Lecture 2, Space Segment (http://www.satcom.co.uk/article.asp?article=29)

Introduction

Welcome to the second lecture in the RPC Satcom Tutorial series.

At any point in the lecture, you can skip to a latter section, or back to earlier sections using the guide on the left.

If you want to check out the other Lectures in this series, you can find Lecture 1 (General Principles) here, and Lecture 3 (Earth Segment) here.

Topics contained in this lecture:

  • Orbit Theory
  • Orbits
  • Hardware
  • Launch Vehicles
  • Stationkeeping

Laws Of Motion

Kepler's laws were originally developed to describe the motion of planetary bodies, but they are just as relevant for theoretical satellite orbits around the earth.

  • Each planet moves around the sun in a ellipse with the sun at one focus (i.e motion is in a plane).
  • A line from the sun to a planet (radius vector) sweeps out equal areas in equal intervals of time.
  • The ratio of the square of the orbit period (T) to the cube of the semi-major axis (a) is a constant (i.e T2/a3 = constant)

The geometry of an ellipse:

and: c2=a2-b2

Eccentricity (e) is defined as:

e2=1-(b/a)2

Newton's universal law of gravitation tells us that:

F=(G.M.m)/r2

From Newton's Second Law of Motion we get:

F=m.a

Centripetal acceleration (assume circular motion for simplicity):

a=v2/r

Taking these three expressions, and simplifying we get the following equation:

v=(G.M/r)0.5

i.e ω=(G.M/r3)0.5

Keplerian Elements
The "Keplerian Elements" are a set of 6 parameters which define the position of a satellite at a given epoch (date and time) as well as defining the shape and position of its elliptical orbit around the Earth.

The 6 parameters are outlined below.

  • Right Ascention of the Ascending Node
    The angle in the equatorial plane between the direction of the first point of Aries and the direction to the ascending node, measured counter-clockwise when viewed from the north side of the equatorial plane.
  • Argument of Perigee
    The angle in the plane of the satellite orbit between the ascending node and the perigee, measured in the direction of the satellite motion.

  • Mean Anomaly
    The angle at the Earth's centre, measured from the perigee in the direction of the satellite's motion, which the satellite would have if it were moving at a constant angular speed, i.e M = 2*π*t/T (radians), where T is the orbital period.
  • Semi Major Axis
    Half the length of the longest diameter of the ellipse.
  • Inclination
    The angle between the Earth's equatorial plane and the plane of the satellite, measured positively above the equatorial plane with reference to the ascending segment of the orbit.
  • Eccentricity
    A term defining the "circularity" of the ellipse; e=0 is a cirlce, e = 1 is a line (i.e a totally flat ellipse).

With these elements at a known epoch, it is possible to fix the position of the satellite in space and predict its theoretical future movement.

Simplifying Assumptions
  • Consider the Earth to be stationary and the origin of all coordinates is located at the Earth's centre
  • Consider the satellite and the Earth (much more significant) to be spherically symmetric (i.e treat m and M as point masses)
  • Assume that the satellite is subject only to one force - the gravitational attraction from the Earth - which varies as the inverse ratio to the square of the distance between centres of mass (this is highly unrealistic in the real world)

Note: The theoretical equations can fully determine the relative orbital motion of two bodies, but the case of three bodies has no analytical solution.

Kepler And Satellite Ephemeris Formulae

Semi-Major Axis of satellite orbit:

Smaj = ((T/(2*π))2*Mu)(1/3)

Notes:

T is the orbit period (seconds)
Mu is the product of the gravitational constant and the earth's mass.
Mu=G*Me=6.67*10-11 * 5.974 * 1024
Mu=3.986*1014 metres3/second

Semi-Minor Axis of satellite orbit:

Smin = (Smaj2-C2)0.5 metres

Notes:

C = E*Smaj=Smaj-Pe=Ap-Smaj
E is the eccentricity of the orbit
Pe-R is the perigee (or the minimum) satellite altitude in metres.
Ap-R is the apogee (or the maximum) satellite altitude in metres.
R is the radius of the Earth (6378 * 103 metres)

Mean Anomaly

M = Ecc - E*sin(Ecc)

Notes:

M is the mean anomaly and the mean angle between perigee and satellite, as seen from the centre of the earth at any date and time.
M=ω*time + Anom
Anom is the reference value of the mean anomaly (M) at a specified date and time.
ω is the mean angular velocity of the satellite as seen from the centre of the earth = 2*π/T
Ecc is the eccentric anomaly which can be treated as a variable defined by the equation above.

Virtual Anomoly

V = tan-1(tan(Ecc/2)*((1+E)/(1-E)))

Notes:

V is the virtual anomoly or the true angle between perigee and satellite, as seen from the centre of the earth, at any date and time.

Radius of Satellite Orbit

Radius = Smaj*(1-E2)/(1-E*cos(V)) metres

Notes:

Radius of the satellite orbit is the distance between the satellite and the centre of the earth at any date and time.
Satellite altitude = Radius - R

Satellite Linear Speed

Speed = (Mu*(2/Radius - 1/Smaj))0.5

Notes:

Speed of the satellite is the linear speed of the satellite at any date and time.

Sub-satellite Latitude

Q = sin-1(sin(I)*sin(V+Per))

Notes:

Per is the argument of the perigee and the angle between the perigee and the ascending node i.e. the angle between perigee and the equator (satellite heading north) within the satellite's orbital plane.
I is the satellite orbit inclination angle and is the maximum angle between the equatorial plane and the plane of the satellite orbit.

Sub-satellite Longitude

U = cos-1(cos(V+Per)/cos(Q)) + Asc

Notes:

Asc is the ascending node and the angle in the earth's equatorial plane between Aries and the satellite's orbital plane (satellite heading north).

Geometric Formulae
Great circle angle between an earth station and a satellite

Ngc = cos-1(sin(P)*sin(I)+cos(P)*cos(I)*cos(Us-Ue))

Notes:

P is the earth station latitude
Ue is the earth station longitude
I(t) is the satellite (instantaneous) inclination
Us(t) is the (instantaneous) longitude of the sub-satellite point

Earth station elevation angle to the satellite

Ee = tan-1((cos(Ngc)-R/(H+R))/sin(Ngc))

Notes:

R is the radius of the earth (6378*103m)
H(t) is the (instantaneous) altitude of the satellite (geostationary satellite: 35786*103m)
Ngc is the great circle angle

Earth station azimuth angle to the satellite

Ae = tan-1(sin(Usat-Ues)/(sin(P)*cos(Us-Ue)-tan(I)*cos(P))

Notes:

It is necessary to investigate the signs of the numerator and denominator to find the quadrant in which the azimuth angle is.

Earth station off-axis angle between the principal axis of the antenna and the direction of a second satellite

Ne = cos-1(sin(Ee1)*sin(Ee2)+cos(Ee1)*cos(Ee2)*cos(Ae1-Ae2))

Notes:

Suffixes 1 and 2 denote angles to the first and second satellites.

Slant range between an earth station and satellite

S = (-)R*sin(Ee)+((R*sin(Ee))2+H*(H+2*R))0.5 metres

S = R*sin(Ngc)/cos(Ee+Ngc) metres

Geostationary satellite azimuth angle where the earth's axis of rotation defines zero degrees azimuth

As = sin-1(R*cos(P)/Z*sin(Us-Ue))

As = tan-1(R*cos(P)*sin(Us-Ue)/(R+H-R*cos(Us-Ue)*cos(P)))

Notes:

Z=(R2*cos2(P)+(R+H)2-2*R*cos(P)*(R+H)*cos(Us-Ue)0.5)
Z=(S2-R2*sin2(P))0.5
I (satellite inclination angle) is zero.

Geostationary satellite elevation angle where the earth's equatorial plane defines zero degrees elevation

Es = sin-1(R*sin(P)/S)

Es = tan-1(sin(As)*tan(P)/sin(Us-Ue))

Notes:

I (satellite inclination angle) is zero.

Satellite off-axis angle between the principal axis of the satellite antenna and the direction of the earth station

Ns = cos-1(sin(Ese)*sin(Esb)+cos(Ese)*cos(Esb)*cos(Ase-Asb))

Notes:

Esb is the satellite elevation angle in the direction of the boresight.
Ese is the satellite elevation angle in the direction of the earth station.
Asb is the satellite azimuth angle in the direction of the boresight.
Ase is the satellite azimuth angle in the direction of the earth station.

Beamwidth of a satellite antenna with an elliptical beam in the direction of an earth station

Phio = (A2*B2/A2(sin(Q))2+B2(cos(Q))2))0.5

Notes:

A is the major axis of the ellipse
B is the minor axis of the ellipse
Q=tan-1((Ese-Esb)/(Ase-Asb)) - O
O is the orientation of the ellipse defined as the counter clockwise angle from a line parallel to the equatorial plane to the major axis of the ellipse.

Earth station latitude expressed in terms of satellite azimuth and elevation angles

P = sin-1(tan(Es)/R/cos(As)*(R+H-R*cos(Ngco)))

Notes:

cos(Ngc)=cos(Us-Ue)*cos(P)
cos(Ngc)=cos(sin-1((R+H)/R*sin(Nso))-Nso)
Ngco is the great circle angle between an earth station and a geostationary satellite (can be found by letting I=0 in our first equation in this section).
Nso=cos-1(cos(Es)*cos(As))
Nso is the angle between the sub-satellite point and the earth station as determined from the geostationary satellite (can be found by letting Esb=0 in our equation for Ns above).

Earth station longitude expressed in terms of satellite azimuth and elevation angles

Us-Ue = sin-1(sin(As)*tan(P)/tan(Es))

The Real World
(Refer to simplifying assumptions from section 1)

The stationary point is the centre of mass, not the centre of the Earth - but the satellite is so small as to make this negligible in virtually all cases.

The earth cannot be treated as a point mass since it is not a sphere:

  • Polar flattening is 1/298th of the equatorial radius (i.e. approximately elliptical polar cross section)
  • "Gravity field" is not smooth - i.e. gravity is stronger or weaker in some areas than a smooth, homogeneous Earth would indicate.

Other forces will act on the satellite to perturb the orbit:

  • Gravitational force of Sun and Moon
  • Atmospheric drag (in lower orbits)
  • Minor perturbations (planetary gravity, solar pressure, magnetic interaction with Earth's magnetic field)

The effects of the "real world" forces are to cause movements of the satellites orbit relative to the Earth which would not be predicted by Kepler:

  • Precession of the orbit plane around the Earth's N-S axis
  • Precession of the orbit perigee n the plane of the orbit

This means that not all orbits are useful!

Approximate magnitudes of relative forces acting on a satellite at specific heights above the Earth's surface:

h=370km h=37,000km
Sun 7 * 10-4 3 * 10-2
Moon 4 * 10-6 1 * 10-4
Earth's oblateness 1 * 10-3 4 * 10-6

[Relative force = (Average force exerted by perturbation) / (Force exerted by a symmetrical Earth)]

Major perturbations of a general satellite orbit:

Relatively complex equations govern rate of precession of argument of perigee and plane of orbit.

Stable or near stable conditions exist which lead to useful orbits:

  • "Molniya" orbit
  • Sun-synchronous orbits

Perturbations mean that real orbits cannot be predicted over extended period, however prediction is reliable over short periods of a few days for most orbits.

So predictions are used based on regularly updated orbital element sets to determine the real world satellite path and position.

Types of Satellite Orbit

Geostationary Orbit
  • 24 hour period
  • 36,000 km altitude
  • circular orbit
  • always visible to an Earth station in the coverage area
  • zero (or very small) inclination for true geostationary case
  • still the most important orbit for telecommunications but overcrowding is a growing problem

Low Earth Orbit

  • short orbital period (few hours)
  • typically 100 - 600 km altitude
  • usually circular orbit
  • each satellite is only visible to an Earth station for typically less than one hour
  • often used in multi-satellite constellations
  • of growing interest at the present

Highly Elliptical Orbit

  • usually refers to special cases such as "Molniya" or "Tundra"
  • make use of special case solution to give zero precession of arguement of perigee (63.4 inclination)
  • Molniya has 24 hour period, perigee of 24,470 km and apogee of 47,100 km
  • very useful because when used in constellations they provide "quasi-stationary" coverage to higher latitudes which cannot be served by geostationary satellites

Intermediate Orbits

  • orbital periods typically several hours
  • typically 10,000 - 20,000 km altitude
  • Earth station visibility typically several hours
Satellite Orbit Implications On Design
Coverage
  • What is the visible area of the Earth from each satellite?
  • Is satellite interlinking required?

Period & Visibility

  • How long can one Earth station see a satellite?
  • What arrangements are required to handover between satellites?

Environment & Power

  • Does the satellite need special arrangements to protect from radiation or to provide power capacity to deal with eclipse periods?

Number of satellites required?

Number of Earth stations required?

Satellite Hardware

A satellite is comprised of a payload supported by a platform.

The platform takes up the largest proportion of the mass of the satellite - design objectives is therefore to support the largest possible payload with the smallest possible platform.

Platform comprises:

  • Physical support structure
  • Power
  • Propulsion
  • Thermal control
  • AOCS (altitude control and stationkeeping)
  • TTC&M (telemetry and telecommand)
  • control processor

Payload comprises:

  • Antenna sub-systems
  • Communications transponders (receivers, amplifiers etc)

Major Spacecraft Sub-Systems:

Payload Block Diagram:

Earth Illumination

One satellite in the GSO can "see" about one third of the Earth's surface so can provide telephone, data and TV links over the whole of that area. 

However, coverage is impossible to the polar regions (beyond about 80 latitudes). (An aircraft at 30,000 feet can still communicate at latitude 85)

MSS satellite antennas commonly have maximum gain (about 21 dBi) at the edge of coverage, and lower gain (18 dBi) at beam centre.

Three geostationary satellites at 120 spacing provide full Earth coverage (except for the polar regions).

 

Satellite Beam Options
Global Beam
  • Low gain (~18 dBi)
  • Shaped (~21 dBi) MSS - uplink budget critical

Shaped Beam

  • Hemispherical coverage (~22 dBi)
  • Zonal coverage (~30 dBi)

Continental Spot

  • CONUS
  • pan-European e.g. EUTELSAT SMS

Spot Beam

  • e.g. INTELSAT Ku-Band spots.

A choice of smaller beam means higher gain and EIRP but at the cost of a reduced coverage and possibly connectivity.

  • Ku-band BSS plan UK 1.84*0.72 elliptical beam (~44 dBi)
  • L-band super GSOs (~42 dBi) with 140 to 250 beams
  • Ka-band super GSO (~44 dBi) e.g. Spaceway
  • L-Band LEOs e.g. Iridium 37 beams per satellite and 2025 beams for earth coverage
  • Satellite on board processing needed for mesh networks

Launch Vehicles

Expendable Vehicles
  • Ariane (Europe)
  • Delta (USA)
  • Atlas Centaur (USA)
  • Proton (Russia)
  • Long March (China)
  • Japan + others?

Reusable Vehicles

  • STS - Space Shuttle (USA)
  • Europe (Hermes)?
  • Russia?

Unconventional Approaches

  • Cruise Missiles
  • Floating platforms

 

Vehicle GTO/kg GSO/kg
Delta 3194 900 480
Delta PAM-D 1250 670
Atlas-Centaur 2000 1070
Titan IIIC - 1400
Ariane 3 2400 1500

 

Space Transportation System (space shuttle) can deliver to LEO/Parking orbit only. Also the payload must have additional PAM/PKM to achieve GTO. Total STS payload bay launch capability is very large, but must take account of the support cradle and also the PAM stage.

All prices are quoted for a dedicated launch. Estimated prices are shown underlined:

Vehicle Mass to GTO GTO Inclination Reliability Cost (1993)
Ariane 44LP 3900kg 7 94.1% $92M
Ariane 5 6900kg 7 ? $120M
Atlas IIAS 3630kg 28.5 94% $137M
Long March 2E/HO 4800kg 28 92% $30M ($58M)*
SL-12 Proton-KM 4500kg to GEO N/A 98% $30-$40M
Titan III 4500kg 28.5 96.4% $120M
Titan IV Centaur 4500kg to GEO N/A >90% $200 - $300M
Delta II 1819kg 28.5 93.6% $50M
H-II 4200kg 30.5 ? $70M
HOTOL 3700kg ? >98% $1-$5M

*Long March have quoted a price of $30 million, but in order to protect the interests of western launch vehicles, the US has used the COCOM rules to prevent Long Match from launching any vehicle commercially for less than $58 million. This is likely to apply also to the Soviet Proton and other soviet vehicles.

Launch Manoeuvres
Target orbit (e.g. GSO) cannot, usually, be achieved in a single trajectory. Launch vehicles are "multi-staged" so propulsion is a series of distinct "burns".

In-plane manoeuvres:

  • changing orbit shape
  • raising or lowering apogee or perigee height
  • can be achieved with relatively low energy input (i.e. low fuel consumption)

Out-of-plane manoeuvres:

  • change of orbit inclination
  • rotating plane of orbit in space
  • requires relatively high energy input (i.e. high fuel consumption)

Launch Flight Plan

The launch flight plan is different for Expendable and Reusable Launch Vehicles.

The flight plan will be comprised of clear stages seperated by motor "burns"

  • boost phase
  • parking orbit
  • transfer orbit
  • final orbit

The objective is usually to achieve target orbital position with the minimum fuel used, but this takes the maximum time to achieve.

An operator can trade off fuel for speed. However, you cant refual a satellite in orbit (yet!).

Reusable Launch Vehicle

Elliptical transfer orbit - "Hohmann Transfer Ellipse" - is minimum energy path between two circular orbits.

Expendable Launch Vehicle

Maintaining The Satellite In Orbit
Stationkeeping:
  • Maintaining the nominal orbital position against perturbing forces
  • re-locating the satellite to a new orbital longitude position

Attitude Control and Stabilisation

  • Maintaining orientation of satellite's communications antennas in the direction of the Earth and with the correct rotational positioning
  • Maintaining orientation of solar panels in the direction of the sun to maximise electrical power generation
  • re-establishing orientation in the event of the satellite "tumbling" in space

Stationkeeping and Stabilisation require two elements:

  • Sensors to fix orientation in space
  • Reaction devices to provide stabilisation forces to move the satellite
Sources of Positional Data
Sun
  • bright and unambiguous
  • but, will not be visible during eclipse
  • accuracy is ~1 arc minute
  • direction must be known to align solar panels

Earth

  • always available, bright and unambiguous
  • but, large angle at most satellites may require a scanning motion, must be protected from sun
  • accuracy is ~0.1 because of horizon definition due to atmosphere
  • direction must be known to align antennas

Magnetic Field

  • economical, low power requirements, always available for low altitude satellites
  • but, poor resolution (~0.5), good only near the Earth, spacecraft must be magnetically clean

Stars

  • available anywhere in the sky with very high accuracy (~0.001)
  • but, sensors are heavy, complex and expensive, identifying targets is slow and complex, sensors need protection from the sun, multiple stars may cause problems

Inertial Space (gyroscopes and accelerometers)

  • requires no external sensors, highly accurate for limited time intervals
  • but, senses changes in orientation only, subject to drift, rapidly moving parts

Sensor Technology

Sun Sensors
  • Cosine Detector

  • Digital Sensor

Spinning Earth Sensor (Earth Horizon Telescope)

Reaction Devices
Gas Thrusters
  • provides stabilisation, stationkeeping and attitude control
  • single or bi-propellant fuel (hydrazine + catalyst, monomethyl hydrazine + oxidiser - nitrogen tetroxide)
  • significant impulses may be generated for major orbit manoeuvres, also suitable for small impulse attitude control
  • but, quantity of fuel is limited by launch mass - more fuel means less payload

Momentum Wheels

  • primarily for stabilisation/attitude control
  • one, two or three axis stabilisation

Reaction Wheels (e.g. Olympus)

  • need gas thrusters for "momentum dumping"

Spin Stabilisation

  • alternative method to provide stabilisation/attitude control
  • antennas must be despun through BAPTA which is a possible single point failure mechanism
  • only provides stabilisation in one axis so other devices (usually gas thrusters) are still required

Ion Thrusters

  • of increasing interest - no on-board fuel
  • only provide low impulse thrust but over an extended period
  • technology not yet proven for space use

Other Approaches

  • solar sails
  • magnetic coils
  • gravity gradient
Gas Thrusters
Mono-propellant system:

Rubber diaphragm or capillary action used to ensure fuel is expelled from output pipe. Heaters are used to increate specific impulse.

Bi-propellant system:

Commonly used for both apogee motor and stationkeeping. Tanks commonly oversized and fuel added until satellite has specified wet mass.

Copyright 2002 Satcom Online (http://www.satcom.co.uk)
21/04/2018  01:19:25