MUHAMAD ASVIALCenter for Information and Communication Engineering Research (CICER)

Electrical Engineering Department, University of IndonesiaKampus UI Depok, 16424, Indonesia

asvial@ee.ui.ac.idhttp://www.ee.ui.ac.id/cicer

Orbital Type and Coverage

Lecture 4

1

• The Orbit of SatelliteThe path of a satellite in the orbital plane is shown in Figure 3.2-1. The lengths a and b of the semi-major and semi-minor axes are given by

a = p/(1 – e2)b = a(1 – e2)1/2

where p is semi-latus rectum (= h 2/µ, where h is the magnitude of the angular momentum of the satellite and µis Kepler’s constant, GMe) of the ellipse, and e = 1 for an elliptical orbit and e = 0 for a circular orbit.The point in the orbit where the satellite is closest to the earth is called perigee and the point where the satellite is farthest from the satellite is called apogee. Perigee and apogee are always opposite to each other.In Figure 3.2-1, the point O is the center of the earth and the point C is the center of the ellipse

Figure 3.2-1 The orbit as it appears in the orbital plane.Figure 3.2-1 The orbit as it appears in the orbital plane.

Eccentricity, e, is measure of elongation and is given by e = [(a2-b2)/a2]1/2

2

• KEPLER’S LAWS- Though originally stated to describe the motion of planets around the sun, Kepler's Laws also apply to comets

First Law: Satellite will orbit the Earth following an elliptical path, with bary-center (center of the mass of two body system) lies at one of its two foci, that is geo-center (center of the Earth)

“The orbit of a satellite is an ellipse with the center of the earth at one focus”

3

• KEPLER’S LAWS- Though originally stated to describe the motion of planets around the sun, Kepler's Laws also apply to comets

Second Law: the radius vector to the satellite sweeps out equal areas in equal times i.e, the rate dA/dt at which it sweeps area A is constant. The rate of change of the swept out area is given by

dA/dt = angular momentum of satellite (mr2ω)/2m (3-7)where m is the mass of the satellite, and ωis the angular velocity of the radius vector. Since the term on right side of eqn. (3-7) is constant, this shows that the rate at which area is swept out by the line connecting the orbiting body to the central one is constant. This means that the satellite/planet will move faster when it is nearer the earth and slower when it is farther from the earth/sun.

“The line joining the center of the earth and the satellite sweeps over equal areas in equal time interval (Figure 3.2-2) ”

Figure 3.2-2 Kepler’s second lawFigure 3.2-2 Kepler’s second law

4

•KEPLER’S LAWS-Third Law: “the square of the orbital period of any satellite/planet is proportional to the cube of the average distance (semi-major axis of its elliptical orbit) from the satellite/planet to the earth/sun”

GMem/r2 = m2/r

Here 2/r is centripetal acceleration and G is a universal gravitational constant = 6.672 X 10-20 km3/kg s2).

The speed of the satellite in its orbit is equal to the circumference of the orbit divided by the time for one revolution, T, called the period of the planet. That is = 2r/T, and the above expression becomes

GMe/r2 = (2r/T)2/rOr, T2 = (42/GMe) x r3

T2 = (4π2 /µ) x r 3 = Ksr3 (3-10)Where Ks constant is given by Ks = (42/GMe) = 2.97 X 10-19 s2/m3

= m2/r

Tangential velocity

r Gravitational force = GMem/r2

Me

r

= m2/r

Tangential velocity

r Gravitational force = GMem/r2

MeMe

r

T 2 = (4π2 /µ)a 3 or, T = 2π√(a3/µ)

Figure 3.2-3 Kepler’s law and orbital forces

5

• BASIC Definitions– Apogee– Perigee– Major Axis– Minor Axis– Line of Apsides

6

• Basic Definitions– Satellite Orbital Paths

• Polar• Equatorial• Inclined

– Angle of Inclination (0-180 deg, 0-90 deg defines prograde orbits, and 90-180 deg defines retrograde orbits)

– Ascending & Descending Nodes• Line of Nodes Next

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(b)(b)

• Polar Orbits

Figure 3.5.2-1 (a) Polar orbit (b) Geostationary orbit and one possible polar orbit

(a) (b)

Figure 3.5.2-2 Polar orbiting satellite (a) first pass; (b) second pass, earth having rotated 25. Satellite period is 102 min.

(a)(a)

8

• Equilateral Orbits

Figure 3.5.1-1 Coverage of an equatorial orbit LEO satellite

Equatorial LEO satellite

Coverage of LEO satellite

S

N

Equatorial LEO satellite

Coverage of LEO satellite

S

N

9

• Inclined Orbits

Figure 3.5.3-1 Inclined orbit

• Provides satellite visibility in the polar regions.• Provides higher elevation angles to user locations at

high northern and southern altitudes.• Requires users to acquire and track the satellites.• Periodically users must switch from a “setting” to a

“rising” satellite (handover problem).• Number of orbital belts and satellites per belt is a

complex function of many parameters (e.g., coverage, elevation angle, viewing time requirement etc.)

Figure 3.5.3-2 Coverage of an equatorial orbit LEO satelliteFigure 3.5.3-2 Coverage of an equatorial orbit LEO satellite

10

• Basic Definitions– Sub-Satellite Point: A point on the earth surface v

ertically under the satellite

Nadir direction

Zenith directionSubsatellite point

C

Figure 3.4-2 Zenith and nadir pointing directions

11

• SATELLITE ORBITS– Satellite Elevation Categories:

LEO (100-500 Miles), MEO (6000-12000

Miles), GEO (19000-25000 Miles) and HEO (400 km-40,000 km)

12

• GEOSYNCHRONOUS SATELLITES-Some basic Facts

– T = 23 hrs, 56 min. and 4.1 sec– Angle of Inclination: 0-90 deg wrt to

equator-a prograde orbit– Orbit eccentricity, e=0, a circular orbit– A system of three such

Geosynchronous satellites can cover the whole globe (81 deg south – 81 deg north) except polar regions

– Beam BW = 17.3 deg, – Three satellites at the nodes of an

Equilateral Triangle with side = 88k km

– Availability = 100%– Today Approx. 150 Comm. Satellites

out of which 100 in Geosynchronous Orbit

– Examples: First GEO Syncom 2 by NASA, Intelsat Series

Geosynchronous inclined orbit

Geostationary satellite

Geostationary equatorial orbit

N

S

i

Geosynchronous satellite

Geosynchronous inclined orbit

Geostationary satellite

Geostationary equatorial orbit

N

S

i

Geosynchronous satellite

Figure 3.6.1-1 Geosynchronous and geostationary satellite orbits

13

• GEOSYNCHRONOUS SATELLITES-

Some basic Facts

Figure 3.6.1-1 Global coverage

120O

17..3 beamwidth for earth coverage

42,162 km geostationary orbit

radius

Atlantic Ocean (relay station)

Pacific Ocean (relay station)

Indian Ocean (relay station)

264,000 km

88,000 km

36,000 km

(a) Equilateral triangle

14

Ground Tracking of Geosynchronous Satellites and Figure of Eight

Figure 3.6.1-2 Satellite in a geo orbit (a) angle of inclination (b)track of a geosynchronous satellite (figure of 8) for different orbit inclination angles (c) correction velocity impulse application

Node

v = 3074.7 m/sΔv

(c)

i

(a)

N

Equator

W

(b)

15

• GEOSYNCHRONOUS SATELLITES

– Geostationary Satellites orbiting Earth in equatorial plane or orbit at about 6840 mph and complete their revolution in 24 hrs (in sync with earth’s rotational speed about its own axis)

– Three Necessary Conditions for Geostationary Orbit:

• Satellite must travel eastward in synch with Earth

• The Eccentricity, e=0 (Circular Orbit)• The inclination angle = 0 deg

– Only one Geostationary Orbit– Orbit height 35, 800 km (22, 300 miles)

above earth surface– Global coverage – 43 % of earth– Due to gravitational pull of moon (three

times greater than sun), orbit tends to be non-circular and inclined (0.86 deg/year)

– Both East-West and North-South Station Keeping is required

16

• GEOSYNCHRONOUS SATELLITES– GEO Satellite Altitude, Orbital Velocity, and Round-T

rip Delay

17

18

• Coverage Geometry – Key parameters with any Satellite in an orbit are:

– Coverage Area, As – portion of the earth surface receiving Satellite Transmission (acceptable signal strength or C/N ratio) with EA > min prescribed EA

– Slant Range, Rs – LoS distance between ES and Satellite

– Satellite Visibility Duration- time duration for Satellite remains visible at ES with given EA

Subsatellite point

= 90 - ( + )

B

Subsatellite point

= 90 - ( + )

B

Figure 3.8.1-2 Coverage area geometry

= 90 - ( + ); Nadir angleh = height of satellite above the earthH = height of satellite from center of earthRs = slant range, terminal-to-satelliteRe = radius of earth = elevation angle at terminal (look angle) = angular radius of visibility, coverage angleC = center of earthAs = coverage areaP = sub-satellite point2 = Communication coverage angle

19

• Coverage AreaThe coverage area, AS, from which the satellite is visible with an elevation of at least α is given by

AS = (2R2e)(1- cos ) (3-44)

Where = cos-1[Recos/(Re+ h)] -

Since the total Earth’s area is 4Re2, we can rewrite AS as a

fraction of the total earth surface: AS/4Re

2 = 0.5(1 - cos) (3-45)

Subsatellitepoint

= 90 - ( +)

B

Subsatellitepoint

= 90 - ( +)

B

Figure 3.8.1-2 Coverage area geometry

= 90 - ( + ); Nadir angleh = height of satellite above the earthH = height of satellite from center of earthRs = slant range, terminal-to-satelliteRe = radius of earth = elevation angle at terminal (look angle) = angular radius of visibility, coverage angleC = center of earthAs = coverage areaP = sub-satellite point2 = Communication coverage angle

20

Antenna Coverage

• GLOBAL coverage antenna

• ZONE coverage antenna

• SPOT BEAM coverage antenna– Example: INTELSAT VI coverage of

Atlantic Ocean Region (AOR)

21

(a) INTELSAT VI COVERAGECONTOURS FOR THE “AOR” from 335.5° E longitude.(b) INTELSAT VI coverage contours for the “IOR” from 63° E longitude.

INTELSAT VI Coverage Areas

22

Geostationary Satellite Orbit

The satellite orbits in the equatorial plane on a circular orbit at an angular velocity equal to that of the Earth.

23

HEO Orbit Options

24

Van Allen Radiation Belts

25

First Generation S-PCN Constellations

Leader No. of Satellites

Altitude

(km)

Coverage No. of beams

New

Technology

Iridium Motorola 66 789 Global 48 ISL/OBP

Globalstar Loral 48 1414 ±70º lat. 17 N/A

ICO Inmarsat 10 10355 Global 163 N/A

Iridium 37,163 and 19 Satellite spotbeams

LEOMEO

LEO

26

Personal Mobile Satellite Communications (3)

27

Personal Mobile Satellite Communications (4)

28

Personal Mobile Satellite Communications (5)