introduction to satellite communication

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basics of orbits,introdction to satellite communication

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Presentation Transcript

SATELLITE COMMUNICATION SYSTEMS : 

SATELLITE COMMUNICATION SYSTEMS

Communication satellites bring the world to you anywhere and any time….. : 

Communication satellites bring the world to you anywhere and any time…..

Slide 3: 

What exactly is a satellite? The word satellite originated from the Latin word “Satellit”- meaning an attendant, one who is constantly hovering around & attending to a “master” or big man. For our own purposes however a satellite is simply any body that moves around another (usually much larger) one in a mathematically predictable path called an orbit. A communication satellite is a microwave repeater staion in space that is used for tele communcation , radio and television signals. The first man made satellite with radio transmitter was in 1957. . There are about 750 satellite in the space, most of them are used for communication.

How do satellite work? : 

How do satellite work?

Slide 5: 

How do Satellites Work? * Two Stations on Earth want to communicate through radio broadcast but are too far away to use conventional means. The two stations can use a satellite as a relay station for their communication. * One Earth Station transmits the signals to the satellite. Up link frequency is the frequency at which Ground Station is communicating with Satellite. * The satellite Transponder converts the signal and sends it down to the second earth station. This frequency is called a Downlink.

Consider the light bulb example: : 

Consider the light bulb example:

Components of a satellite : 

Components of a satellite

Advantages of satellite over terrestrial communication : * The coverage area of a satellite greatly exceeds that of a terrestrial system. * Transmission cost of a satellite is independent of the distance from the center of the coverage area. * Satellite to Satellite communication is very precise. * Higher Bandwidths are available for use. Disadvantages of satellites: * Launching satellites into orbit is costly. * Satellite bandwidth is gradually becoming used up. * There is a larger propagation delay in satellite communication than in terrestrial communication.

How does a satellite stay in it’s orbit? : 

How does a satellite stay in it’s orbit?

How do we escape gravity & place an object in orbit? : 

How do we escape gravity & place an object in orbit? If an object is fired fast enough it should escape the earths pull. This is done through the use of Rocket Launchers

Multi-stage Rockets : 

Multi-stage Rockets Stage 1: Raises the payload e.g. a satellite to an elevation of about 50 miles. Stage 2: Satellite 100 miles and the third stage places it into the transfer orbit. Stage 3: The satellite is placed in its final geo-synchronous orbital slot by the AKM, a type of rocket used to move the satellite.

Applications : 

Applications

Major problems for satellites : 

Major problems for satellites Positioning in orbit Stability Power Communications Harsh environment

Positioning : 

Positioning This can be achieved by several methods One method is to use small rocket motors These use fuel - over half of the weight of most satellites is made up of fuel Often it is the fuel availability which determines the lifetime of a satellite Commercial life of a satellite typically 10-15 years

Stability : 

Stability It is vital that satellites are stabilised - to ensure that solar panels are aligned properly, communication antennae are aligned properly Early satellites used spin stabilisation - either this requires an inefficient omni-directional aerial Or antennae were precisely counter-rotated in order to provide stable communications. * Modern satellites use reaction wheel stabilisation - a form of gyroscopic stabilisation.

Power : 

Power Modern satellites use a variety of power means Solar panels are now quite efficient, so solar power is used to generate electricity Batteries are needed as sometimes the satellites are behind the earth - this happens about half the time for a LEO satellite Nuclear power has been used - but not recommended

Satellite - satellite communication : 

Satellite - satellite communication It is also possible for satellites to communicate with other satellites Communication can be by microwave or by optical laser

Harsh Environment : 

Harsh Environment Satellite components need to be specially “hardened” Circuits which work on the ground will fail very rapidly in space Temperature is also a problem - so satellites use electric heaters to keep circuits and other vital parts warmed up - they also need to control the temperature carefully

Early satellites : 

Early satellites Telstar Allowed live transmission across the Atlantic Syncom 2 First Geosynchronous satellite TELSTAR SYNCOM 2

Satellite orbits : 

Satellite orbits Classification of orbits:

Slide 21: 

* Circular orbits are simplest * Inclined orbits are useful for coverage of equatorial regions * Elliptical orbits can be used to give quasi stationary behavior viewed from earth using 3 or 4 satellites * Orbit changes can be used to extend the life of satellites

Classification of orbits: : 

Classification of orbits: Satellite orbits are also classified based on their heights above the earth: GEO LEO MEO Molniya Orbit HAPs

Satellite orbit altitudes : 

Satellite orbit altitudes

Geostationary Earth Orbit (GEO) : 

Geostationary Earth Orbit (GEO) These satellites are in orbit 35,786 km above the earth’s surface along the equator. Objects in Geostationary orbit revolve around the earth at the same speed as the earth rotates. This means GEO satellites remain in the same position relative to the surface of earth.

GEO contd. : 

GEO contd. Advantages A GEO satellite’s distance from earth gives it a large coverage area, almost a fourth of the earth’s surface. GEO satellites have a 24 hour view of a particular area. These factors make it ideal for satellite broadcast and other multipoint applications Minimal doppler shift Disadvantages A GEO satellite’s distance also cause it to have both a comparatively weak signal and a time delay in the signal, which is bad for point to point communication. GEO satellites, centered above the equator, have difficulty for broadcasting signals to near polar regions Launching of satellites to orbit are complex and expensive.

Low Earth Orbit (LEO) : 

Low Earth Orbit (LEO) LEO satellites are much closer to the earth than GEO satellites, ranging from 500 to 1,500 km above the surface. LEO satellites don’t stay in fixed position relative to the surface, and are only visible for 15 to 20 minutes each pass. A network of LEO satellites is necessary for LEO satellites to be useful

The Iridium system has 66 satellites in six LEO orbits, each at an altitude of 750 km. : 

The Iridium system has 66 satellites in six LEO orbits, each at an altitude of 750 km. Iridium is designed to provide direct worldwide voice and data communication using handheld terminals, a service similar to cellular telephony but on a global scale

LEO Contd. : 

LEO Contd. Advantages A LEO satellite’s proximity to earth compared to a GEO satellite gives it a better signal strength and less of a time delay, which makes it better for point to point communication. A LEO satellite’s smaller area of coverage is less of a waste of bandwidth. Disadvantages A network of LEO satellites is needed, which can be costly LEO satellites have to compensate for Doppler shifts cause by their relative movement. Atmospheric drag effects LEO satellites, causing gradual orbital deterioration.

Medium Earth Orbit (MEO) : 

Medium Earth Orbit (MEO) A MEO satellite is in orbit somewhere between 8,000 km and 18,000 km above the earth’s surface. MEO satellites are similar to LEO satellites in functionality. MEO satellites are visible for much longer periods of time than LEO satellites, usually between 2 to 8 hours. MEO satellites have a larger coverage area than LEO satellites.

MEO contd. : 

MEO contd. Advantage A MEO satellite’s longer duration of visibility and wider footprint means fewer satellites are needed in a MEO network than a LEO network. Disadvantage A MEO satellite’s distance gives it a longer time delay and weaker signal than a LEO satellite, though not as bad as a GEO satellite.

MEO satellites : 

MEO satellites Glonass (Russian) The GPS constellation calls for 24 satellites to be distributed equally among six circular orbital planes

Molniya Orbit : 

Molniya Orbit Used by Russia for decades. Molniya Orbit is an elliptical orbit. The satellite remains in a nearly fixed position relative to earth for eight hours. A series of three Molniya satellites can act like a GEO satellite. Useful in near polar regions.

High Altitude Platform (HAP) : 

High Altitude Platform (HAP) One of the newest ideas in satellite communication. A blimp or plane around 20 km above the earth’s surface is used as a satellite. HAPs would have very small coverage area, but would have a comparatively strong signal. Cheaper to put in position, but would require a lot of them in a network.

HAP : 

HAP

Slide 35: 

Satellite frequency band

Solar day and Sidereal day : 

Solar day and Sidereal day A day is defined as the time that it takes the Earth to rotate on its axis. However, there is more than one way to define a day: A sidereal day is the time that it takes for the Earth to rotate with respect to the distant stars. A solar day is the time that it takes to rotate with respect to the Sun.

The Length of the Day : 

The Length of the Day A solar day is slightly longer than a sidereal day. A sidereal day is 23h 56m 4.091s. We set our watches according to the solar day. Astronomers use sidereal time because we are mostly interested in distant celestial objects.

Solar day and Sidereal day : 

Solar day and Sidereal day A solar day is measured using the passage of the Sun across the sky—it lasts 24 hours A sidereal day (from the Latin word meaning star) is measured with respect to fixed stars—it lasts a little less than 24 hours. Each solar day the Earth rotates 360 degrees with respect to the Sun Each sidereal day the Earth rotates 360 degrees with respect to the background stars During each solar day the motion of the Earth around the Sun means the Earth rotates 361 degrees with respect to the background stars

Slide 39: 

The actual length of a sidereal day on Earth is 23 hours 56 minutes 4 seconds This means that the Earth has to rotate slightly more than one turn with respect to a fixed star to reach the same Earth-Sun orientation (solar day)

Solar day and Sidereal day : 

Solar day and Sidereal day The difference between solar days and sidereal days means that a given star will rise earlier each day These 3 photos show how Orion reaches the same position in the sky 4 minutes earlier on each consecutive day.

Apparent Solar Time : 

Apparent Solar Time Apparent solar time is the time measured with respect to the actual position of the Sun. At noon, the Sun would be exactly on the meridian. 1 P.M. would be exactly one hour after the Sun was on the meridian. 9 A.M. would be exactly 3 hours before the Sun was on the meridian. The apparent solar time depends on your longitude.

Origin of planetary laws : 

Origin of planetary laws Sir. Johannes Keppler Derived 3 laws based upon his observations of planetary motion. Sir.Tycho Brahe Introduced precision into astronomical measurements. Mentor to Johannes Keppler

Kepler’s 1st Law: Law of Ellipses : 

Kepler’s 1st Law: Law of Ellipses The orbits of the planets are ellipses with the sun at one focus

Kepler’s 2nd Law: Law of Equal Areas : 

Kepler’s 2nd Law: Law of Equal Areas The line joining the planet to the center of the sun sweeps out equal areas in equal times

Kepler’s 3rd Law: Law of Harmonics : 

Kepler’s 3rd Law: Law of Harmonics The squares of the periods of two planets’ orbits are proportional to each other as the cubes of their semi-major axes:T12/T22 = a13/a23 In English: Orbits with the same semi-major axis will have the same period

Newton’s Laws : 

Newton’s Laws Kepler’s laws only describe the planetary motion without attempting to suggest any explanation as to why the motion takes place in that manner. Sir .Issac Newton Derived three laws of motion. Derived the Law of Universal Gravitation. Explained why Kepler’s laws worked.

Newton’s 1st Law: Law of Inertia : 

Newton’s 1st Law: Law of Inertia Every body continues in a state of uniform motion unless it is compelled to change that state by a force imposed upon it

Newton’s 2nd Law: Law of Momentum : 

Newton’s 2nd Law: Law of Momentum Change in momentum is proportional to and in the direction of the force applied Momentum equals mass x velocity Change in momentum gives: F = ma

Newton’s 3rd Law: Action - Reaction : 

Newton’s 3rd Law: Action - Reaction For every action, there is an equal and opposite reaction Hints at conservation of momentum

Newton’s Law of Universal Gravitation : 

Newton’s Law of Universal Gravitation Between any two objects there exists a force of attraction that is proportional to the product of their masses and inversely proportional to the square of the distance between them

Classical orbital elements : 

Classical orbital elements

Apogee and Perigee : 

Apogee and Perigee In astronomy, an apsis is the point of greatest or least distance of the elliptical orbit of an astronomical object from its center of attraction, which is generally the center of mass of the system. The point of closest approach is called the periapsis (Perigee) or pericentre and the point of farthest excursion is called the apoapsis (apogee) A straight line drawn through the perigee and apogee is the line of apsides. This is the major axis of the ellipse. Ascending & Descending nodes These are the 2 points at which the orbit of a satellite penetrates the equatorial plane.

Classical orbital elements : 

Classical orbital elements Six independent quantities are sufficient to describe the size, shape and orientation of an orbit. These are a, the semi-major axis , the eccentricity i, the inclination , the right ascension of the ascending node , the argument of perigee tp, mean anamoly

Slide 54: 

The semi-major axis describes the size of the orbit. It connects the geometric center of the orbital ellipse with the periapsis, passing through the focal point where the center of mass resides. The eccentricity shows the ellipticity of the orbit. The inclination is the angle between the plane of the orbit and the equatorial plane measured at the ascending node in the northward direction. The right ascension of an ascending node is the angle between the x axis and the ascending node. The argument of periapsis (perihelion) is the angle in the orbital plane between the line of nodes and the perigee of the orbit. The mean anomaly is the time elapsed since the satellite passed the perigee.

Major parameters of an elliptical orbit : 

Major parameters of an elliptical orbit Satellite trajectory Satellite period Satellite velocity Satellite position

Satellite Trajectory : 

Satellite Trajectory The path of a satellite in space may be obtained under the following assumptions: 1.The satellite and earth are symmetric spherically and may be treated as point masses. 2.There are no other forces acting on the system besides the gravitational forces. 3.The mass of the earth is much greater than satellite. These assumptions lead to the two body problem.

Slide 57: 

Applying Newton's laws to such systems, .. ∑F = m r (second law) …………(1) F = -GMm. r (third law) ……………..(2) r2 r Substituting (1) in (2) we get, .. .. r + GM .r = 0 (or) r + μ .r = 0 r3 r3 .. Where r = vector acceleration in the given coordinate system r = vector from M (mass of earth) to m (mass of satellite) r = distance between M and m , μ = GM (gravitational parameter) A partial system is easy to obtain and is adequate for illustrating the size and shape of an orbit. The resulting trajectory equation has a general form of conic section: r = P ; p = a geometric constant called parameter of conic 1+e cos θ = (r v cos ф)2 / μ e = the eccentricity which determines type of conic section =√(1-P/a) θ = angle between r and the point on the conic nearest the focus ф = flight elevation angle , v = satellite velocity a = semi-major axis = (ra+rb)/2

Satellite period : 

Satellite period The period T of a satellite is given as: T2= 4 П2 .a3 (period depends only on semi major axis,a) μ For a satellite in circular orbit around earth- T2= 4 П2 .(R+h)3 μ Where , R= radius of earth, h= satellite altitude

Satellite velocity : 

Satellite velocity Total specific mechanical energy ε of a satellite is the sum of kinetic energy/unit mass and potential energy/unit mass, but there is an interchange between these energies. Thus a satellite slows down when it moves up and gains speed as it loses height. The velocity of a satellite in an elliptic orbit is : V2= μ(2/r -1/a) also ε = V2/2 - μ /r and ε = –μ /2a For circular orbit the equation reduces to: V2 = μ /r

Satellite position with time : 

Satellite position with time The origin O is the geocentre. The satellite at any instant tp is assumed to be at S. The circle is drawn from centre C of the ellipse with a radius equal to the semi major axis and a perpendicular BM is drawn passing through the point S. Angle E is called eccentric anomaly and angle θ is the true anomaly.

Satellite position : 

Satellite position For an elliptic orbit, the time tp elapsed from a perigee pass is defined as- tp = T/2Π (E-e sin E) = (T/2Π)M ; where M = E-e sin E Eccentric anomaly is defined as E = arccos[ (e + cosθ)/(1+ e cosθ)] where θ = true anomaly = 2tan-1 {[( 1+e)/(1-e)]1/2 tanE/2} When θ=0 ,the mean and true anomalies are equal. Hence distance between satellite and geocentre is r = a(1-e2)/(1-ecosθ)

GEOSYNCHRONOUS AND GEOSTATIONARY ORBITS : 

GEOSYNCHRONOUS AND GEOSTATIONARY ORBITS

GEOSYNCHRONOUS ORBITS : 

GEOSYNCHRONOUS ORBITS A geosynchronous orbit is the one with an orbital period (the time needed to orbit once around the Earth) that matches the rotation rate of the Earth. This is a sidereal day, which is 23 hours 56 minutes and 4 seconds in length. A geosynchronous earth orbit is sometimes referred to as the Clarke orbit or Clarke belt, after Arthur C. Clarke, who first suggested its‘ existence in 1945 and proposed its use for communications satellites

Clarke Orbit : 

Clarke Orbit The Clarke orbit meets the concise set of specifications for geosynchronous satellite orbits: (1) be located directly above the equator (2) travel in the same direction as Earth's rotation at 6840 mph (3) have an altitude of 22,300 miles above Earth (4) complete one revolution in 24 hours

Clarke Orbit : 

Clarke Orbit

Geo synchronous Satellites : 

Geo synchronous Satellites There is only one geosynchronous earth orbit. It is occupied by a large number of satellites. In fact, the geosynchronous orbit is the most widely used earth orbit for the obvious reason. An international agreement initially mandated that all satellites placed in the Clarke orbit must be separated by at least 1833 miles. This stipulation equates to an angular separation of 4° or more, which limits the number of satellite vehicles in a geosynchronous earth orbit to less than 100. Today, however, international agreements allow satellites to be placed much closer together.

Geo stationary orbit : 

Geo stationary orbit A geostationary orbit is a special case of a geosynchronous orbit. A satellite is in a geostationary orbit when it appears stationary from the point of view of an observer on the Earth's surface. This can only occur when: The orbit is geosynchronous The orbit is a circle The orbit lies in the plane of the Earth's equator Thus, a geosynchronous satellite will be geostationary only with the additional restrictions of it being in a circular orbit situated over the equator.

Geostationary Vs. Polar Orbiting : 

Geostationary Vs. Polar Orbiting http://cimss.ssec.wisc.edu/satmet/modules/sat_basics/images/orbits.jpg

Geostationary Satellites : 

Geostationary Satellites The satellite velocity in this orbit is 3075 m/s. Operate in the 2.0 GHz to 18 GHz range When the inclination and eccentricity of the orbit is zero, the satellite appears to be stationary to an observer from ground.

Geostationary Satellites in Orbit : 

Geostationary Satellites in Orbit

Geostationary Satellite Coverage : 

Geostationary Satellite Coverage http://www.ssec.wisc.edu/mcidas

Geostationary Satellite Coverage : 

Geostationary Satellite Coverage http://www.ssec.wisc.edu/mcidas

Geostationary Satellite Coverage : 

Geostationary Satellite Coverage http://www.ssec.wisc.edu/mcidas

Geo-stationary satellites : 

Geo-stationary satellites The geometric considerations like satellite elevation/look angle etc are very vital for reliable communication satellite system design. Applications: Telecommunication systems Radio Data Transmission systems

Satellite elevation: : 

Satellite elevation: The elevation of a satellite,η is the angle which a satellite makes with the tangent at the specified point on the earth. η = arc tan [(cosψ-σ)/ sin ψ] Where, coverage angle ψ = arc cos (cosθc cosφcs ) φcs = φc - φs and σ =R /(R+h) = 0.151 In terms of elevation angle: ψ = 900 – η-sin-1(cos η / 6.63235) In terms of tilt angle : ψ = sin -1(6.6235 sinγ- γ) where θc = latitude of earth station, φc = the longitude, φs = longitude of sub satellite point, R=radius of earth, h=satellite height above equator Tilt angle γ = arc tan [sin ψ / (6.6235-cos ψ)

Azimuth:The azimuth ξ is the angle which the satellite direction makes with the direction of true north measured in the clockwise direction.The azimuth ξ = arc tan [tan φcs /sinθc] in northern hemisphere:ξ =1800 + A0;when the satellite is to the west of earth stationξ =1800 - A0;when the satellite is to the east of earth stationin southern hemisphere:ξ =3600 - A0;when the satellite is to the west of earth stationξ =A0;when the satellite is to the east of earth station : 

Azimuth:The azimuth ξ is the angle which the satellite direction makes with the direction of true north measured in the clockwise direction.The azimuth ξ = arc tan [tan φcs /sinθc] in northern hemisphere:ξ =1800 + A0;when the satellite is to the west of earth stationξ =1800 - A0;when the satellite is to the east of earth stationin southern hemisphere:ξ =3600 - A0;when the satellite is to the west of earth stationξ =A0;when the satellite is to the east of earth station

Range: : 

Range: The range d of a geostationary satellite is given by, d = 35786[1+0.4199{1-cos ψ}1/2 In terms of radius of earth (ie, der = d/r) der= [13.47(1-cosβ+31.624)1/2 also der = 6 .6235 sin ψ/cos η The angle , is the angle between the solar vector and the orbit plane. If the solar vector is in the orbit plane,  = 0. Beta can go to  90. The general convention is that  is positive when the sun is on the same side of the orbit plane as the positive orbit normal (right hand rule).

Launching of geostationary satellite: : 

Launching of geostationary satellite: Initially place spacecraft with the final rocket stage into LEO. After a couple of orbits, during which the orbital parameters are measured, the final stage is reignited and the spacecraft is launched into a geostationary transfer orbit(GTO). Perigee of GTO is that of LEO altitude and apogee that of GEO altitude. After a few orbits in GTO, while the orbital parameters are measured, a rocket motor (AKM) is ignited at apogee and GTO is raised until it is circular geostationary orbit. AKM (Apogee Kick Motor) is used to circularize the orbit at GEO and to remove any inclination error so that the final orbit is very close to geostationary.

Launching of geostationary satellite : 

Launching of geostationary satellite

Geostationary Transfer Orbit : 

Geostationary Transfer Orbit BUT, if we fire a rocket motor when the satellite's at apogee, and speed it up to the required circular orbit speed, it will stay at that altitude in circular orbit. Firing a rocket motor at apogee is called "apogee kick", and the motor is called the "apogee kick motor". If we speed the satellite up while it's in low circular earth orbit it will go into elliptical orbit, heading up to apogee. If we do nothing else, it will stay in this elliptical orbit, going from apogee to perigee and back again.

Phase I and II of launching spacecraft : 

Phase I and II of launching spacecraft Phase I ↑ Phase II Few Geostationary satellites: EDUSAT, INTELSAT , INSAT , PAKSAT, AMERICOM …….

ORBITAL MANEUVERS Hohmann Transfer : 

ORBITAL MANEUVERS Hohmann Transfer Can be used to raise or lower altitude Most efficient method At minimum, requires completion of half revolution of transfer orbit

Hohmann transfer : 

Hohmann transfer Most satellites launched today are initially placed into an low earth orbit. In the next phase the satellite is injected into an elliptical transfer orbit which has an apogee at the height of GEO and its apsides (line joining perigee-apogee) in the equatorial plane. Finally satellite is injected into GEO by imparting a velocity increment at the apogee equal to the difference between satellite velocity at GTO and velocity in GEO. A transfer between two coplanar circular orbits via elliptical transfer orbit requires the least velocity increment (and hence fuel). This principle was recognized by Hohmann in 1925 and is referred as Hohmann transfer.

Slide 85: 

A Hohmann transfer is a fuel efficient way to transfer from one circular orbit to another circular orbit that is in the same plane (same inclination), but a different altitude. To change from a lower orbit (A) to a higher orbit (C), an engine is first fired in the opposite direction from the direction the vehicle is traveling. This will add velocity to the vehicle causing its trajectory to become an elliptic orbit (B). This elliptic orbit is carefully designed to reach the desired final altitude of the higher orbit (C). In this way the elliptic orbit or transfer orbit is tangent to both the original orbit (A) and the final orbit (C). This is why a Hohmann transfer is fuel efficient. When the target altitude is reached the engine is fired in the same manner as before but this time the added velocity is planned such that the elliptic transfer orbit is circularized at the new altitude of orbit (C).

Hohmann Transfer : 

Hohmann Transfer The orbital inclination is given by, cos i= sinξ1 cos θ1 where i=inclination ξ1 =azimuth of launch θ1 =latitude of launching site

PERTURBATIONS : 

PERTURBATIONS Perturbation is a term used in astronomy to describe alterations to an object's orbit caused by gravitational interactions with other bodies. Major sources are: Effect of earth Third Body Effects Atmospheric Drag Solar radiation pressure Electro-Magnetic effect

Space Weather Effects : 

Space Weather Effects Space Weather Effects

Effect of earth on satellites : 

Effect of earth on satellites The effect of gravitational force is non uniform because of the non uniform distribution of earth’s mass - a slight bulge at the equator, with a difference of 21 km between polar and the equator radius. This deviation from spherical shape causes additional forces on the satellite. The effect of earth’s gravitational pull may be expressed as the harmonic series of the field. The first term represents the principal gravitational law and the higher order terms in the series as the perturbations.

Slide 90: 

The main effects of perturbations are: 1. The component of perturbations in the orbital plane causes the perigee to rotate in the orbital plane. 2. Another effect of perturbations is that the orbital plane rotates around the earth’s north-south axis. 3. The perturbating force along the orbital plane imparts a force vector on a satellite 1. The component of perturbations in the orbital plane causes the perigee to rotate in the orbital plane. The rate of change of argument of perigee is ω = 4.97[R/a]3.5 (5cos2i-1)/(1-e2)2 deg/day where R= mean equatorial radius , a=semi major axis i = inclination, e=eccentricity when i=63.40 , ω reduces to zero, implying that perigee remains fixed in space.

2. The orbital plane rotates around the earth’s north-south axis.The rate of change of rotation of ascending node is Ω = 9.95[r/a]3.5 cos i /(1-e2)2 deg/day Where r = satellite-geo centre distanceThe rotation is in a direction opposite to the satellite motion. For a geostationary orbit magnitude is 4.90/year ,implying the ascending node rotates around the earth in 73 years.3. The perturbating force along the orbital plane imparts a force vector on a satellite. For most orbits such components cancel out as the satellite position changes continuously.In the geostationary orbits, resultant perturbating component do not cancel but cause a satellite to drift towards one of the two nearest stable points on the orbit.Stable points are approximately on the minor axis, showing that the elliptical approx. of earth is not precisely accurate. : 

2. The orbital plane rotates around the earth’s north-south axis.The rate of change of rotation of ascending node is Ω = 9.95[r/a]3.5 cos i /(1-e2)2 deg/day Where r = satellite-geo centre distanceThe rotation is in a direction opposite to the satellite motion. For a geostationary orbit magnitude is 4.90/year ,implying the ascending node rotates around the earth in 73 years.3. The perturbating force along the orbital plane imparts a force vector on a satellite. For most orbits such components cancel out as the satellite position changes continuously.In the geostationary orbits, resultant perturbating component do not cancel but cause a satellite to drift towards one of the two nearest stable points on the orbit.Stable points are approximately on the minor axis, showing that the elliptical approx. of earth is not precisely accurate.

Third Body Effects (heavenly bodies) : 

Third Body Effects (heavenly bodies) Gravitational pull of other massive bodies, i.e. Sun, moon Mainly noticeable in deep space orbits

Gravitational effects from heavenly bodies: : 

Gravitational effects from heavenly bodies: In LEO satellites, the influence of gravitational forces from sun and moon are small when compared to the gravitational force of earth. The order of magnitude of gravitational force of moon and sun are main sources of perturbations in GEO satellites. When nearer to heavenly bodies, the gravitational pull is stronger and hence causes a gravity gradient. main effect of such gradient is to change the inclination of the orbit. The combined effect of sun and moon is to cause a change in inclination of GEO satellites between 0.750 and 0.940

Slide 94: 

The inclination of orbital plane caused by moon changes cyclically between 0.480 and 0.670 with a period of 18.6 years. Maximum inclination change occurred in year 1987 and minimum in Feb 1997 The change in inclination due to sun is 0.270 /year. Note: Among the three forces affecting the inclination (gravity pull, sun and non spherical nature of earth) the later force has a component in the direction opposite to the former two forces. Hence these forces cancel out at an inclination angle of about 7.50 Thus the inclination of satellite when left uncorrected oscillates around the stable inclination with the period of about 53 years reaching a maximum of 150 and a minimum of 00

Atmospheric Drag : 

Atmospheric Drag Satellites below 2000 kilometres, are actually travelling through the Earth’s atmosphere. Collisions with air particles, even at these high altitudes slowly act to circularise the orbit and slow down the spacecraft causing it to drop to lower altitudes , this effect is known as atmospheric drag Emissions from the Sun cause the upper atmosphere to heat and expand. These energetic solar outputs increase dramatically during periods of high solar activity, and may result in Earth-orbiting satellites experiencing an increase in atmospheric drag

A satellite orbiting the Earth would continue to orbit forever if gravity were the only force acting on it. : 

A satellite orbiting the Earth would continue to orbit forever if gravity were the only force acting on it. Perigee remains same, Apogee decreases

Slide 97: 

Reduces satellite’s energy Changes the size (semi-major axis) and shape (eccentricity) The effect of drag is more severe at about 180km and causes excess heat on satellite .Unless such LEO satellites are routinely boosted to higher orbits, they slowly fall, and eventually burn up Orbital life time of satellite at 400km circular earth orbit is typically few months, where as the life time is several decades if they are at 800km altitude In the former case, functional life time depends on orbital life time and for latter the life time of satellite equipments is the deciding factor. However, for GEO satellites the governing factors are equipment life time and fuel capacity of the satellite (typically 10-15 years).

Solar radiation pressure : 

Solar radiation pressure Solar radiation pressure is the force exerted by solar radiation on objects within its reach The effect of solar radiation pressure increases as the surface area of the satellite projected in the direction of sun increases. The net effect is the increase in the orbital eccentricity and also introduces disturbing torque that effects the north-south axis of the satellite.

Slide 99: 

Solar wind causes radiation pressure on the satellite The solar wind is a stream of charged particles (a plasma) that are ejected from the upper atmosphere of the sun. It consists mostly of electrons and protons with energies of about 1 keV. These particles are able to escape the sun's gravity because of the high temperature of the corona, and also because of high kinetic energy These perturbations are corrected periodically

Effects of Solar radiation pressure : 

Effects of Solar radiation pressure 1. HUMAN HEALTH Intense solar flares produce very high energy particles that can be as harmful to people as low-energy radiation from nuclear blasts. Earth’s atmosphere and magnetosphere provide protection for people on the ground, but astronauts in space are subject to potentially lethal doses of radiation. The penetration of high energy particles into living cells leads to chromosome damage and, potentially, cancer. Airline pilots and flight crews, as well as frequent fliers, also receive increased doses of radiation from solar flares. If you were travelling in an aircraft at high altitudes during a major solar flare, the amount of radiation you would be exposed to can be equivalent to getting a chest x-ray.

Slide 101: 

2. COMMUNICATIONS Stormy space weather can damage Earth-orbiting satellites such as those carrying TV and mobile phone signals. During high levels of solar activity, satellites are bombarded with high energy particles. If the deeply penetrating electrons build up faster than the charges are able to dissipate out of the satellite material, a discharge can result that is capable of damaging the satellite electronics. These processes can result loss of control and even satellite failure.

Slide 102: 

3. NAVIGATION A Global Positioning System (GPS) receiver uses radio signals from several orbiting satellites to determine the range, or distance, from each satellite, and determines from these ranges the actual position of the receiver. The radio signals must pass through the ionosphere, the uppermost part of the Earth’s atmosphere, and in doing so are subjected to variations in the electron density structure of the ionosphere. Changes in the electron density due to space weather activity can change the speed at which the radio waves travel introducing a “propagation delay” in the GPS signal. Changing propagation delays cause errors in the determination of the range. An increase in space weather activity may cause widespread disruption to aircraft and ship navigation and emergency location systems that rely heavily on satellite navigation data.

Electro-Magnetic effect : 

Electro-Magnetic effect Interaction between the Earth’s magnetic field and the satellite’s electro-magnetic field results in magnetic drag

Magnetic storm : 

Magnetic storm A geomagnetic storm is a temporary disturbance of the earth’s magnetosphere caused by a disturbance in space weather. A geomagnetic storm is caused by a solar wind shock wave. This only happens if the shock wave travels in a direction toward Earth. The solar wind pressure on the magnetosphere will increase or decrease depending on the Sun's activity. These solar wind pressure changes modify the electric currents in the ionosphere. Magnetic storms usually last 24 to 48 hours, but some may last for many days.

Non geostationary constellations : 

Non geostationary constellations The design of constellations can be categorized according to inclination, altitude and eccentricity. On the basis of inclination, two types of constellations are designed. Type I constellations are those having their orbital planes with a common intersection point. Eg: Polar constellations Type II constellations have optimized inclined orbit constellations and distribute satellites uniformly. Eg: inclined constellations Depending on altitudes, constellations may be LEO,MEO etc. A hybrid of orbital altitudes are also possible within a system (A LEO satellite can be used together with a geostationary orbit satellite)

LEO Satellite coverage : 

LEO Satellite coverage

Demo of satellite coverage : 

Demo of satellite coverage

Advantages of Non-geostationary constellations : 

Advantages of Non-geostationary constellations Since these orbits are closer to earth, the free space loss is lower and hence it is possible to use hand held terminals. Path loss at 1.5 GHz for LEO=152.87 dB, MEO=175.96 dB and GEO=187.10dB. 2. LEO and MEO reduces the propagation delay which reduces or eliminates delay related problems. 3. These orbits offer a higher frequency reuse. Maximum distance between two points which view a satellite at an elevation angle 100 is LEO (at altitude 700km) = 3885 km MEO (10000km) = 12790 km GEO (36000km) = 15914 km Hence note that 4 LEO satellites would cover the same geographical distance as a single GEO. Thus LEO has 4 times frequency reuse than GEO.

Slide 109: 

4 . Distributed architecture of LEO and MEO orbits make them more resistant to satellite failures and hence more reliable. Competitions between operators has triggered a feverish technical, regulatory and financial activity in the industry. Current non geostationary proposals are- MEO system -Offers a real time services. Medium/high bit rates communication facility. eg: ICO system Little LEO -Offers a low bit rate non-real time services such as messaging (bit rate< 4kbps). eg. ORBCOM Big LEO -Offering medium bit rate interactive services such as voice (bit rate 1-10 kbps) eg: Iridium. Broad band LEO -Offers broadband services such as internet high speed file download (bit rate=16kbps to 1 Gbps) eg: Teledesic.

Polar constellations : 

Polar constellations A polar orbit is an orbit in which a satellite passes above or nearly above both poles of the body (usually a planet such as the earth) being orbited on each revolution. It therefore has an inclination of (or very close to) 900 to the equator. Polar orbits are often used for earth-mapping, earth observation, as well as some weather satellites The disadvantage to this orbit is that no one spot on the Earth's surface can be sensed continuously from a satellite in a polar orbit. Polar satellites include: Defense meteorological satellite program (DMSP), Landsat, SPOT and NOAA. Landsat and SPOT are Commercial polar orbiters and are intended for geophysical remote sensing To achieve a polar orbit requires more energy, thus more propellant is needed than an orbit of low inclination

Slide 111: 

Polar orbits

Eg. of the positions of a sun-synchronous satellite in 12 hour intervals : 

Eg. of the positions of a sun-synchronous satellite in 12 hour intervals Sun synchronous satellites pass over any given latitude at almost the same local time during each orbital pass

Polar constellations : 

Polar constellations Here : Ψ = coverage circle m = number of orbital planes n = satellites /plane Δ = cos-1[cos Ψ/cos Π/m]

Slide 114: 

Single coverage: Satellites in adjacent planes move in same direction, shifted with respect to each other by half intra-orbit satellite separation (Π/m), where m = number of planes. The separation between adjacent planes is (Ψ+Δ) and the relative geometry remains constant because they move in phase. Satellites are separated by 2Δ,when the satellites move in opposite directions and the relative geometry is not constant. The total number of satellites, N = 4 /(1-cos Ψ) ; 1.3n < m < 2.2n In the cases of non integer, next highest integer satisfying the inequality can be taken. If the N is much large, then the condition (n-1) Ψ + (n+1) Δ = П

Slide 115: 

When the coverage is required beyond a latitude λ,the equations are – (n-1) Ψ+(n+1) Δ = П cos λ and N = 4cos λ/(1-cos Ψ) The coverage efficiency of the constellations is given by NΩ/4П Where NΩ = total solid angle Ω = solid angle bounded by a single satellite=2П(1-cos Ψ) Triple coverage: The constellation geometry is similar to single coverage case, with at least three satellites must be visible at all points. The coverage angle is adjusted such that at least 3 satellites lie within angle Ψ of each point of set. The resulting relationship for providing triple coverage from pole up to latitude λ is N = 11cos λ/(1-cos λ) ; 1.4n < mcos λ < 2.4n

Inclined orbit : 

Inclined orbit A satellite is said to occupy an inclined orbit around the earth if the orbit exhibits an angle other than zero degrees with the equatorial plane They have an inclination between 0 degrees (equatorial orbit) and 90 degrees This family of satellites provides unbiased worldwide coverage by deploying satellites in circular orbits of same period and inclination, distributed uniformly on the sphere. The orbital altitude of these satellites is generally on the order of a few hundred km, so the orbital period is on the order of a few hours. These satellites are not sun-synchronous, however, so they will view a place on Earth at varying times.

Slide 117: 

Adjacent orbital planes are separated equally around a reference plane (equatorial). Within each orbit ,neighboring satellites have equal angular separation.

Inclined constellations : 

Inclined constellations αi = right ascension angle of ith orbital plane =2Пi / P βi = inclination angle of ith orbit γi = initial phase angle of ith satellite = m αi m = (0 to N-1)/Q ; N = PQ (P,Q are integers) Q = number of satellites per plane

Hybrid constellations : 

Hybrid constellations This combines the various types orbits for full earth coverage These orbits have different orbital period Eg: using circular orbits for covering equatorial regions and elliptical orbits for higher altitude regions Eg: using GEO for covering equatorial regions and inclined orbits for polar regions

Regional coverage:In some cases it is necessary to cover only a part of the world. This is made possible by number of spot beams. Here it is necessary to ensure that all the satellites pass over the same service area.Eg: equatorial regions may be covered by deploying satellites in equatorial planesUsing elliptical orbits inclined at 63.40 can be used for covering high altitude because satellites in these orbits dwell over high altitudes over a considerable time. : 

Regional coverage:In some cases it is necessary to cover only a part of the world. This is made possible by number of spot beams. Here it is necessary to ensure that all the satellites pass over the same service area.Eg: equatorial regions may be covered by deploying satellites in equatorial planesUsing elliptical orbits inclined at 63.40 can be used for covering high altitude because satellites in these orbits dwell over high altitudes over a considerable time. Thuraya allows to create more than 200 spot beams and handle 13,750 simultaneous phone calls. Telecommunications Services offered are: Voice Fax at 9.6 Kbps Data at 9.6 Kbps

Slide 121: 

Footprint and spot beams

Slide 122: 

Constellations for store and forward system: Systems which do not require real time coverage (messaging/paging) is less stringent because gaps in coverage are allowed, provided at least one satellite is visible within (ta-td) where ta=specified end to end delay , td=delay in message transfer Eg :A single satellite in polar orbit can cover every regions of earth within a time dependent on the orbital period ORBCOMM provides low cost, reliable, two-way data communications services around the world through a global network of 29 low-earth orbit (LEO) satellites and accompanying ground infrastructure. The system can send and receive short messages, between six bytes and several kilobytes

Random and phased constellations : 

Random and phased constellations Constellations can be categorized on the basis of phase relationship between satellites with respect of each other. In random constellation all or some constellation parameters such as altitude inclination, inter orbital plane separation and inter satellite phase are chosen at random. In phased constellation all these parameters are well defined. Random constellations are simpler to maintain but are inefficient in terms of coverage property and tend to randomly crowd the celestial sphere around the chosen altitude.

Design considerations of a non GEO satellite systems : 

Design considerations of a non GEO satellite systems 1.Traffic distribution and coverage: A constellation design depends on service area and geographical distribution of traffic within that area. A worldwide coverage is essential for an operator interested in global operations, but regional operator is interested in only a specific region. Hence the constellations are completely different. Good RF visibility ensures adequate signal strength before a connection is established and the increase in spectrum reuse. Complexity in coverage design is the dynamic variation in position of the footprint of each satellite and the constellation as a whole, making the geometric relationship time dependent. Hence an estimate can be made on the basis of known growth trends from existing systems, population density, per capita income, existing infrastructure, market segmentation due to competition and prevailing economic /political condition of the target market.

Slide 125: 

2. Satellite capacity: The capacity required per satellite increases as the orbit altitude increases because a satellites field of view and captured traffic increases with the altitude Total constellation capacity is the sum of capacities of satellites At higher altitudes satellite capacities are better shared Hence as the altitude increases, total constellation capacity reduces and more efficient constellation capacity is utilized 3. State of spacecraft technology: Antenna size and complexity -as the altitude increases , larger antennas are required to meet link quality objective and maintain frequency reusability Spacecraft DC power -DC power determines the capacity of the satellite Inter satellite link -satellites with inter links influence the network routing scheme

Slide 126: 

4.Terminal characteristic and communication requirement- The size of terminals and their communication capability influence a satellites power and sensitivity requirements RF power of a handset is limited by radiation safety considerations, battery size /capacity and the target terminal cost If the satellites are brought closer , power required can be reduced but number of satellites in the constellations increases. 5.Quality of service: Quality of service refers to RF link reliability, propagation delay and signal quality measured as bit error rate Higher link reliability requires higher elevation angle Propagation conditions improve as the elevation angle increases because number of obstructions reduces Propagation delay is related to the altitude of orbit Hence for interactive applications lower orbits are best and non real time applications are insensitive to altitude Signal quality is related to link conditions and issues such as carrier to noise power density/modulation/coding schemes

Slide 127: 

6. Spectrum availability: Frequency reusability can be increased by spatial/polarization diversity This is achieved by using spot and shaped beams For a given spot beam size lower altitude constellations can give increased reusability Additional measures like modulation, coding and multiple access schemes can maximize radio resource 7. Orbital considerations: Space environment affects the orbit selection Atmospheric drag, eclipses, ionization 8. Launch considerations Important practical consideration is the launch cost, feasibility of launching the satellites in the acceptable time frame Probability of launch failure and in-orbit satellite failure increases as the number of satellites in the constellation increases.

Assignment 01 : 

Assignment 01 Explain about the effect of a) eclipse due to earth b) eclipse due to moon c) solar interference on geo-stationary satellites. Submit before:18.08.2008

Problems : 

Problems Q1. Find out the radius of a geostationary satellite orbit. Given: T = 23Hr 56Min 4.1Sec G = 6.672 X10-11 m3/kg/s2 M = 5974 X1024 kg r = 6378.1414 km take μ = √GM

Slide 130: 

Answer: T2 = 4 П2 .(R)3 μ R = [T√GM]2/3 ------------- 2П = [23x60x60+56x60+4.1√ 6.672 X10-11x 5974 X1024 ] 2П = 42164.17 km Altitude, h = R-r = 42164.17-6378.1414 = 35786.02 km

Slide 131: 

Q2. A satellite orbiting in equatorial plane has a period from perigee-perigee of 12 Hrs. Given that the eccentricity is 0.002. Calculate semi-major axis. Given: G = 6.672 X10-11 m3/kg/s2 M = 5974 X1024 kg r = 6378.1414 km

Slide 132: 

Answer: Eccentricity is 0.002 (0<e<1), hence orbit is elliptical. For an elliptical orbit, T2 = 4 П2 .(a)3 μ 12x60x60 =2 П √ a3/6.672x10-11 x 5974x1024 a3 = 1.886x1025 a = 266183.1516 km

Slide 133: 

Q3. Calculate the apogee and perigee heights for the given orbital parameters. e=0.0011501 and a= 7192.3 km Given: r = 6378.1414 km

Slide 134: 

Answer: ra=a(1+e) = 7200.57 km rp= a(1-e) = 7184.03 km Apogee height, ha = ra – r = 822.14 km Perigee height, hp = rp – r = 805.89 km

Slide 135: 

Q4. A satellite is in elliptical orbit with a perigee of 1000 km and an apogee of 4000 km. Using a mean earth radius of 6378.14 km , find the period of the orbit in hours ,minutes and seconds. Also find the ‘e’ of the orbit.

Slide 136: 

Answer: ra = ha+R =4000+6378.14=10378.14 km rp =hp +R=1000+6378.14=7378.14 km a= (ra + rp) T=√4П2a3/GM =8320.94 sec = 2hr 19 mts 8 sec ra = a(1+e) e= (ra/a) -1 = 0.169

Communication Satellites : 

Communication Satellites

Communication satellites (comsat) : 

Communication satellites (comsat) Satellite is a RF repeater in orbit. The design of a satellite is governed by the communication capacity, physical environment in which it is operated and state of technology. Main considerations of a comm. satellite are:- i) Type of service to be provided (eg: mobile communication, DTH) ii) communication capacity (transponder BW and satellite EIRP) iii) coverage area iv) Technological limitations Basic specifications are laid out for satellite depending on the communication requirement. A domestic fixed satellite service it is the EIRP per carrier, number of carriers and coverage area. A direct broadcast satellite it is the number of television channels and coverage area.

First TV image of weather (1960) : 

First TV image of weather (1960)

First complete view of world’s weather, photographed by TIROS 9 (13/2/1965).Image assembled from 450 individual photographs : 

First complete view of world’s weather, photographed by TIROS 9 (13/2/1965).Image assembled from 450 individual photographs

Environmental Conditions: : 

Environmental Conditions: A spacecraft must be reliable in all types of environments beginning from launch to the in-orbit deployment and throughout its operation phase. Most important stresses are- a) Zero gravity :- At GEO, gravitational force is negligible giving rise to zero gravity effects. Major effect is on liquid fuel flow and hence external means are to be provided for liquid flow. The absence of gravity facilitates operation of the deployment mechanisms used for stowing antennas and solar panels during launch. b) Atmospheric pressure and temperature :- At high altitudes, atmospheric pressure is extremely low (10-7 torr). This makes thermal conduction negligible and increase friction between surfaces. Hence special materials are used for lubrication of moving parts. However, pressure inside the spacecraft is higher because of out gassing of electronic components. The temperature of a spacecraft is mainly affected by heat from sun and various spacecraft subsystems. The excursion in the external temperature varies from 330-350K during sunlight and 95-120K during eclipses.

Slide 142: 

c) Space Particles :- Various types of particles like cosmic rays, protons, electrons, meteoroids, manmade debris etc exist in space. Main effect of bombardment of particles on a satellite is the degradation of solar cells and certain solid state components within the satellite. Effect of meteoroids is negligible in GEO satellites. d) Magnetic fields :- Magnitude of earth’s magnetic field is very weak at GEO (1/300 of earths surface). The effect of magnetic field can be compensated by the use of large coil. While Satellites passing through Van Allen belt ,deflected charged particles that are trapped in this region affect electronic components Hence special manufacturing mechanisms are used to harden the components against radiations. e) Other Considerations :- Due to the variation of distance of earth from sun, a variation in DC generation capability must be taken into account in design of satellite power system. Also satellites must be prepared for loss of power during eclipses and may result in gradual degradation of solar cell efficiency. There are several perturbations affecting the satellites due to movement of mechanical parts and fuel within it. There may be a small drift in position of antennas.

Life time and reliability : 

Life time and reliability Lifetime of a geostationary satellite is determined by the maximum acceptable deviation in inclination and orbital location. Satellite is maintained in its orbital location by firing thrusters regularly, using stored fuel Hence the operational lifetime of a satellite is determined by- a) Increasing fuel capacity b) Saving fuel by accepting orbital deviation to the maximum extent possible. However there is a practical limit to a satellites fuel storage capacity. Hence satellite lifetime is between 12-15 years.

Reliability : 

Reliability The overall reliability of a satellite is governed by its critical components. Reliability is improved by employing redundancy in the critical sub systems and in components such as TWT amplifiers. Reliability is defined as the probability that a given component/system performs its function within a specified time t. R= where λ= failure rate of a component Unit of λ is specified as FIT, the number of failures in 109 Hr.

Slide 145: 

Three regions can be identified An early high failure rate region attributed to manufacturing faults, defects in materials etc A region of low failure attributed to random component failures A region of high failure rate attributed to component wear-out. In a satellite system, early failures are eliminated to a large extent during testing and burn-in. The main aim is to minimize the random failures which occur during the operational phase of the satellite by using reliability engineering techniques. The beginning of wear-out failure can best be delayed by improving the manufacturing technique and the type of material used.

Slide 146: 

The reliability can be expressed as R = e-λt = e-t/m ; where m =1/ λ (mean time between failures) When several components or sub-systems are connected in series, the overall reliability is Rs=R1 R2…….Rn where Ri is the reliability of the ith component. In terms of the failure rate : Rs= e-(λ1+ λ2+… λn)t Parallel redundancy is useful when the reliability of an individual subsystem is high. If Qi is the unreliability of the ith parallel element, the probability that all units will fail is the product of the individual unreliabilities Qs=Q1 Q2…Qi When the unreliabilities of all elements are equal, this expression reduces to Qs = Qi ;Where Q is the unreliability of each element. Therefore the reliability is R = 1-Qs = 1- Qi =1- (1- R)i =1- (1- e-λt)i

Slide 147: 

A Typical reliability model of a Geostationary Satellite: All the major sub-systems are shown in series. Simplified reliability model Applying the equation for series and parallel combination, the reliability of the communication system is obtained as Rs =RRXRTX [1-(1-RT)2] When RT=0.9,reliability of transponder increases to 0.99 Figure of merit, Fγ = r/M ;where r = R’/R R’= reliability with redundancy employed R= reliability without employing redundancy M= increase in mass due to added redundancy The addition of redundant equipment increases the cost of the transponder

Back up slides : 

Back up slides

Transponder : 

Transponder

Solar eclipses : 

Solar eclipses

Slide 155: 

----Introduction to Solar System Dynamics---- 2.a a: semimajor axis e: eccentricity v: true anomaly (0…360 deg) rp ra Basic orbital elements (ellipse) rp: Radius of periapsis (perihelion) ra: Radius of apoapsis (aphelion) e=0: circle e<1: ellipse e=1: parabola e>1: hyperbola v r

Slide 156: 

----Introduction to Solar System Dynamics---- Useful orbital parameters (elliptical orbit) Velocity: Period: Energy: Angular momentum: M: mass of central body m: mass of orbiting body r: distance of m from M (M>>m) (Constant!) (Constant!)

Spin stabilization : 

Spin stabilization With spin stabilization, the entire spacecraft rotates around its own vertical axis, spinning like a top. This keeps the spacecraft's orientation in space under control. The spinning spacecraft resists perturbing forces. Designers of early satellites used spin-stabilization for their satellites, which most often have a cylinder shape and rotate at one revolution every second. Spin stabilization was used for NASA's Pioneer 10 and 11 spacecraft, the Lunar Prospector, and the Galileo Jupiter orbiter.

Slide 159: 

The advantage of spin stabilization is that it is a very simple way to keep the spacecraft pointed in a certain direction. A disadvantage of this stabilization is that the satellite cannot use large solar arrays to obtain power from the Sun. Thus, it requires large amounts of battery power. Another disadvantage of spin stabilization is that the instruments or antennas also must perform “despin” maneuvers so that antennas or optical instruments point at their desired targets.

Reaction wheel stabilisation : 

Reaction wheel stabilisation With three-axis stabilization, satellites have small spinning wheels, called reaction wheels or momentum wheels, that rotate so as to keep the satellite in the desired orientation in relation to the Earth and the Sun. If satellite sensors detect that the satellite is moving away from the proper orientation, the spinning wheels speed up or slow down to return the satellite to its correct position. Some spacecraft may also use small propulsion-system thrusters to continually nudge the spacecraft back and forth to keep it within a range of allowed positions. Voyagers 1 and 2 stay in position using 3-axis stabilization. An advantage of 3-axis stabilization is that optical instruments and antennas can point at desired targets without having to perform “despin” maneuvers

Alignment : 

Alignment There are a number of components which need alignment Solar panels Antennae These have to point at different parts of the sky at different times, so the problem is not trivial

Solar and sidereal day : 

Solar and sidereal day

Elliptical Orbit Geometry & Nomenclature : 

Elliptical Orbit Geometry & Nomenclature Periapsis Apoapsis Line of Apsides  R a c V Rp b Line of Apsides connects Apoapsis, central body & Periapsis Apogee~ Apoapsis; Perigee~ Periapsis (earth nomenclature) S/C position defined by R & ,  is called true anomaly R = [Rp (1+e)]/[1+ e cos()]

ORBITAL ELEMENTSKeplerian Elements: True Anomaly : 

ORBITAL ELEMENTSKeplerian Elements: True Anomaly