Satellite Overview

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1.1 Introduction

A satellite consists of various systems designed to meet the mission specific requirements. All but the simplest satellites require a common set of systems shown by the solid lines in Figure 1.1. Complex satellites require additional systems shown by the dotted lines. The systems are classified into two groups, the payload and the bus. The payload consists of the communications equipment in commercial satellites or science instruments in research satellites. The bus consists of all remaining equipment grouped into several functional systems that support the payload. The power system is one of the bus systems that consist of the solar array, battery, power electronics, distribution harness, and controls. Other essential bus systems are the communications and data handling system to receive commands and return information, telemetry sensors to gage the satellite state, and a

Transmit Receive antenna antenna

Software

Attitude mechanisms

Communications^^) V. mechanisms .

Communications^^) V. mechanisms .

FIGURE 1.1 Satellite systems.

C Power regulation and ) energy storage J

C Common systems in all satellites C.~"--> Additional systems in complex designs

FIGURE 1.1 Satellite systems.

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

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

where X1 = cost per kg of the power system mass launched, X2 = cost per liter of the power system volume launched, X3 = cost per watt of the power system generation capacity, and X4 = 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 independent functions:

It receives and demodulates information transmitted to the satellite from the ground station via command links. It transmits data, both recorded (remote) and real-time, from the satellite to the ground station via data links. It transmits bus equipment and other telemetry data from the satellite to the ground station via telemetry links.

1.2.2 Attitude and Orbit Control System

The attitude and orbit control system determines the exact position of the satellite with respect to the local vertical, thus providing precise pointing of the communications antennas, imaging sensors, and any other mission sensors. The attitude control function accepts error signals from which the basic or the precision attitude determination function provides 3-axis attitude control using three reaction wheels. The basic attitude determination function obtains the pitch and roll data from the Earth sensor and yaw data from the gyroscopes with updates from the sun sensor to provide a basic 3-axis pointing within 0.1° accuracy. The precise attitude determination function uses three gyroscopes with updates from a star sensor 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, and processes them into a continuous data stream for direct transmission to the ground or for on-board storage for later transmission. These data are analyzed and evaluated on the ground to determine the spacecraft state of health and the operational configuration. The command and control function is all digital. It provides ascent guidance from the booster separation through transfer orbit, and controls the satellite attitude and operating modes on orbit. The control is exercised in accordance with commands and data received from the ground station, supplemented by signals and data supplied by other systems of the satellite. This system also provides the error correction coding, a key function of the system.

1.2.4 Electrical Power System

The electrical power system generates, stores, conditions, controls, and distributes power within the specified voltage band to all bus and payload equipment. The protection of the power system components in case of all credible faults is also included. The basic components of the power system are the solar array, solar array drive, battery, battery charge and discharge regulators, bus voltage regulator, load switching, fuses, and the distribution harness. The harness consists of conducting wires and connectors that connect various components together.

In the Earth orbiting satellite, the solar array is rotated once per orbit by the solar array drive to track the sun at or near normal angle. The rotation is rate-servo controlled. The body information and position errors are computed by the satellite computer to derive rate control signals. The nominal rate of rotation is 0.06°pers. Using slip rings and carbon brushes is one way of providing the rotary joint between the rotating array and the satellite body. The control signals for required rotation rate come from the TT&C system, which also selects the rotation direction.

1.2.5 Thermal Control System

The thermal control system maintains the temperature of all equipment within the specified limits during normal and abnormal operations. It provides both passive and active cooling as needed. Typical components of this 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 input from the sun, the Earth's reflected sunlight (albedo), and the long wavelength (infrared) heat radiated from the Earth.

1.2.6 Structure and Mechanisms System

The structure and mechanisms system primarily provides a frame for mounting and linking various mechanical components together. Mechanisms for deploying the booms, the solar array and other components after orbit injection are often included in this system. The deployment power circuits and devices are well shielded for electromagnetic interference (EMI) to prevent unspecified deployment. The deployment motion is derived by spring-loaded rotary mechanisms. A rotary vane damper filled with viscous silicone fluid governs the deployment rate. The solar array deployment generally involves cable cutting and/or rod cutting. Structures are often made of magnesium and aluminum. Composites are also common. Some steel and occasionally beryllium are used where needed.

1.2.7 Propulsion System

The propulsion system provides propulsion torque for 3-axis control during ascent and for maintaining the satellite momentum below a specified maximum level during the mission. It often uses a mixed system of high-pressure regulated helium or nitrogen and liquid hydrazine. The gaseous helium or nitrogen and hydrazine are carried in high-pressure cylindrical titanium alloy tanks. The propulsion systems also provides the translational delta-V for orbit changes and orbit trims

Figure 1.2 depicts the anatomy of the Global Positioning Satellite (GPS), a mid-Earth orbit communications satellite fleet of the U.S. Air Force. The payload antenna is facing the Earth. The solar array panels are oriented north-south on two booms running through the solar array drive. Mounted inside 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 is 12,713.54 km at the poles and 12,756.32 km at the equator, the difference being 42.78 km. Air surrounds the Earth and extends up to 160 km above the surface, beyond which the atmosphere gradually fades into space. The satellites orbiting the Earth are classified into several groups with their typical parameters listed in Table 1.1. The orbits are often described by the following abbreviations:

Gps Satellite Array
FIGURE 1.2 Configuration and evolution of GPS, mid-Earth orbit navigation satellites of the U.S. Air Force.

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 area for point-to-point, point-to-multi-point, and broadcast communications. It can 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 signal from a ground station, frequency converts, amplifies and retransmits it to the ground.

Table 1.1 Classification of the Earth's orbits

Orbit type

(km)b

Eccentricity0

Inclinationd (degrees)

Periode

Geostationary

35,786

35,786

0

0

1 sidereal

day

Geosynchronous

35,786

35,786

Near 0

0-90°

1 sidereal

day

Elliptical

39,400

1000

High

62.9°

1k sidereal

Molniya

day

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.

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.

In the case of LEO and MEO, the orbit parameters are chosen to avoid the radiation belts that surround the Earth at altitudes of 1.3 to 1.7 and 3.1 to 4.1 Earth radii. A typical LEO satellite has an altitude of 500 to 1500 km, an orbit period of 1.5 to 2h, and is visible to a given Earth station for only a few minutes in every orbit period. A typical MEO satellite is between 5000 and 12000 km altitude with orbit period of several hours. In a highly elliptical inclined orbit, it can see the polar regions for a large fraction of its orbit period.

A GEO satellite moving west to east at an altitude of 35,786 km (22,237 miles) results in a nominal orbit period of 24 h, and remains stationary with respect to the Earth. Three such satellites spaced 120° apart in the equatorial plane can provide continuous coverage of the globe except near the poles. The launch vehicle booster and its upper stages deliver the satellite in the transfer orbit, which is an elliptical orbit with the Earth at one of its foci and the apogee at the geosynchronous orbit. An apogee kick motor is then fired to circularize the orbit at the geosynchronous height. The primary features of 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's equatorial plane with zero degree inclination and zero eccentricity. A satellite placed in this orbit is synchronized with the Earth's rotation rate and direction (eastward). It does not move with respect to the Earth, and sees the same object on the Earth steadily. The orbit period is the same as that of the Earth's rotation, i.e., 23 h 56 m 4.09 s. As a result, the satellite's beam-to-Earth and the ground station's beam-to-satellite are steady in position. This simplifies the design and operating requirements of both the satellite and the ground station. However, it takes more fuel to reach and maintain the geostationary orbit than any other orbit around the Earth at that altitude. Numerous satellites already placed there make it difficult to get a desirable location in this orbit that would avoid radio frequency interference from neighboring satellites. The Tracking and Data Relay Satellite (TDRS) of the U.S. Department of Defense is an example of a geostationary satellite. A satellite placed in this orbit tends to drift away from its assigned station. Hence, a periodic station-keeping operation is required.

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

The geostationary orbit period is exactly 1 sidereal day. It is slightly shorter than the mean solar day of 24 h because of the sun's apparent motion resulting from the Earth's rotation around the sun, which is 360° in 365.24 days, i.e., 0.9856° per day. By the time the Earth has rotated once in relation to a distant star, it has moved westward along its orbit, as depicted in Figure 1.3. The sun is then 0.9856° east of its position at the start of the Earth's rotation. The Earth needs additional time to rotate eastward to come back in line with the sun. The Earth must thus rotate a total of 360.9856° in 1 mean solar day so that the meridian will align itself with the sun from one noon to the next in exactly 24 h (86,400 s). The time for the Earth to rotate 0.9856° past one rotation is 86,400/(0.9856/360.9856) = 235.91 s. The sidereal period of rotation is therefore 86,400 - 235.91 = 86,164.09 s, or 23 h, 56 m, 4.09 s, which is shorter by 3 m and 55.91 s than the mean solar day.

1.3.2 Geosynchronous Orbit

Most commercial communications satellites operate in numerous geosynchronous orbits. The geostationary orbit described above is one unique orbit in the entire class of the geosynchronous orbit. The distinction between the two is minor and fine, but is important. The geosynchronous orbit is similar to the geostationary orbit, except that its inclination can be any value between 0 and 90°. Inclinations other than 0° requires ground station tracking antennas. Sometimes, that may not be a disadvantage because 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

Pics Mean Solar Day
FIGURE 1.3 Sidereal day and mean solar day for Earth.

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

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

appears as the satellite moves towards the equator. The maximum longitudinal deviation is (ot'°/180)2/4. The variation in distance is ±(rn'°/180)Ro, where Ro is the orbit radius. The ground stations must be aligned with the north-south (N-S) motion of the satellite in an inclined orbit.

When the sun and the moon are not in the equatorial plane, the N-S components of their combined gravity force change the orbit inclination of the geostationary and geosynchronous satellites at a rate about 0.85° per year. Station-keeping maneuvers are required to compensate for such orbit drift. This consumes some fuel, which must be carried on board to last for the mission duration. The use of arc jets minimizes the fuel requirement by increasing the propulsion efficiency. The arc jets and station-keeping fuel requirement can be eliminated if 0.85° drift per year is acceptable, or can be accommodated in the mission design, as in TDRS. In exchange, the satellite would require several degrees of yaw maneuvering on daily basis to remain pointed at the ground station.

1.3.3 Highly Elliptical Orbit

Among highly elliptical orbits, Molniya is one specific orbit named after a Russian communications satellite with a 1000-km perigee and a 39,400-km apogee. Having the period of V2 sidereal day in this orbit, the satellite comes to the same longitude on every other apogee. The advantage of the Molniya orbit is good coverage of the entire northern hemisphere. The disadvantage is no coverage over the southern hemisphere. Moreover, it requires more satellites and needs two tracking antennas at each ground station. GPS, although not in a Molniya orbit, has an orbit period of V2 sidereal day because of its selected MEO location in a circular orbit. Some US military satellites have used the elliptical Molniya orbit with 63.4° inclination to cover 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 International Space Station (ISS) and NASA's space shuttle orbiter operate in low Earth orbit. Most communications satellites operate in GEO, but some newer constellations are planned and/or placed in LEO between 500 and 2000-km altitudes and 30 to 90° (polar) inclinations. Being closer to the Earth, smaller and simpler satellites can be used in this orbit. Also, two-way communications introduces a time delay of only 0.02 s versus 0.5 s in geosynchronous orbits. On the negative side, LEO communications satellites require tracking of omni-directional antennas, and many birds are needed for wide coverage.

1.3.5 Sunsynchronous Orbit

A satellite in this orbit maintains a constant angle between the sun's direction and the orbit plane, and always sees the sun at the same angle. It is used for special applications.

1.4 Orbit Mechanics

Kepler's three laws of planetary motion, based on Newton's laws, apply to a satellite 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 equal areas in equal times. If the time intervals At: and At2 in Figure 1.5 are equal, then the swept areas A1 and A2 are also equal. Third law: The square of the orbit period is proportional to the cube of the semi-major axis, where a is the semimajor axis of the orbit, and ß is the gravity constant of the planet. For the Earth, ß is 3.986 x 1014m3/s2 or 3.986 x 105km3/s2.

Satellite

FIGURE 1.5 Kepler's second law of planetary motion.

Satellite

FIGURE 1.5 Kepler's second law of planetary motion.

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

0 V398600 0 0

For the orbit period to be 1 sidereal day of 86,164.09 s, the orbit radius must be 42,164 km. Deducting the mean radius of the Earth surface 6378 km, we get the geosynchronous satellite altitude of 35,786 km above the Earth surface. This altitude is about six times the Earth's radius. The satellite velocity in circular orbit is given by v = ^ (1.4)

which is 3.075 km/s in GEO orbit. In comparison, the Earth travels in its orbit 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 passive method described below.

1.5.1 Gravity Gradient Method

Gravity gradient is a passive method, sometimes used in small LEO satellites. The difference in the attractive force of gravity on the parts closest and farthest from the Earth creates a moment that maintains the satellite aligned with the local vertical. This method requires long booms in order to have adequate moment, and it does not work in geosynchronous orbits because of near-zero gravity there.

1.5.2 Magnetic Damping

Magnetic damping is another passive method. It uses long booms with magnets that interact with the Earth's magnetic dipole field to produce the stabilization moment.

1.5.3 Spin Stabilization

Spin stabilization is an active method that has been commonly used in most satellites until recently. It is still used for small satellites. The spinning bicycle wheel and the spinning top are stable above certain minimum spin rate. 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 that about any orthogonal axis. Small satellites are spun in entirety. Large satellites using complex antennas are split in two sections, the despun antenna section and a spinning cylindrical body. The solar cells are mounted on the spinning body as shown in Figure 1.6. A typical spin rate is 30 to 60 revolutions per minute. Heavier satellites require higher spin rates for stability. Spin-stabilized satellites are also called dual-spin or gyrostat satellites.

1.5.4 Three-axis Stabilization

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

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

Spin Stabilized Satellite

FIGURE 1.6 Spin-stabilized gyrostat satellite.

Moment Inertia Solar Array
to Earth

South solar panel

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

introduced by the attitude and/or orbit control system to restore the vehicle to the stable position. Fuel movement in the tanks may also add in to the oscillations, but it is normally controlled by baffles. There are five points within the reference frame in space at which a stationary body will be in equilibrium. All these points are in the plane in which the dominant masses rotate. They are referred to as the Lagrangian or Libration points, and are of potential 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 two main steps. The launch vehicle places the satellite first into a low Earth

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 the

stability

Simple mechanical structure

Complex attitude control

Only 1/3rd of the solar array generate power at

Full solar array generates power all the

any time

time

Power limited by body size that fits the launch

Can have high power by adding solar

vehicle

panels

Less flexibility in design

Great flexibility in design

Suitable for small satellites

Suitable for large satellites

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

The fully deployed satellite, which is 3-axis stabilized in the operational orbit, can use spin stabilization in the transfer orbit when the solar panels are stowed into a box shaped body. The satellite is despun by applying reaction wheel torque to bring to a non-spinning state at the end of transfer orbit. The de-spinning operation takes about 10 min. Until the solar array is fully deployed, the sunlit panel radiates heat from the front face only, as opposed to both the front and back faces after the deployment. Moreover, the exposed panel is oriented normal to the sun for maximizing the power generation except during maneuvering. To keep the temperature of the sun side panel from rising above the tolerance limit, the satellite is spun at a low rate, such as 1/10th to 1 revolution per minute. Spinning at such a slow barbecue rate is merely for thermal reasons even when the spinning is not required for stability. The spin rate is gyro controlled. One can deploy the array in the transfer orbit, but it adds a mechanism and structural complexity, resulting in added mass, low reliability, and difficult transfer orbit 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 respect to the sun with seasons as depicted in Figure 1.8. The north of the Earth rotation 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 vernal equinox 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 to 90°. The corresponding incident solar flux varies from 91.75% on a solstice day to 100% on an equinox day. However, the satellite on equinox days encounters longest eclipse once per day when the Earth blocks the sunlight from illuminating the satellite.

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

EN (Ecliptic Normal)

Ecliptic plane

Ecliptic plane

Satellite orbit Satellite

Equatorial plane

Satellite orbit Satellite

Equatorial plane i0 = obliquity of the ecliptic i = satellite orbit Inclination

Autumnal equinox September 21

Winter si Decemb

Autumnal equinox September 21

Winter si Decemb

Vernal equinox March 21

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

Summer solstice June 22

Vernal equinox March 21

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

duration is, therefore, important for the spacecraft power system design. For the geosynchronous satellite, the longest eclipse occurs on the vernal and autumnal equinoxes when the sun is in the equatorial plane as shown in Figure 1.9. The duration for which the entire sun is blocked is called the umbra (total eclipse marked by dotted arc). The total arc when the sun is fully or partially blocked is called the penumbra (arc a-b). It is proportional to the mean solar day accounting for the Earth's orbital motion during the eclipse. The umbra duration varies with the seasons, the longest being 69.4 min occurring around March 21 and September 21. From the geometrical considerations of the geosynchronous orbit in Figure 1.9, the penumbra duration is 73.7 min (1.228 h) and the umbra is 4.3 min shorter than the penumbra. Since the solar array output voltage and current during this 4.3 min would not meet the requirement for the power system operation, penumbra is taken as the eclipse duration for the power system design.

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

Satellite Eclipse

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

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

Winter. Shadow misses the satellite

Spring. Shadow intercepts the satellite

Summer. Shadow misses the satellite

Autumn. Shadow intercepts the satellite

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

Spring. Shadow intercepts the satellite

Summer. Shadow misses the satellite

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

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

dependent on the orbit altitude, inclination, and the sunlight incidence angle 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

Earth orbit /

where ft = angle of the sunlight incidence on the orbit plane, i.e., the angle between the Sun-Earth line and the local normal of the orbit plane.

The ft angle varies seasonally between ±(i + y), where i = orbit inclination with respect to the equator and y = angle between the sun line and the ecliptic plane (23.45°). As ft increases, the eclipse duration decrease, which improves the load capability of the electrical power system. At certain value of high ft, no eclipse occurs. There are polar and near-polar low Earth orbits

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

Earth shadow intercepts the satellite every orbit in all seasons

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

200 1000 3000 10000 35000

Circular orbit altitude (km) FIGURE 1.13 Eclipse duration and orbit period vs circular orbit altitude.

200 1000 3000 10000 35000

Circular orbit altitude (km) FIGURE 1.13 Eclipse duration and orbit period vs circular orbit altitude.

that never have an eclipse of the sun. On the other hand, the longest eclipse occurs at fi = 0.

1.8.1 Example

For a satellite in a 6343-mile radius and 20° inclination orbit, the above equation gives Te = 0.63 h or 38 min long eclipse (note that the argument of the sin-1 must be in radians).

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

10000

1000 3000 10000 35000

Circular orbit altitude (km) FIGURE 1.14 Maximum number of eclipse per year vs orbit altitude.

Circular orbit altitude (km) FIGURE 1.15 Minimum sun time and maximum eclipse duration in circular Earth orbits.

challenge posed to the power system design engineer. The greater the ratio, the heavier the battery requirement to power the load during an eclipse. It also requires a larger solar array to capture the energy required during shorter periods of sunlight, and to divert a higher fraction of it to charge the battery while simultaneously supplying full load to the payload. Such a demand is greater on a low Earth orbit satellite, as seen in Figures 1.15 and 1.16.

1.9 Eclipse due to Moon

In addition to eclipses due to the Earth's shadow on the satellite, the moon can also obstruct the sun as seen by the satellite. Such eclipses are irregular in occurrence, varying from 0 to 4 per year, with an average of two. Usually they are spaced far apart, but in the worst case two eclipses can occur in 24 h. The duration can vary from several minutes to more than 2 h, with an

1000 3000 10000 35000 Circular orbit altitude (km) FIGURE 1.16 Ratio of maximum eclipse to minimum sun time in circular Earth orbits.

1000 3000 10000 35000 Circular orbit altitude (km) FIGURE 1.16 Ratio of maximum eclipse to minimum sun time in circular Earth orbits.

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

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Responses

  • Massawa
    Which of satellite is called solar array?
    1 year ago

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