eele 6335 telecom. chapter 3: system the geostationary...

Dr.Mohammed Taha El Astal, IUG, EE dept, 2016

10/5/2016

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EELE 6335

Telecom. System

Part I:

Satellite Communic

ations

Winter 2016

Prepared by

Dr. Mohammed Taha El Astal

Chapter 3:

The Geostationary Orbit

Content

Introduction

Antenna Look Angles

The Polar Mount Antenna

Limits of Visibility

Near Geostationary Orbits

Earth Eclipse of Satellite

Sun Transit Outage

Launching Orbits


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3.1 Introduction

• Three conditions to be geostationary:

The sat. must travel eastward at same speed ofearth, why?

The orbit must be circular, why?

The inclination (i) of the orbit =0, why?

• It appears stationary with respect o the earth

Otherwise, it will not appear stationary

the 2nd Kepler law (fixed interval swept same areas) and the fixed speed can not be hold unless the orbit is circular

Otherwise, it will not appear stationary as it will shift to north & south

Cont.

• N.B. If the our normal day is assumed to be meansidereal day (earth-axis rotation period) not themean solar day, then ??

• In practice, a precise geostationary orbit can not beattained, due to:The disturbance forces in space (shift in i= 0.85◦ /day)

Earth’s equatorial bulge & ellipticity (shift eastword alongthe orbit)

Example 3.0 : Find the height of the geostationary orbit, given that p=23 h, 56 min, 4 sec mean solar time(ordinary clock time)

Answer : ℎ𝐺𝑆𝑂 = 35786 ≅ 36000𝑘𝑚 N.B.: Earth rotation about its axis =p not 24h

It results that in a day the sun is clear in midnight !!

This difference is resulted due to earth movement =(1/365) /day

You need to

correct this shift

periodically


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Cont.

• There is only one geostationary orbit because there is only one value of a thatsatisfy eq(2.3) for p=23h, 56min, 4 sec.

Geostationary orbit=natural resource.

• National authorities use it carefully through national and international agreements.

3.2 Antenna Look Angles

• The look angles for the ES antenna are:

1. The azimuth angle 𝐴𝑧2. The elevation angle 𝐸𝑙

• They are required to point the antennadirectly to the satellite.

• Sec 2.9.8 consider the general case ofelliptical orbits (where pointing changeswith time and ES position)

• the situation here is much simpler, becauseit is stationary with respect to the earth


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• The azimuth angle: measuredclockwise from geographic north tothe projection of path to thesatellite on horizontal plane atearth station

• The elevation angle: Measuredupward from the local horizontalplane at the ES to the satellite path

Cont.

Cont.

• To determine the look angles for geostationary satellites:

1. ES latitude, 𝜆𝐸?

2. ES longitude, 𝜙𝐸?

3. SS point longitude, 𝜙𝑆𝑆?

(why not 𝜆𝑆𝑆?)

• +ve for 𝜙: the East of GM

• -ve for 𝜙: the West of GM

• +ve for 𝜆: the north of equator,

• -ve for 𝜆 : the south of equator.

𝜆𝑆𝑆 = 0 for geostationary satellites


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Cont.

The Spherical Triangle • Sides are all arcs of the great circles

• Arcs defined by the angles subtended

by them at the earth center, 6 key

angles (A, a, B, b, C, c)

• From Geometry: a=90, c=90- 𝜆𝐸 ,

B=𝜙𝐸 −𝜙𝑆𝑆Note :• when the ES is west of the SS point, B is -ve,

and when east, B is +ve. • When the ES latitude is north, c is less than

90°, and when south, c is greater than 90°.

• Using Napier’s rules (used to solve

spherical triangle),

𝑏 = arccos(𝑐𝑜𝑠𝐵 𝑐𝑜𝑠𝜆𝐸) 𝐴 = arcsin(sin |𝐵|/ 𝑠𝑖𝑛𝑏)

The Spherical Triangle

The plane Triangle

Cont.

The plane Triangle

• Two values will satisfy 𝐴 = arcsinsin 𝐵

sin 𝑏, A and

180°-A, and these must be determined by

inspection.

• Applying cos & sin rules to the plane triangle,

allows that


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Cont.

• Notes:

Where d more accurate is needed (i.e. propagation time is required), the range is

determined by measurement.

In practice,

the look angles are estimated then actual tuning is done to get best signal.

In case of neighbor satellites, one estimation process of look angles is sufficient.

Cont.

• Fig 3.4 shows look angles for ES located in

Thunder Bay (48.42 N, 89.26 W)- Ku band.

• Previous discussion do not take into account the

case when ES on the equator.

• The case of ES on the equator:• Case 1: directly under the satellite:

El=90, Az is irrelevent.

• Case 2: SS point is east of ES (B<0): Az is 90. Ez need to be calculated

• Case 3: SS point is west of ES (B>0): Az is 270. Ez need to be calculated

2 3


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3.3 The Polar Mount Antenna

• To have steerable ES, you needtwo actuator (azimuth andelevation).

• In geostationary satellites, ??

you need one actuator only (This move antenna in

circular arc) [ Polar mount antenna]

1. The polar mount is aligned along a true north line(polar axis), hence the antenna boresight is normal tothis axis. & 𝜆𝐸,

N.B. This lets the boresight parallelto the equator plane.

2. Next, the dish is tilted by 𝛿 relative to the polarmount until the boresight is pointing at a satelliteposition due south of the earth station.

Cont.


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3.4 Limits of Visibility

• From any given ES, there will be east & west limits on the geostationaryvisibility.

• The limits is determined by :

1. The geographic coordinates of ES.

2. The antenna elevation.

• Case 1 : On equator (𝜆𝐸=0)& El=0 (East or West):

• To avoid the excessive noise from Earth:

𝐸𝑙𝑚𝑖𝑛 = 5°

𝑎𝐸 = 6378 Km𝑎𝐺𝑆𝑂 = 42164Km

Cont.

• Case 2 (General case) : 𝜆𝐸 ≠ 0 & 𝐸𝑙𝑚𝑖𝑛

1. Applying the sine rule:

2. Assuming mean radius 6371 km,

3. Then,


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3.5 Near Geostationary Orbit

• # of perturbing forces that causes orbit to depart from ideal keplerianorbit.

• In case of Geostationary orbits,• the gravitational fields of the moon and the sun,

• the nonspherical shape of the earth,

• solar radiation pressure,

• reaction of the satellite itself to motor movement.

• An exact geostationary orbit therefore is not attainable in practice, and the orbital parameters vary with time.

• TLE are published at regular intervals.

• p= 23 h, 56 min, 4 s. =1.00273896 rev/day, same as in TLE (geosynch. sat.).

• Geosynchronous sat.: is a satellite. that rotate in synchronism with the rotation of the earth.

You need to correct this

shift periodically and

maintain them within the

limits

Cont.

• In other places (most common),it is something completelydifferent but only has sameperiod

• sometimes instead of geostationaryto describe the near-geostationarysatellites (near-geostationary withsome perturbing effects)

• The Geosynchronous satellite term is used :


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Cont.

• The longitude of the SS point can be determined as:

• Because of small eccentricity, (2.31) can be approximated as

3.6 Earth Eclipse of Satellite

• If the earth’s equatorial plane coincided with theplane of the earth’s orbit around the sun (theecliptic plane), geostationary satellites would beeclipsed by the earth once each day.

• Otherwise, the satellite in full view of the sun for most days of the year, why?

• Eclipses begin 23 days before equinox and end 23 days after equinox.

• Start 10 minute, then ++ till 72min, then --10min.

• Why Earth eclipse of satellite is important?

As the equatorial plane is tilted at an angle of 23.4° to the ecliptic plane

no shadow unless sun beam intersect with the equator

During an eclipse, the solar cells do not function, and operating powermust be supplied from batteries.


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Cont.

Cont.

• The satellite longitudes which are west,rather than east, of the earth stationare more desirable, why?

1. Where ∅𝑆 is east of the ES, thesatellite enters eclipse during daylight(and early evening) hours for the ES.

This can be undesirable if the satellitehas to operate on reduced battery powerwhile full load is required (businesshours).

2. Where ∅𝑆 is west of the ES, eclipsedoes not occur until the ES is in darkness,(or early morning)

• This is desirable as the usage is likely tobe low.


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3.7 Sun Transit Outage

• Another important event during theequinoxes is the transit of the satellitebetween earth and sun.

• the sun comes within the beamwidth of theearth-station antenna the sun appears asan extremely noisy source which completelyblanks out the signal from the satellite.

• The occurrence and duration depends on the latitude of the ES, 10 min is themaximum typical duration

3.8 Launching Orbits

• Will be covered in comprehensive in research topics

• You are asked for any tiny letter in this section of textbook.


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Dr. Mohammed Taha El [email protected]@gmail.com

4/10/2016

eele 6335 telecom. chapter 3: system the geostationary...

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