2 Satellite Systems

The typical communications satellite bus consists of the following systems.

1.2.1 Communications and Data Handling

The communications and data handling system performs three indepen-dent functions:

It receives and demodulates information transmitted to the satellite fromthe ground station via command links.

It transmits data, both recorded (remote) and real-time, from the satelliteto the ground station via data links.

It transmits bus equipment and other telemetry data from the satellite tothe ground station via telemetry links.

1.2.2 Attitude and Orbit Control System

The attitude and orbit control system determines the exact position of thesatellite with respect to the local vertical, thus providing precise pointing ofthe communications antennas, imaging sensors, and any other missionsensors. The attitude control function accepts error signals from which thebasic or the precision attitude determination function provides 3-axisattitude control using three reaction wheels. The basic attitude deter-mination function obtains the pitch and roll data from the Earth sensor andyaw data from the gyroscopes with updates from the sun sensor toprovide a basic 3-axis pointing within 0.1� accuracy. The precise attitude


Satellite Overview 5

determination function uses three gyroscopes with updates from a starsensor to provide a 3-axis pointing within 0.01� accuracy.

1.2.3 Tracking, Telemetry, and Command System

The tracking, telemetry, and command (TT&C) system accepts analog,discrete, and digital data from various systems of the spacecraft, andprocesses them into a continuous data stream for direct transmission to theground or for on-board storage for later transmission. These data areanalyzed and evaluated on the ground to determine the spacecraft state ofhealth and the operational configuration. The command and controlfunction is all digital. It provides ascent guidance from the boosterseparation through transfer orbit, and controls the satellite attitude andoperating modes on orbit. The control is exercised in accordance withcommands and data received from the ground station, supplemented bysignals and data supplied by other systems of the satellite. This system alsoprovides the error correction coding, a key function of the system.

1.2.4 Electrical Power System

The electrical power system generates, stores, conditions, controls, anddistributes power within the specified voltage band to all bus and payloadequipment. The protection of the power system components in case of allcredible faults is also included. The basic components of the power systemare the solar array, solar array drive, battery, battery charge and dischargeregulators, bus voltage regulator, load switching, fuses, and the distributionharness. The harness consists of conducting wires and connectors thatconnect various components together.

In the Earth orbiting satellite, the solar array is rotated once per orbit bythe solar array drive to track the sun at or near normal angle. The rotation israte-servo controlled. The body information and position errors arecomputed by the satellite computer to derive rate control signals. Thenominal rate of rotation is 0.06�per s. Using slip rings and carbon brushes isone way of providing the rotary joint between the rotating array and thesatellite body. The control signals for required rotation rate come from theTT&C system, which also selects the rotation direction.

1.2.5 Thermal Control System

The thermal control system maintains the temperature of all equipmentwithin the specified limits during normal and abnormal operations. Itprovides both passive and active cooling as needed. Typical components ofthis system are fixed radiators, louvers, multi-layer blankets, coatings,tapes, heaters, thermostats, temperature sensors, and control electronics.Thermistors are widely used as temperature sensors. The components are



sized for the average electrical power dissipation, the external heat inputfrom the sun, the Earth’s reflected sunlight (albedo), and the longwavelength (infrared) heat radiated from the Earth.

1.2.6 Structure and Mechanisms System

The structure and mechanisms system primarily provides a frame formounting and linking various mechanical components together.Mechanisms for deploying the booms, the solar array and other compo-nents after orbit injection are often included in this system. The deploymentpower circuits and devices are well shielded for electromagnetic inter-ference (EMI) to prevent unspecified deployment. The deployment motionis derived by spring-loaded rotary mechanisms. A rotary vane damperfilled with viscous silicone fluid governs the deployment rate. The solararray deployment generally involves cable cutting and/or rod cutting.Structures are often made of magnesium and aluminum. Composites arealso common. Some steel and occasionally beryllium are used whereneeded.

1.2.7 Propulsion System

The propulsion system provides propulsion torque for 3-axis control duringascent and for maintaining the satellite momentum below a specifiedmaximum level during the mission. It often uses a mixed system of high-pressure regulated helium or nitrogen and liquid hydrazine. The gaseoushelium or nitrogen and hydrazine are carried in high-pressure cylindricaltitanium alloy tanks. The propulsion systems also provides the translationaldelta-V for orbit changes and orbit trims

Figure 1.2 depicts the anatomy of the Global Positioning Satellite (GPS), amid-Earth orbit communications satellite fleet of the U.S. Air Force. Thepayload antenna is facing the Earth. The solar array panels are orientednorth–south on two booms running through the solar array drive. Mountedinside the north and south panels of the spacecraft body are the batteries,power regulators, and the control electronic boxes (not shown).

1.3 Earth Orbit Classification

The Earth is a sphere with a slight flatness at the top. Its diameter is12,713.54 km at the poles and 12,756.32 km at the equator, the differencebeing 42.78 km. Air surrounds the Earth and extends up to 160 km abovethe surface, beyond which the atmosphere gradually fades into space. Thesatellites orbiting the Earth are classified into several groups with theirtypical parameters listed in Table 1.1. The orbits are often described by thefollowing abbreviations:



GEO: geosynchronous Earth orbit, circular at 35,786-km altitude

MEO: mid Earth orbit, circular at 2000 to 20,000-km altitude

LEO: low Earth orbit, generally circular at 200 to 2000-km altitude

HEO: highly elliptical orbit, such as Molniya

A communications satellite provides interconnectivity over a large areafor point-to-point, point-to-multi-point, and broadcast communications. Itcan serve fixed as well as mobile terminals anywhere — on land, on the sea,in air or in space. A typical satellite transponder receives an uplink signalfrom a ground station, frequency converts, amplifies and retransmits it tothe ground.


FIGURE 1.2 Configuration and evolution of GPS, mid-Earth orbit navigation satellites of theU.S. Air Force.


In the case of LEO and MEO, the orbit parameters are chosen to avoid theradiation belts that surround the Earth at altitudes of 1.3 to 1.7 and 3.1 to 4.1Earth radii. A typical LEO satellite has an altitude of 500 to 1500 km, an orbitperiod of 1.5 to 2 h, and is visible to a given Earth station for only a fewminutes in every orbit period. A typical MEO satellite is between 5000 and12000 km altitude with orbit period of several hours. In a highly ellipticalinclined orbit, it can see the polar regions for a large fraction of its orbitperiod.

A GEO satellite moving west to east at an altitude of 35,786 km (22,237miles) results in a nominal orbit period of 24 h, and remains stationary withrespect to the Earth. Three such satellites spaced 120� apart in the equatorialplane can provide continuous coverage of the globe except near the poles.The launch vehicle booster and its upper stages deliver the satellite in thetransfer orbit, which is an elliptical orbit with the Earth at one of its foci andthe apogee at the geosynchronous orbit. An apogee kick motor is then firedto circularize the orbit at the geosynchronous height. The primary featuresof various orbits are described below.

1.3.1 Geostationary Orbit

The geostationary orbit is a very special geosynchronous orbit, and, in fact,is unique. It is exactly circular with a radius of 42,164 km in the Earth’sequatorial plane with zero degree inclination and zero eccentricity. Asatellite placed in this orbit is synchronized with the Earth’s rotation rateand direction (eastward). It does not move with respect to the Earth, andsees the same object on the Earth steadily. The orbit period is the same asthat of the Earth’s rotation, i.e., 23 h 56m 4.09 s. As a result, the satellite’sbeam-to-Earth and the ground station’s beam-to-satellite are steady in


Table 1.1 Classification of the Earth’s orbits

Orbit type

Apogee

(km)aPerigee

(km)b EccentricitycInclinationd

(degrees) Periode

Geostationary 35,786 35,786 0 0 1 siderealday

Geosynchronous 35,786 35,786 Near 0 0-90� 1 siderealday

EllipticalMolniya

39,400 1000 High 62.9� 1=2 siderealday

Low Earth Various Various 0 to high 0 to 90� >90 min

aClosest distance from the Earth surface.bFarthest distance from the Earth surface.cRatio of difference to sum of apogee and perigee radii.dAngle between orbit plane and equatorial plane.eOne sidereal day is 23h, 56 min, 4.09 s.


position. This simplifies the design and operating requirements of both thesatellite and the ground station. However, it takes more fuel to reach andmaintain the geostationary orbit than any other orbit around the Earth atthat altitude. Numerous satellites already placed there make it difficult toget a desirable location in this orbit that would avoid radio frequencyinterference from neighboring satellites. The Tracking and Data RelaySatellite (TDRS) of the U.S. Department of Defense is an example of ageostationary satellite. A satellite placed in this orbit tends to drift awayfrom its assigned station. Hence, a periodic station-keeping operation isrequired.

The time in space is kept in sidereal time, which measures the rotation ofthe Earth in relation to a fixed star. Solar time is used on Earth to measurethe Earth’s rotation in relation to the sun. The same star is not in the sameplace at the same solar time, but is at the same place at the same siderealtime from day to day. A sidereal day consisting of 24 sidereal hours is thetime the Earth takes to rotate once on its axis past an imaginary line fromthe Earth’s center to any star. Thus, the sidereal time is measured from apoint in the sky called the vernal equinox, although no bright start marksthis point.

The geostationary orbit period is exactly 1 sidereal day. It is slightlyshorter than the mean solar day of 24 h because of the sun’s apparentmotion resulting from the Earth’s rotation around the sun, which is 360� in365.24 days, i.e., 0.9856� per day. By the time the Earth has rotated once inrelation to a distant star, it has moved westward along its orbit, as depictedin Figure 1.3. The sun is then 0.9856� east of its position at the start of theEarth’s rotation. The Earth needs additional time to rotate eastward to comeback in line with the sun. The Earth must thus rotate a total of 360.9856� in 1mean solar day so that the meridian will align itself with the sun from onenoon to the next in exactly 24 h (86,400 s). The time for the Earth to rotate0.9856� past one rotation is 86,400/(0.9856/360.9856) ¼ 235.91 s. The side-real period of rotation is therefore 86,400 � 235:91 ¼ 86,164.09 s, or 23 h,56m, 4.09 s, which is shorter by 3m and 55.91 s than the mean solar day.

1.3.2 Geosynchronous Orbit

Most commercial communications satellites operate in numerous geosyn-chronous orbits. The geostationary orbit described above is one uniqueorbit in the entire class of the geosynchronous orbit. The distinctionbetween the two is minor and fine, but is important. The geosynchronousorbit is similar to the geostationary orbit, except that its inclination can beany value between 0 and 90�. Inclinations other than 0� requires groundstation tracking antennas. Sometimes, that may not be a disadvantagebecause the ground stations require tracking antennas for other reasons.Mobil platforms, such as planes and ships, also require tracking antennas.The geosynchronous orbit is chosen for fuel-efficient launch and orbit



maintenance. If a satellite is placed in i� inclination orbit, the point directlybelow the satellite oscillates between i� north and i� south every day, andappears to drift to the north and south in a figure eight as shown inFigure 1.4. The angular height of this figure is just the magnitude of ��i�/180 radians. This motion away from the equator induces a longitudinaldifference between the ideal and actual satellite points. The difference


FIGURE 1.3 Sidereal day and mean solar day for Earth.

FIGURE 1.4 Satellite motion in geosynchronous orbit with i� inclination.


appears as the satellite moves towards the equator. The maximumlongitudinal deviation is (�i�/180)2/4. The variation in distance is�(�i�/180)Ro, where Ro is the orbit radius. The ground stations must bealigned with the north–south (N–S) motion of the satellite in an inclinedorbit.

When the sun and the moon are not in the equatorial plane, the N–Scomponents of their combined gravity force change the orbit inclination ofthe geostationary and geosynchronous satellites at a rate about 0.85� peryear. Station-keeping maneuvers are required to compensate for such orbitdrift. This consumes some fuel, which must be carried on board to last forthe mission duration. The use of arc jets minimizes the fuel requirement byincreasing the propulsion efficiency. The arc jets and station-keeping fuelrequirement can be eliminated if 0.85� drift per year is acceptable, or can beaccommodated in the mission design, as in TDRS. In exchange, the satellitewould require several degrees of yaw maneuvering on daily basis to remainpointed at the ground station.

1.3.3 Highly Elliptical Orbit

Among highly elliptical orbits, Molniya is one specific orbit named after aRussian communications satellite with a 1000-km perigee and a 39,400-kmapogee. Having the period of 1=2 sidereal day in this orbit, the satellite comesto the same longitude on every other apogee. The advantage of the Molniyaorbit is good coverage of the entire northern hemisphere. The disadvantageis no coverage over the southern hemisphere. Moreover, it requires moresatellites and needs two tracking antennas at each ground station. GPS,although not in a Molniya orbit, has an orbit period of 1=2 sidereal daybecause of its selected MEO location in a circular orbit. Some US militarysatellites have used the elliptical Molniya orbit with 63.4� inclination tocover Russia for 10 h out of a 12-h period.

1.3.4 Low Earth Orbit

This is approximately a circular orbit at low altitude. The InternationalSpace Station (ISS) and NASA’s space shuttle orbiter operate in low Earthorbit. Most communications satellites operate in GEO, but some newerconstellations are planned and/or placed in LEO between 500 and 2000-kmaltitudes and 30 to 90� (polar) inclinations. Being closer to the Earth, smallerand simpler satellites can be used in this orbit. Also, two-way communica-tions introduces a time delay of only 0.02 s versus 0.5 s in geosynchronousorbits. On the negative side, LEO communications satellites require trackingof omni-directional antennas, and many birds are needed for widecoverage.



1.3.5 Sunsynchronous Orbit

A satellite in this orbit maintains a constant angle between the sun’sdirection and the orbit plane, and always sees the sun at the same angle. It isused for special applications.

1.4 Orbit Mechanics

Kepler’s three laws of planetary motion, based on Newton’s laws, apply to asatellite orbiting a planet. They are as follows:

First law: The satellite orbit is an ellipse with the planet at one focal point.

Second law: The line joining the planet and the satellite sweeps equalareas in equal times. If the time intervals it1 and it2 in Figure 1.5are equal, then the swept areas A1 and A2 are also equal.

Third law: The square of the orbit period is proportional to the cube ofthe semi-major axis,

i:e:; T2o ¼

4�2a3

�ð1:2Þ

where a is the semimajor axis of the orbit, and � is the gravity constant of theplanet. For the Earth, � is 3.986� 1014m3/s2 or 3.986� 105 km3/s2.


FIGURE 1.5 Kepler’s second law of planetary motion.


For circular orbits, the third law gives the orbit period To in terms of theorbit radius Ro,

To ¼2�R1:5

offiffiffiffiffiffiffiffiffiffiffiffiffiffiffi398600

p s; or To ¼ 2:7644� 10�6R1:5o h ð1:3Þ

For the orbit period to be 1 sidereal day of 86,164.09 s, the orbit radius mustbe 42,164 km. Deducting the mean radius of the Earth surface 6378 km, weget the geosynchronous satellite altitude of 35,786 km above the Earthsurface. This altitude is about six times the Earth’s radius.

The satellite velocity in circular orbit is given by

v ¼2�Ro

Toð1:4Þ

which is 3.075 km/s in GEO orbit. In comparison, the Earth travels in itsorbit around the sun at speed of 30 km/s, about ten times faster.

1.5 Satellite Stabilization Methods

The satellite stabilization in orbit is achieved by either an active or passivemethod described below.

1.5.1 Gravity Gradient Method

Gravity gradient is a passive method, sometimes used in small LEOsatellites. The difference in the attractive force of gravity on the parts closestand farthest from the Earth creates a moment that maintains the satellitealigned with the local vertical. This method requires long booms in order tohave adequate moment, and it does not work in geosynchronous orbitsbecause of near-zero gravity there.

1.5.2 Magnetic Damping

Magnetic damping is another passive method. It uses long booms withmagnets that interact with the Earth’s magnetic dipole field to produce thestabilization moment.

1.5.3 Spin Stabilization

Spin stabilization is an active method that has been commonly used in mostsatellites until recently. It is still used for small satellites. The spinningbicycle wheel and the spinning top are stable above certain minimum spinrate. The satellite stability can be similarly maintained by storing angular



momentum in a spinning body on board the satellite. For spin stabilization,the moment of inertia about the desired spin axis must be greater than thatabout any orthogonal axis. Small satellites are spun in entirety. Largesatellites using complex antennas are split in two sections, the despunantenna section and a spinning cylindrical body. The solar cells aremounted on the spinning body as shown in Figure 1.6. A typical spinrate is 30 to 60 revolutions per minute. Heavier satellites require higher spinrates for stability. Spin-stabilized satellites are also called dual-spin orgyrostat satellites.

1.5.4 Three-axis Stabilization

Three-axis or body stabilization is another active method commonly used inmodern satellites. In this method, the satellite uses several spinningmomentum wheels located inside the body as shown in Figure 1.7. Theorientation is automatically maintained by servo-control that adds orsubtracts momentum from the spinning momentum wheels. Thrusters areused periodically to maintain the orientation as necessary. The satelliteusually has a box-shaped body with flat solar panels (wings) extendingfrom the north and south faces. Table 1.2 compares key features of the spin-stabilized and 3-axis stabilized satellites. The 3-axis stabilization generallyresults in lower dry mass for satellites with solar array power exceeding afew hundred watts. For this reason, it is widely used in modern large high-power satellites.

All spacecraft, once disturbed from their stable position, may oscillate fora long time in characteristic modes which may be close to being unstable. Itis important that these modes are identified and suitable damping is


FIGURE 1.6 Spin-stabilized gyrostat satellite.


introduced by the attitude and/or orbit control system to restore the vehicleto the stable position. Fuel movement in the tanks may also add in to theoscillations, but it is normally controlled by baffles. There are five pointswithin the reference frame in space at which a stationary body will be inequilibrium. All these points are in the plane in which the dominant massesrotate. They are referred to as the Lagrangian or Libration points, and are ofpotential use for the spacecraft in the Earth–Moon type systems.

1.6 Launch and Transfer Orbits

The communications satellite is placed in a geosynchronous orbit in twomain steps. The launch vehicle places the satellite first into a low Earth


FIGURE 1.7 Three-axis body-stabilized satellite with definition of attitude axes.

Table 1.2 Key features of spin-stabilized and 3-axis stabilized satellites

Spin-stabilized 3-axis stabilized

Inherently stiff due to rotational inertia Bias or zero momentum maintains thestability

Simple mechanical structure Complex attitude controlOnly 1/3rd of the solar array generate power atany time

Full solar array generates power all thetime

Power limited by body size that fits the launchvehicle

Can have high power by adding solarpanels

Less flexibility in design Great flexibility in designSuitable for small satellites Suitable for large satellites

circular orbit, called the parking orbit. Then, the so-called Hohmanntransfer takes the satellite to the final orbit using minimum fuel. The firstvelocity increment changes the low circular orbit into a highly ellipticaltransfer orbit with perigee that of the final circular orbit. The secondvelocity increment at the apogee of transfer orbit places the satellite in thefinal circular orbit. When the perigee and the apogee kick motors are fired,some sort of stabilization is needed because the thrust would tumble thesatellite and cause incorrect orbit injection.

The fully deployed satellite, which is 3-axis stabilized in the operationalorbit, can use spin stabilization in the transfer orbit when the solar panelsare stowed into a box shaped body. The satellite is despun by applyingreaction wheel torque to bring to a non-spinning state at the end of transferorbit. The de-spinning operation takes about 10min. Until the solar array isfully deployed, the sunlit panel radiates heat from the front face only, asopposed to both the front and back faces after the deployment. Moreover,the exposed panel is oriented normal to the sun for maximizing the powergeneration except during maneuvering. To keep the temperature of the sunside panel from rising above the tolerance limit, the satellite is spun at a lowrate, such as 1/10th to 1 revolution per minute. Spinning at such a slowbarbecue rate is merely for thermal reasons even when the spinning is notrequired for stability. The spin rate is gyro controlled. One can deploy thearray in the transfer orbit, but it adds a mechanism and structuralcomplexity, resulting in added mass, low reliability, and difficult transferorbit maneuvers.

1.7 Operational Orbit

As the satellite revolves around the Earth in operational orbit at inclination� measured from the equatorial plane, it changes its orientation with respectto the sun with seasons as depicted in Figure 1.8. The north of the Earthrotation axis is inclined 23.45� towards the sun on the summer solstice day,and 23.45� away on the winter solstice day. On the autumnal and vernalequinox days, the axis inclination is zero, resulting in equal day and night.

1.8 Eclipse due to Earth

Since the ecliptic and equatorial planes are inclined to each other by 23.45�,the angle of incidence of the sunlight on the solar arrays varies from 66.55 to90�. The corresponding incident solar flux varies from 91.75% on a solsticeday to 100% on an equinox day. However, the satellite on equinox daysencounters longest eclipse once per day when the Earth blocks the sunlightfrom illuminating the satellite.

When the satellite is in shadow of the Earth, the solar array powergeneration ceases and its temperature drops sharply. Predicting the eclipse



duration is, therefore, important for the spacecraft power system design.For the geosynchronous satellite, the longest eclipse occurs on the vernaland autumnal equinoxes when the sun is in the equatorial plane as shownin Figure 1.9. The duration for which the entire sun is blocked is called theumbra (total eclipse marked by dotted arc). The total arc when the sun isfully or partially blocked is called the penumbra (arc a–b). It is proportionalto the mean solar day accounting for the Earth’s orbital motion during theeclipse. The umbra duration varies with the seasons, the longest being69.4min occurring around March 21 and September 21. From thegeometrical considerations of the geosynchronous orbit in Figure 1.9, thepenumbra duration is 73.7min (1.228 h) and the umbra is 4.3min shorterthan the penumbra. Since the solar array output voltage and current duringthis 4.3min would not meet the requirement for the power systemoperation, penumbra is taken as the eclipse duration for the power systemdesign.

As the sun moves above or below the equator after an equinox, theeclipse duration becomes shorter and shorter, and finally becomes zerowhen the inclination of the sun becomes high enough (Figure 1.10). Thenumber of days the geosynchronous satellite sees an eclipse, and the eclipse



FIGURE 1.8 Satellite in Earth’s orbit with seasonal variations.

duration on that day, are shown in Figure 1.11. The eclipse onset time on aparticular day is of interest to the satellite design engineer, because itdetermines the required services and the battery requirement onboard thesatellite.

In near-equatorial, circular, low Earth orbits, eclipses of approximatelyequal duration occur once every orbit period. The eclipse duration is



FIGURE 1.9 Eclipse in geosynchronous orbit — umbra and penumbra.

FIGURE 1.10 GEO eclipse, once per orbit in spring and autumn seasons only.

dependent on the orbit altitude, inclination, and the sunlight incidenceangle on the orbit plane (Figure 1.12). It can vary by a factor of two in LEO.

For a circular orbit, the eclipse duration (in h) is given by

Te ¼1

2þ

1

�sin�1

1�REarth

Rorbit

� �2 !1=2

cos�

8>>>>><>>>>>:

9>>>>>=>>>>>;

ð1:5Þ

where � ¼ angle of the sunlight incidence on the orbit plane, i.e., the anglebetween the Sun–Earth line and the local normal of the orbit plane.

The � angle varies seasonally between �(i þ �), where i ¼ orbit inclina-tion with respect to the equator and � ¼ angle between the sun line and theecliptic plane (23.45�). As � increases, the eclipse duration decrease, whichimproves the load capability of the electrical power system. At certain valueof high �, no eclipse occurs. There are polar and near-polar low Earth orbits



FIGURE 1.11 GEO eclipse duration longest on vernal and autumnal equinox days.

FIGURE 1.12 Eclipse in near-equatorial LEO, once per orbit in all seasons.

that never have an eclipse of the sun. On the other hand, the longest eclipseoccurs at � ¼ 0.

1.8.1 Example

For a satellite in a 6343-mile radius and 20� inclination orbit, the aboveequation gives Te ¼ 0.63 h or 38min long eclipse (note that the argument ofthe sin�1 must be in radians).

For circular orbits, the eclipse duration and the number of eclipses peryear are plotted in Figures 1.13 and 1.14, respectively. The ratio of themaximum eclipse to minimum sunlight duration is an indicator of a



FIGURE 1.13 Eclipse duration and orbit period vs circular orbit altitude.

FIGURE 1.14 Maximum number of eclipse per year vs orbit altitude.

challenge posed to the power system design engineer. The greater the ratio,the heavier the battery requirement to power the load during an eclipse. Italso requires a larger solar array to capture the energy required duringshorter periods of sunlight, and to divert a higher fraction of it to charge thebattery while simultaneously supplying full load to the payload. Such ademand is greater on a low Earth orbit satellite, as seen in Figures 1.15 and1.16.

1.9 Eclipse due to Moon

In addition to eclipses due to the Earth’s shadow on the satellite, the mooncan also obstruct the sun as seen by the satellite. Such eclipses are irregularin occurrence, varying from 0 to 4 per year, with an average of two. Usuallythey are spaced far apart, but in the worst case two eclipses can occur in24 h. The duration can vary from several minutes to more than 2 h, with an



FIGURE 1.15 Minimum sun time and maximum eclipse duration in circular Earth orbits.

FIGURE 1.16 Ratio of maximum eclipse to minimum sun time in circular Earth orbits.

average of 40min. The satellite may experience additional battery depth ofdischarge and fall in temperature in the case where an eclipse due to themoon occurs adjacent to an eclipse due to the Earth. In most missions,however, eclipses due to the moon impose no additional design require-ment, but that has to be ascertained. Otherwise, shedding a noncritical loadtemporarily during the worst moon eclipse often circumvents the situation.

1.10 Solar Flux

The energy received from the sun in space varies with the distance squared.The Earth’s orbit around the sun is approximately circular with a slighteccentricity of 0.01672. The distance, therefore, varies within �0.01672 timesthe average distance between the sun and the Earth, which is 149.6million km, defined as one astronomical unit (AU) of distance. Thus, thesolar flux varies over (1 � 0.01672)2 or 1 � 0.034 of the yearly average.Within these small variations, the Earth is closest to the sun around January2 (perihelion), and farthest around July 2 (aphelion). For many years, theaverage solar radiation in the Earth orbit has been taken as 1358 � 5W/m2

on the surface normal to the sun. Measurements reported by Frohlich1 showa higher average value of 1377 � 5W/m2, which is now generally accepted.However, the conservative number of 1358 � 5 ¼ 1353W/m2 continues inwide use.

Table 1.3 shows the ratio of the seasonal flux over the yearly average fluxon the equinox and solstice days. It also shows the seasonal variations in theorbit inclination. Satellites using solar arrays with single-axis trackinggimbals generate less power in accordance with the cosine of the sun angle.The last column gives the combined effect of the cosine and the fluxvariation due to eccentricity on the solar array output power. The output onthe summer solstice day is 11% lower than that on the vernal equinox day.



Table 1.3 Variation of solar flux and angle of incidence with the seasons

Day of the year

Seasonal flux/

yearly average

Angle of incidence

with single-axis

tracking gimbals

Flux on array/yearly

average on sun-

tracking surface

Vernal equinox,March 21

1.001 0� 1.001

Summer solstice,June 22

0.967 23.45� 0.887

Autumn equinox,September 21

0.995 0� 0.995

Winter solstice,December 22

1.034 23.45� 0.949

The seasonal variations in solar parameters in geosynchronous orbit arecollectively depicted in Figure 1.17.

1.11 Beta Angle

The beta angle, �, is defined as the angle between the Earth–Sun line andthe orbit plane when the spacecraft is closets to the sun (orbit noon). Itvaries seasonally between 0� and (i þ io)

�, where i ¼ orbit inclination, andio ¼ angle between equator and ecliptic plane, which is 23.45�.

The value of � ¼ 90� results in the greatest solar flux on the satellite body,and � ¼ 0� gives zero flux. In most satellites with the array always pointedto the sun by the solar array drive motor, the � angle has an insignificanteffect on the generation of electric power. However, the thermal controlsystem is impacted by the � angle. Low � may require additional heaters,while high � may require additional cooling. The � angle impacts the solararray temperature, which in turn has a small secondary effect on the powergeneration. The most significant effect of the � angle on the power systemdesign comes from the eclipse duration as given by Equation 1.5. As �



FIGURE 1.17 Seasonal variations in solar parameters over 1 year in geosynchronous orbit.

increases, the eclipse duration decreases, which consequently requires asmaller battery and less charging power during sunlight.

The � angle is not to be confused with the sun angle, �, often used todefine the sunlight incidence angle on the solar array, which could becanted to catch the sun normally in case � is not 90�. The sun angle isdefined as the angle between the solar array plane and the sun-pointingvector. The power generation is proportional to cos �, so � of 90� results inthe maximum power generation, and 0� gives zero power.

The power system engineer starts with the orbit parameters specified bythe customer, which primarily set the orbit period, eclipse duration and the� angle. These parameters in turn have the greatest impact on the powersystem design.

1.12 Spacecraft Mass

Hundreds of small spin-stabilized and large 3-axis stabilized satellites havebeen built and deployed in various orbits. The spacecraft dry mass and thecorresponding electrical power requirements for GEO satellites have beensteadily rising as seen in Figure 1.18. The new technological developmentsin solar cells and evolutionary design improvements have jointly con-tributed to the higher solar array output power per kilogram for moderncommunications satellites. For large 3-axis body stabilized GEO satelliteswith total eclipse load of 5 to 10 kW, the electrical power system (EPS) massis about 30% of the total spacecraft dry mass, the payload mass is also about30%, and the remaining 40% is in the structure and all other spacecraftsystems.

The average mass of 16 commercial satellites contracted in 2002 wasabout 3600 kg each, which is considered the mass of medium size satellites.On the large side, Thuraya for the United Arab Emirates will have lift offmass of 5200 kg.



FIGURE 1.18 Power vs dry mass of GEO communications satellites.

Reference

1. Frohlich, R.C., Contemporary Measures of the Solar Constant: The Solar Outputand its Variations, Colorado Associated University Press, Boulder, CO,1977, pp. 93–109.



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Spacecraft Power Systems: Chapter 1. Satellite Overview