Satellite Communication

Ashok Kumar

Origin of planetary laws

Sir.Tycho Brahe
Introduced precision into
astronomical measurements.
Mentor to Johannes Keppler

Sir. Johannes Keppler

Derived 3 laws based

upon his observations
of planetary motion.

Keplers 1st Law: Law of Ellipses

The orbits of the planets are ellipses with

the sun at one focus

Keplers 2nd Law: Law of Equal Areas

The line joining the planet to the center of the sun

sweeps out equal areas in equal times
T4

T5
A5

A4

T3
A3

T2
A2
A1

T6

A6

T1

Keplers 3rd Law: Law of Harmonics

The squares of the periods of
two planets orbits are
proportional to each other
as the cubes of their semimajor axes:
T12/T22 = a13/a23
In English:
Orbits with the same semimajor axis will have the
same period

1/ 2

Velocity of satellite in a circular orbit v

r
kepller constant= 3.98 105 km3 / s 2
3/ 2
2 2 r
Orbital period T

1/ 2
v

radius of satellite orbit r0

h2
p
2

p
1 e cos(0 0 )

h is the orbital angular momentum of satellite

orbital period T 2

4 2

a3

Parameters which define the form of the orbit:

p
Semi major axis a
2
1

e

Semi minor axis b a 1 e

2 1/2

Distance from the centre of the earth to the perigee rp a 1 e

Distance from the centre of the earth to the apogee ra a(1 e)
Eccentricity e

ra rp
ra rp

0 for circle and 0<e<1 for ellipse

True anomaly (v):

The position of the satellite is determined by the angle v, called
the true anomaly, an angle counted positively in the direction of
movement of the satellite from 0 to 360, between the direction of
the perigee and the direction of the satellite.
Eccentric anomaly (E):
The position of the satellite can also be defined by the eccentric
anomaly E, which is the argument of the image in the mapping
which transforms the elliptical trajectory into its principal circle,

 The distance r of the satellite from the center of the earth can be
written:

Mean movement (n). It is permissible to define the mean movement

of the satellite n as the mean angular velocity of the satellite of
period T in its orbit:

Mean anomaly (M). The position of the satellite can thus be defined
by the mean anomaly M which would be the true anomaly of a
satellite in a circular orbit of the same period T. The mean anomaly
is expressed as a function of time t by:

Locating satellite in the orbit

Calculate n using
Calculate M

Solve equation for E:

Find r from E using:
Solve for

a (1 e 2 )
r
1 e cos 0

Sidereal and Solar Day

Locating the satellite w.r.t. earth

Where is the satellite from observation point on earth?
Geocentric equatorial coordinate system.

First point of Aries is direction of a line from center of earth to

the sun at vernal equinox (21st march in northern hemisphere)

Geocentric equatorial coordinate System

Locating Sat. w.r.t. Earth

Right ascension of ascending node and inclination
angle is sufficient to locate the orbital plane w.r.t.
equatorial plane.
Argument of perigee is required to locate orbital
coordinate system wrt the equatorial coordinate
system.

Omega (right ascension of the ascending node) and inclination

(angle orbital plane makes with equatorial plane) define the sat
orbital plane wrt to equatorial plane.
W= Argument of perigee

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

 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.

Look angle
Longitude
Latitude
The coordinates at which earth station antenna
must be pointed to communication with
satellite is called look angle.
Azimuthal
Elevation

 Sub satellite point:

Location that lies on earth surface on line joining satellite
and center of earth.

Nadir point
Located w.r.t. east/ in US wrt west.

Look angle determination

Latitude
Longitude
Reference for Lat and Long.
Coordinate to which an earth station antenna must be
pointed to communicate with satellite is called look angle
Azimuth and Elevation.
Subsatellite point.
Zenith direction.
Nadir direction.

Elevation and Azimuthal angle

Elevation angle calculation

Le Earth station north latitude, le - Earth station

west longitude
Ls Sat north latitude, ls Sat. west longitude

Specialization to Geostationary satellites

Azimuthal Angle communication

Elevation angle for Geostationary Sat.( Ls = 0)

cos( ) cos( Le ) cos(ls le )

Azimuthal (Intermediate angle)
tan

tan ls le

sin( Le )

 Earth station is in Northern Hemisphere with:

Satellite to the SE of earth station Az= 180-
Satellite to the SW of earth station Az= 180+
Earth station is in Southern Hemisphere with:
Satellite to the NE of earth station Az=
Satellite to the NW of earth station Az= 360-

Coverage angle and Slant Range

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

Orbital Perturbations
Osculating orbit (at particular instant of time, orbital
elements).
a0

da
(t1 t0 )......etc.
dt

Longitudinal Changes ( Effects of earths oblateness):

Triaxial ellipsoid.
Flat at poles diff. 20Kms
Equatorial diff. 100m
Regions of mass concentrations- Mascons.
Leo averaging of forces

Effect of earth on satellites

The effect of gravitational force is
non uniform because of the non
uniform distribution of earths mass a slight bulge at the equator, with a
difference of 20 km between polar
and the equator radius.
This deviation from spherical shape
causes additional forces on the
satellite.
The effect of earths 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.

Orbital Perturbations

Geo sat. force along the equatorial plane (+/-)

Four equilibrium points.
Gravity Hill- 1620E, 3480E
Gravity Valley- 750E, 2520E
Graveyard geosync. Orbits
Graveyard orbit of geo sat.
Inclination changes (Effect of Sun and Moon)

Orbital Perturbations

Plane of earths orbit around sun- Ecliptic.

Geo plane change 0.850/year
Rate of plane change high when sun and moon same side
(0.940/year), 1988,2006
Rate of plane change minimum when sun and moon opposite
side (0.750/year), 1997, 2015
Plane changes from 0 inclination to max. 14.670 in 26.6
years.then again 0

Orbital Perturbations

In plane changes (longitude drift) EW-maneuver

Out of plane changes ( elevation drift) NS-maneuver

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 earths north-south axis.
3. The perturbating force along the orbital plane imparts a force vector
on a satellite
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
= 4.97[R/a]3.5 (5cos2(i-1))/(1-e2)2 deg/day
where R= mean equatorial radius , a=semi major axis
i = inclination, e=eccentricity

when i=63.40 , reduces to zero, implying that perigee remains

fixed in space.

The rate of change of rotation of ascending node is

= 9.95[r/a]3.5 cos i /(1-e2)2 deg/day
Where r = satellite-geo center distance
The 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.

Atmospheric Drag

Satellites below 2000 kilometres, are actually travelling

through the Earths 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

 Reduces satellites 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
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 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.

 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

Electro-Magnetic effect
Interaction between the Earths magnetic field and
the satellites electro-magnetic field results in
magnetic drag

Magnetic storm

A geomagnetic storm is a temporary disturbance of the earths 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.

Placing Sat into Geostationary orbit

LEO placement.
GTO Hohmann transfer orbit.
Apogee Kick motor

Orbital effects in communication subsystem

performance
Doppler shift: VT/
Solar Eclipse: 23 days before and 23 days after
equinox (21 March, 23 Sept.)
Batteries drainage.
Thermal shock- damage to the satellite.

Sun transit outage

11 year sun cycles (4-50GHz)
Very high noise.
Communication failure.

Satallites
Satellite sub systems

Attitude and Orbit Control System (AOCS)

Telemetry, Tracking, Command, and Monitoring (TT&M)
Power System
Communication Sub-system
Antenna

AOCS

 AOCS
Attitude control
Gyroscopic force on weightless sat. to stabilize the spin axis
(Spinner)
Tree axis stabilized satellite ( Momentum Wheel for each
axis)

Telemetry Tracking command and monitoring

Communication subsystem

Communication subsystem
500 MHz BW/ Transponder
1-2W earlier, TV up to 200 W.
6/4 , 14/11, 30/20----1000MHz

Major parameters of an elliptical orbit

Satellite

trajectory
Satellite period
Satellite velocity
Satellite position

Effect of rain attenuation on system noise

temperature
Rain affects the system noise temperature of earth
station. No effect on satellite noise temperature
Antenna noise temperature is function of sky noise
temperature.
Increase in noise temperature caused by rain attenuation
Lr:

1
T Tr 1
Lr

Tr is taken as 273 K
Increase in noise temperature is directly added to the
earth station system temperature

Carrier to noise + interference ration including rain

induced attenuation

Uplink carrier to interference ratio

Uplink carrier to interference ratio with uplink
rain:
C
C
Lr ,u
I u , r I u

When rain occurs in downlink only, the carrier

to interference ratio remains at clear sky value

=
d,

System availability
System availability:
Rain attenuation or cross polarization
C/N reduced
Digital link: Probability of error increases
P percent of year (outage) when average
probability of error exceeds the Pb threshold value
Pb threshold outage = sum of uplink outage and
downlink outage

 Probability of link availability

System availability:
PA=PA1PA2PALPAS

Satellite link design

Adjacent channel interference- low side lobe antenna.

Terrestrial interference: site selection.
Cross polarization interference: good antenna design.
Adjacent channel interference: good filtering.
Inter symbolic interference: modulation selection.
Inter modulation interference: proper TWTA back off.
Rain induced interference: operate TWTA at sat. or
earth station diversity.
Antenna pointing loss: better antenna tracking.

Digital Satellite link design

Link requirement Pb>10-4, for P%=0.15% of the year at most