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M.A.M SCHOOL OF ENGINEERING, TRICHY
DEPARTMENT OF ELECTRONICS AND
COMMUNICATION ENGINEERING
UNIT I SATELLITE ORBITS
• Kepler’s Laws
• Newton’s Law
• Orbital Parameters
• Orbital Perturbations
• Station Keeping
• Geo Stationary And Non Geo-stationary Orbits
• Look Angle Determination
• Limits Of Visibility
• Eclipse
• Sub Satellite Point
• Sun Transit Outage
• Launching Procedures
• Launch Vehicles And Propulsion
Introduction
• A satellite is a body that orbits around another
body in space.
• There are two different types of satellites –
1.Natural
2.Man-made.
• Examples of natural satellites :
Earth and Moon.
• The Earth rotates around the Sun and the Moon rotates
around the Earth.
• A man-made satellite is a machine that is launched into
space and orbits around a body in space.
• Examples of man made satellites: Sputnik,
Aryabhata,GSAT…
• The world's first artificial satellite, the Sputnik 1,
was launched by the Soviet Union on October
4,1957.
• Sputnik 2 was launched on November 3, 1957
• The United States launched their first satellite,
called Explorer 1 on January 31, 1958
• Aryabhata was the first unmanned Earth satellite
built by India, assembled at Peenya, near
Bangalore, but launched from the nion by a
Russian-made rocket in 1975.
FREQUENCY BANDS USED FOR
SATELLITE SERVICES
KEPLER’S LAWS
• Johannes Kepler derived Kepler’s laws.
• Kepler’s laws apply quite generally to any two
bodies in space which interact through
gravitation.
• The more massive of the two bodies is
referred to as the primary, the other, the
secondary or satellite.
• https://www.youtube.com/watch?v=N5a9npp
0Qbw
Kepler’s First Law
• Kepler’s first law states that the path
followed by a satellite around the primary
will be an ellipse
• An ellipse has two focal points shown as F1 and F2 in
Fig.
• The center of mass of the two-body system, termed
the bary center, is always centered on one of the
foci.
• In our specific case, because of the enormous
difference between the masses of the earth and the
satellite, the center of mass coincides with the center
of the earth, which is therefore always at one of the
foci.
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• The semimajor axis of the ellipse is denoted by a,
and the semiminor axis, by b.
• The eccentricity e is given by
• The eccentricity and the semimajor axis are two
of the orbital parameters specified for satellites
(spacecraft) orbiting the earth.
• For an elliptical orbit, e is 1.
• When e is 0, the orbit becomes circular
Kepler’s Second Law
• Kepler’s second law states that, for equal
time intervals, a satellite will sweep out
equal areas in its orbital plane, focused at the
barycenter.
• Assuming the satellite travels distances S1 and
S2 meters in 1 s, then the areas A1 and A2 will
be equal.
• The average velocity in each case is S1 and S2
m/s, and because of the equal area law, it
follows that the velocity at S2 is less than that
at S1.
• The satellite takes longer to travel a given
distance when it is farther away from earth.
Kepler’s Third Law
• Kepler’s third law states that the square
of the periodic time of orbit is
proportional to the cube of the mean
distance between the two bodies.
• The mean distance is equal to the
semimajor axis a.
• For the artificial satellites orbiting the
earth, Kepler’s third law can be written in
the form
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• n - the mean motion of the satellite in radians
per second and
• μ - the earth’s geocentric gravitational
constant
• Equation applies only to the ideal situation of
a satellite orbiting a perfectly spherical earth
of uniform mass, with no perturbing forces
acting, such as atmospheric drag.
• With n in radians per second, the orbital
period in seconds is given by
CEC 352 - SATELLITE COMMUNICATION UNIT 1
NEWTON’S LAWS
Newton’s first law
• Newton’s first law states that, if a body is at
rest or moving at a constant speed in a
straight line, it will remain at rest or keep
moving in a straight line at constant speed
unless it is acted upon by a force
Newton’s second law
• Newton’s second law states that If a force, F,
works on a body of mass M, and acceleration
A, F is given by
• F = M A
Newton’s third law
• Newton’s third law states that when two
bodies interact, they apply forces to one
another that are equal in magnitude and
opposite in direction.
• If one body exerts a force on a second body,
the second body exerts an equal and opposite
force on the first.
Newton's Universal Law of
Gravitation
• The Universal Law of Gravitation is usually stated
as an equation:
• The attractive force that occurs between
two masses is given by
Fgravity = G M1 M2 / r2
• Fgravity - the attractive gravitational force between
two objects of mass M1 and M2 separated by a
distance r.
• The constant G in the equation is called
the Universal Constant of Gravitation.
• The value of G is:
• G = 6.67 X 10-11 meters3 kilograms-1 seconds-2
DEFINITIONS
Definitions
• Subsatellite path.
This is the path traced out on the earth’s
surface directly below the satellite
• Apogee.
The point farthest from earth. Apogee
height is shown as ha in Fig.
• Perigee.
The point of closest approach to earth. The
perigee height is shown as hp
CEC 352 - SATELLITE COMMUNICATION UNIT 1
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• Ascending node.
The point where the orbit crosses the
equatorial plane going from south to north.
• Descending node.
The point where the orbit crosses the
equatorial plane going from north to south.
• Line of nodes.
The line joining the ascending and descending
nodes through the center of the earth
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• Inclination.
The angle between the orbital plane and the
earth’s equatorial plane.
It is measured at the ascending node from the
equator to the orbit, going from east to north. The
inclination is shown as i in Fig.
• There are four types of orbits based on the angle of
inclination.
• Equatorial orbit − Angle of inclination is either zero
degrees or 180 degrees.
• Polar orbit − Angle of inclination is 90 degrees.
• Prograde orbit − Angle of inclination lies between
zero and 90 degrees.
• Retrograde orbit − Angle of inclination lies
between 90 and 180 degrees.
• Prograde orbit.
• An orbit in which the satellite moves in the same
direction as the earth’s rotation, as shown in Fig.
• The prograde orbit is also known as a direct
orbit. The inclination of a prograde orbit always
lies between 0° and 90°
• Retrograde orbit.
• An orbit in which the satellite moves in a
direction counter to the earth’s rotation, as shown
in Fig. 2.4.
• The inclination of a retrograde orbit always lies
between 90° and 180°.
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• Argument of perigee.
• The angle from ascending node to perigee,
measured in the orbital plane at the earth’s
center, in the direction of satellite motion.
• The argument of perigee is shown as w in Fig
• Argument of perigee.
• The angle from ascending node to perigee,
measured in the orbital plane at the earth’s
center, in the direction of satellite motion.
• The argument of perigee is shown as w in Fig
• Right ascension of the ascending node.
• To define completely the position of the orbit in space, the
position of the ascending node is specified.
• However, because the earth spins, while the orbital plane
remains stationary (slow drifts that do occur are discussed
later), the longitude of the ascending node is not fixed, and it
cannot be used as an absolute reference.
• For the practical determination of an orbit, the longitude and
time of crossing of the ascending node are frequently used.
However, for an absolute measurement, a fixed reference in
space is required.
• The reference chosen is the first point of Aries, otherwise
known as the vernal, or spring, equinox. The vernal equinox
occurs when the sun crosses the equator going from south to
north, and an imaginary line drawn from this equatorial
crossing through the center of the sun points to the first point
of Aries (symbol ϒ). This is the line of Aries.
• The right ascension of the ascending node is then the angle
measured eastward, in the equatorial plane, from the ϒ line
to the ascending node, shown as Ω in Fig. 2
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• Mean anomaly.
• Mean anomaly M gives an average value of the
angular position of the satellite with reference to
the perigee.
• For a circular orbit, M gives the angular position
of the satellite in the orbit.
• True anomaly.
• The true anomaly is the angle from perigee to the
satellite position, measured at the earth’s center.
• This gives the true angular position of the
satellite in the orbit as a function of time.
• https://youtu.be/QZrYaKwZwhI
ORBITAL ELEMENTS
Orbital Elements
• Earth-orbiting artificial satellites are defined by
six orbital elements referred to as the keplerian
element set
1. Semi Major Axis A
2. Eccentricity E
3. Mean Anomaly M0
4. Argument Of Perigee W,
5. Inclination I
6. Right Ascension Of The Ascending Node Ω
• The semimajor axis a and the eccentricity e give
the shape of the ellipse.
• Mean Anomaly M0, gives the position of the
satellite in its orbit at a reference time known as
the epoch.
• The argument of perigee w, gives the rotation of
the orbit’s perigee point relative to the orbit’s
line of nodes in the earth’s equatorial plane
• The inclination i and the right ascension of the
ascending node Ω, relate the orbital plane’s
position to the earth
• Apogee and Perigee Heights
• In order to find the apogee and perigee heights,
the radius of the earth must be subtracted from
the radii lengths
• Epoch is a moment in time used as a reference
point for some time
CEC 352 - SATELLITE COMMUNICATION UNIT 1
ORBITAL PERTURBATIONS
Orbit Perturbations
• The keplerian orbit described so far is ideal in the sense
that it assumes that the earth is a uniform spherical
mass and that the only force acting is the centrifugal
force resulting from satellite motion balancing the
gravitational pull of the earth.
• (Perturbation – Deviation of a system)
• Orbital perturbations are due to
• 1. Effects of a nonspherical earth
• 2. Atmospheric drag
• 3. Gravitational forces of the sun and the moon
• The gravitational pulls of sun and moon have
negligible effect on low-orbiting satellites, but
they do affect satellites in the geostationary
orbit.
• Atmospheric drag, on the other hand, has
negligible effect on geostationary satellites
but does affect low orbiting earth satellites
below about 1000 km.
1.Effects of a nonspherical earth
• For a spherical earth of uniform mass, Kepler’s third law gives the
nominal mean motion n0 as
• Mean motion (represented by n) is the angular speed required for a
body to complete one orbit,
• The 0 subscript is included as a reminder that this result applies for
a perfectly spherical earth of uniform mass.
• However, it is known that the earth is not perfectly spherical, there
being an equatorial bulge and a flattening at the poles, a shape
described as an oblate spheroid.
• When the earth’s oblateness is taken into account, the mean
motion, denoted in this case by symbol n, is modified to
• K1 is a constant (66,063.1704 km2.)
• The orbital period taking into account the earth’s
oblateness is termed the anomalistic period.
• The mean motion is the reciprocal of the
anomalistic period.
• The anomalistic period is
• n is in radians per second.
• The oblateness of the earth also produces two
rotations of the orbital plane
1. REGRESSION OF THE NODES
2. ROTATION OF APSIDES IN THE ORBITAL PLANE
1.REGRESSION OF THE NODES:
• Regression of the nodes, is where the nodes
appear to slide along the equator.
• In effect, the line of nodes, which is in the
equatorial plane, rotates about the center of the
earth.
• Thus Ω, the right ascension of the ascending
node, shifts its position
• If the orbit is prograde ,the nodes slide westward,
and if retrograde, they slide eastward.
• A satellite in prograde orbit moves eastward, and
in a retrograde orbit, westward.
• The nodes therefore move in a direction opposite
to the direction of satellite motion, hence the
term regression of the nodes.
• For a polar orbit (i 90°), the regression is zero
2.ROTATION OF APSIDES IN THE ORBITAL PLANE
• Line of apsides – Line connecting apogee and
perigee(major axis)
• Both effects depend on the mean motion n, the
semimajor axis a, and the eccentricity e.
• These factors can be grouped into one factor K
given by
• An approximate expression for the rate of change
of Ω with respect to time is
• i is the inclination
• When the rate of change is negative, the
regression is westward, and when the rate is
positive, the regression is eastward.
• For eastward regression, i must be greater than
90°, or the orbit must be retrograde
• It is possible to choose values of a, e, and i such
that the rate of rotation is 0.9856°/day eastward.
• Such an orbit is said to be Sun Synchronous
• The other major effect produced by the equatorial
bulge is a rotation of the line of apsides.
• This line rotates in the orbital plane, resulting in
the argument of perigee changing with time.
• The rate of change is given by
• Denoting the epoch time by t0, the right ascension
of the ascending node by Ω0, and the argument of
perigee by w0 at epoch gives the new values for Ω
and w at time t as
2.Atmospheric drag
• For near-earth satellites, below about 1000 km,
the effects of atmospheric drag are significant.
• Because the drag is greatest at the perigee, the
drag acts to reduce the velocity at this point, with
the result that the satellite does not reach the
same apogee height on successive revolutions
• The result is that the semimajor axis and the
eccentricity are both reduced
• An approximate expression for the change of
major axis is
• The mean anomaly is also changed. An
approximate value for the change is given by
GEOSTATIONARY ORBIT
• A satellite in a geostationary orbit appears to be
stationary with respect to the earth, hence the
name geostationary.
• Geostationary Earth Orbit Satellites are used for
weather forecasting, satellite TV, satellite radio
and other types of global communications.
• Three conditions are required for an orbit to be
geostationary:
1. The satellite must travel eastward at the same
rotational speed as the earth.
2. The orbit must be circular.
3. The inclination of the orbit must be zero.
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• The first condition is obvious. If the satellite is
to appear stationary, it must rotate at the
same speed as the earth, which is constant.
• The second condition follows from this and
from Kepler’s second law.
• Constant speed means that equal areas must
be swept out in equal times, and this can only
occur with a circular orbit
• The third condition, that the inclination must
be zero, follows from the fact that any
inclination would have the satellite moving
north and south, and hence it would not be
geostationary
• Kepler’s third law may be used to find the radius
of the orbit (for a circular orbit, the semimajor axis
is equal to the radius).
• Denoting the radius by aGSO
• The period P for the geostationary is 23 h, 56 min,
4 s mean solar time (ordinary clock time).
• This is the time taken for the earth to complete
one revolution
• Substituting this value along with the value for
•In practice, a precise geostationary orbit cannot be
attained because of disturbance forces in space and the
effects of the earth’s equatorial bulge.
• The gravitational fields of the sun and the moon
produce a shift of about 0.85°/year in inclination
NON GEO STATIONARY ORBIT
• Non-geostationary orbits do not maintain a
stationary position, but instead move in relation
to the Earth's surface.
• Types of Non-geostationary Satellite
1. LEO - Low Earth Orbit
2. MEO – Medium Earth Orbit
3. Polar Orbiting Satellites
• They occupy a range of orbital positions
• LEO satellites are located between 700km-
1,500km from the Earth,
• MEO satellites are located at 10,000km from the
Earth
• LEO' is a small non-geostationary satellite
which operates in Low Earth Orbit, providing
mainly mobile data services.
• A 'MEO' is a non-geostationary satellite which
operates in Medium Earth Orbit, again
providing mobile telephony services.
• Polar orbiting satellites orbit the earth in such
a way as to cover the north and south polar
regions.
Polar orbit
STATION KEEPING
Station Keeping
• A geostationary satellite should be kept in its
correct orbital slot.
• The orbit control process required to
maintain a stationary orbit is called station-
keeping.
• https://www.youtube.com/watch?v=6SLYos
1VNpU
• https://www.youtube.com/watch?v=YcfitG
oip2g
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• A geostationary satellite also will drift in
latitude.
• https://www.youtube.com/watch?v=toyuU6Q
1IW8
• The main perturbing forces being the
gravitational pull of the sun and the moon.
• These forces cause the inclination to change
at a rate of about 0.85°/year.
CEC 352 - SATELLITE COMMUNICATION UNIT 1
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• Satellite altitude also will show variations of about 0.1
percent of the nominal geostationary height
• The total variation in the height is 72 km.
• Thus both the latitude and longitude sides of the box
are 147 km.
• This 30m dia antenna beam does not encompass the
whole of the box and therefore could miss the satellite.
• Such narrow-beam antennas therefore must track the
satellite of the box and therefore could miss the
satellite.
• The diameter of the 5-m antenna beam at the satellite
will be about 464 km, and this does encompass the
box, so tracking is not required.
• By placing the satellite in an inclined orbit, the north-
south station keeping maneuvers may be reduced
CEC 352 - SATELLITE COMMUNICATION UNIT 1
• The satellite is placed in an inclined orbit of
about 2.5° to 3°, in the opposite sense to that
produced by drift.
• Over a period of about half the predicted
lifetime of the mission, the orbit will change to
equatorial and then continue to increase in
inclination.

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CEC 352 - SATELLITE COMMUNICATION UNIT 1

  • 1. M.A.M SCHOOL OF ENGINEERING, TRICHY DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
  • 2. UNIT I SATELLITE ORBITS • Kepler’s Laws • Newton’s Law • Orbital Parameters • Orbital Perturbations • Station Keeping • Geo Stationary And Non Geo-stationary Orbits • Look Angle Determination • Limits Of Visibility • Eclipse • Sub Satellite Point • Sun Transit Outage • Launching Procedures • Launch Vehicles And Propulsion
  • 3. Introduction • A satellite is a body that orbits around another body in space. • There are two different types of satellites – 1.Natural 2.Man-made. • Examples of natural satellites : Earth and Moon. • The Earth rotates around the Sun and the Moon rotates around the Earth. • A man-made satellite is a machine that is launched into space and orbits around a body in space. • Examples of man made satellites: Sputnik, Aryabhata,GSAT…
  • 4. • The world's first artificial satellite, the Sputnik 1, was launched by the Soviet Union on October 4,1957. • Sputnik 2 was launched on November 3, 1957 • The United States launched their first satellite, called Explorer 1 on January 31, 1958 • Aryabhata was the first unmanned Earth satellite built by India, assembled at Peenya, near Bangalore, but launched from the nion by a Russian-made rocket in 1975.
  • 5. FREQUENCY BANDS USED FOR SATELLITE SERVICES
  • 7. • Johannes Kepler derived Kepler’s laws. • Kepler’s laws apply quite generally to any two bodies in space which interact through gravitation. • The more massive of the two bodies is referred to as the primary, the other, the secondary or satellite. • https://www.youtube.com/watch?v=N5a9npp 0Qbw
  • 8. Kepler’s First Law • Kepler’s first law states that the path followed by a satellite around the primary will be an ellipse • An ellipse has two focal points shown as F1 and F2 in Fig. • The center of mass of the two-body system, termed the bary center, is always centered on one of the foci. • In our specific case, because of the enormous difference between the masses of the earth and the satellite, the center of mass coincides with the center of the earth, which is therefore always at one of the foci.
  • 10. • The semimajor axis of the ellipse is denoted by a, and the semiminor axis, by b. • The eccentricity e is given by • The eccentricity and the semimajor axis are two of the orbital parameters specified for satellites (spacecraft) orbiting the earth. • For an elliptical orbit, e is 1. • When e is 0, the orbit becomes circular
  • 11. Kepler’s Second Law • Kepler’s second law states that, for equal time intervals, a satellite will sweep out equal areas in its orbital plane, focused at the barycenter.
  • 12. • Assuming the satellite travels distances S1 and S2 meters in 1 s, then the areas A1 and A2 will be equal. • The average velocity in each case is S1 and S2 m/s, and because of the equal area law, it follows that the velocity at S2 is less than that at S1. • The satellite takes longer to travel a given distance when it is farther away from earth.
  • 13. Kepler’s Third Law • Kepler’s third law states that the square of the periodic time of orbit is proportional to the cube of the mean distance between the two bodies. • The mean distance is equal to the semimajor axis a. • For the artificial satellites orbiting the earth, Kepler’s third law can be written in the form
  • 15. • n - the mean motion of the satellite in radians per second and • μ - the earth’s geocentric gravitational constant
  • 16. • Equation applies only to the ideal situation of a satellite orbiting a perfectly spherical earth of uniform mass, with no perturbing forces acting, such as atmospheric drag. • With n in radians per second, the orbital period in seconds is given by
  • 19. Newton’s first law • Newton’s first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force
  • 20. Newton’s second law • Newton’s second law states that If a force, F, works on a body of mass M, and acceleration A, F is given by • F = M A
  • 21. Newton’s third law • Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. • If one body exerts a force on a second body, the second body exerts an equal and opposite force on the first.
  • 22. Newton's Universal Law of Gravitation • The Universal Law of Gravitation is usually stated as an equation: • The attractive force that occurs between two masses is given by Fgravity = G M1 M2 / r2 • Fgravity - the attractive gravitational force between two objects of mass M1 and M2 separated by a distance r. • The constant G in the equation is called the Universal Constant of Gravitation. • The value of G is: • G = 6.67 X 10-11 meters3 kilograms-1 seconds-2
  • 24. Definitions • Subsatellite path. This is the path traced out on the earth’s surface directly below the satellite • Apogee. The point farthest from earth. Apogee height is shown as ha in Fig. • Perigee. The point of closest approach to earth. The perigee height is shown as hp
  • 27. • Ascending node. The point where the orbit crosses the equatorial plane going from south to north. • Descending node. The point where the orbit crosses the equatorial plane going from north to south. • Line of nodes. The line joining the ascending and descending nodes through the center of the earth
  • 29. • Inclination. The angle between the orbital plane and the earth’s equatorial plane. It is measured at the ascending node from the equator to the orbit, going from east to north. The inclination is shown as i in Fig. • There are four types of orbits based on the angle of inclination. • Equatorial orbit − Angle of inclination is either zero degrees or 180 degrees. • Polar orbit − Angle of inclination is 90 degrees. • Prograde orbit − Angle of inclination lies between zero and 90 degrees. • Retrograde orbit − Angle of inclination lies between 90 and 180 degrees.
  • 30. • Prograde orbit. • An orbit in which the satellite moves in the same direction as the earth’s rotation, as shown in Fig. • The prograde orbit is also known as a direct orbit. The inclination of a prograde orbit always lies between 0° and 90° • Retrograde orbit. • An orbit in which the satellite moves in a direction counter to the earth’s rotation, as shown in Fig. 2.4. • The inclination of a retrograde orbit always lies between 90° and 180°.
  • 32. • Argument of perigee. • The angle from ascending node to perigee, measured in the orbital plane at the earth’s center, in the direction of satellite motion. • The argument of perigee is shown as w in Fig
  • 33. • Argument of perigee. • The angle from ascending node to perigee, measured in the orbital plane at the earth’s center, in the direction of satellite motion. • The argument of perigee is shown as w in Fig
  • 34. • Right ascension of the ascending node. • To define completely the position of the orbit in space, the position of the ascending node is specified. • However, because the earth spins, while the orbital plane remains stationary (slow drifts that do occur are discussed later), the longitude of the ascending node is not fixed, and it cannot be used as an absolute reference. • For the practical determination of an orbit, the longitude and time of crossing of the ascending node are frequently used. However, for an absolute measurement, a fixed reference in space is required. • The reference chosen is the first point of Aries, otherwise known as the vernal, or spring, equinox. The vernal equinox occurs when the sun crosses the equator going from south to north, and an imaginary line drawn from this equatorial crossing through the center of the sun points to the first point of Aries (symbol ϒ). This is the line of Aries. • The right ascension of the ascending node is then the angle measured eastward, in the equatorial plane, from the ϒ line to the ascending node, shown as Ω in Fig. 2
  • 36. • Mean anomaly. • Mean anomaly M gives an average value of the angular position of the satellite with reference to the perigee. • For a circular orbit, M gives the angular position of the satellite in the orbit. • True anomaly. • The true anomaly is the angle from perigee to the satellite position, measured at the earth’s center. • This gives the true angular position of the satellite in the orbit as a function of time. • https://youtu.be/QZrYaKwZwhI
  • 38. Orbital Elements • Earth-orbiting artificial satellites are defined by six orbital elements referred to as the keplerian element set 1. Semi Major Axis A 2. Eccentricity E 3. Mean Anomaly M0 4. Argument Of Perigee W, 5. Inclination I 6. Right Ascension Of The Ascending Node Ω
  • 39. • The semimajor axis a and the eccentricity e give the shape of the ellipse. • Mean Anomaly M0, gives the position of the satellite in its orbit at a reference time known as the epoch. • The argument of perigee w, gives the rotation of the orbit’s perigee point relative to the orbit’s line of nodes in the earth’s equatorial plane • The inclination i and the right ascension of the ascending node Ω, relate the orbital plane’s position to the earth
  • 40. • Apogee and Perigee Heights • In order to find the apogee and perigee heights, the radius of the earth must be subtracted from the radii lengths • Epoch is a moment in time used as a reference point for some time
  • 43. Orbit Perturbations • The keplerian orbit described so far is ideal in the sense that it assumes that the earth is a uniform spherical mass and that the only force acting is the centrifugal force resulting from satellite motion balancing the gravitational pull of the earth. • (Perturbation – Deviation of a system) • Orbital perturbations are due to • 1. Effects of a nonspherical earth • 2. Atmospheric drag • 3. Gravitational forces of the sun and the moon
  • 44. • The gravitational pulls of sun and moon have negligible effect on low-orbiting satellites, but they do affect satellites in the geostationary orbit. • Atmospheric drag, on the other hand, has negligible effect on geostationary satellites but does affect low orbiting earth satellites below about 1000 km.
  • 45. 1.Effects of a nonspherical earth • For a spherical earth of uniform mass, Kepler’s third law gives the nominal mean motion n0 as • Mean motion (represented by n) is the angular speed required for a body to complete one orbit, • The 0 subscript is included as a reminder that this result applies for a perfectly spherical earth of uniform mass. • However, it is known that the earth is not perfectly spherical, there being an equatorial bulge and a flattening at the poles, a shape described as an oblate spheroid. • When the earth’s oblateness is taken into account, the mean motion, denoted in this case by symbol n, is modified to
  • 46. • K1 is a constant (66,063.1704 km2.) • The orbital period taking into account the earth’s oblateness is termed the anomalistic period. • The mean motion is the reciprocal of the anomalistic period. • The anomalistic period is • n is in radians per second.
  • 47. • The oblateness of the earth also produces two rotations of the orbital plane 1. REGRESSION OF THE NODES 2. ROTATION OF APSIDES IN THE ORBITAL PLANE 1.REGRESSION OF THE NODES: • Regression of the nodes, is where the nodes appear to slide along the equator. • In effect, the line of nodes, which is in the equatorial plane, rotates about the center of the earth. • Thus Ω, the right ascension of the ascending node, shifts its position • If the orbit is prograde ,the nodes slide westward, and if retrograde, they slide eastward.
  • 48. • A satellite in prograde orbit moves eastward, and in a retrograde orbit, westward. • The nodes therefore move in a direction opposite to the direction of satellite motion, hence the term regression of the nodes. • For a polar orbit (i 90°), the regression is zero 2.ROTATION OF APSIDES IN THE ORBITAL PLANE • Line of apsides – Line connecting apogee and perigee(major axis) • Both effects depend on the mean motion n, the semimajor axis a, and the eccentricity e. • These factors can be grouped into one factor K given by
  • 49. • An approximate expression for the rate of change of Ω with respect to time is • i is the inclination • When the rate of change is negative, the regression is westward, and when the rate is positive, the regression is eastward. • For eastward regression, i must be greater than 90°, or the orbit must be retrograde • It is possible to choose values of a, e, and i such that the rate of rotation is 0.9856°/day eastward. • Such an orbit is said to be Sun Synchronous
  • 50. • The other major effect produced by the equatorial bulge is a rotation of the line of apsides. • This line rotates in the orbital plane, resulting in the argument of perigee changing with time. • The rate of change is given by • Denoting the epoch time by t0, the right ascension of the ascending node by Ω0, and the argument of perigee by w0 at epoch gives the new values for Ω and w at time t as
  • 51. 2.Atmospheric drag • For near-earth satellites, below about 1000 km, the effects of atmospheric drag are significant. • Because the drag is greatest at the perigee, the drag acts to reduce the velocity at this point, with the result that the satellite does not reach the same apogee height on successive revolutions • The result is that the semimajor axis and the eccentricity are both reduced • An approximate expression for the change of major axis is
  • 52. • The mean anomaly is also changed. An approximate value for the change is given by
  • 54. • A satellite in a geostationary orbit appears to be stationary with respect to the earth, hence the name geostationary. • Geostationary Earth Orbit Satellites are used for weather forecasting, satellite TV, satellite radio and other types of global communications. • Three conditions are required for an orbit to be geostationary: 1. The satellite must travel eastward at the same rotational speed as the earth. 2. The orbit must be circular. 3. The inclination of the orbit must be zero.
  • 56. • The first condition is obvious. If the satellite is to appear stationary, it must rotate at the same speed as the earth, which is constant. • The second condition follows from this and from Kepler’s second law. • Constant speed means that equal areas must be swept out in equal times, and this can only occur with a circular orbit • The third condition, that the inclination must be zero, follows from the fact that any inclination would have the satellite moving north and south, and hence it would not be geostationary
  • 57. • Kepler’s third law may be used to find the radius of the orbit (for a circular orbit, the semimajor axis is equal to the radius). • Denoting the radius by aGSO • The period P for the geostationary is 23 h, 56 min, 4 s mean solar time (ordinary clock time). • This is the time taken for the earth to complete one revolution • Substituting this value along with the value for
  • 58. •In practice, a precise geostationary orbit cannot be attained because of disturbance forces in space and the effects of the earth’s equatorial bulge. • The gravitational fields of the sun and the moon produce a shift of about 0.85°/year in inclination
  • 60. • Non-geostationary orbits do not maintain a stationary position, but instead move in relation to the Earth's surface. • Types of Non-geostationary Satellite 1. LEO - Low Earth Orbit 2. MEO – Medium Earth Orbit 3. Polar Orbiting Satellites • They occupy a range of orbital positions • LEO satellites are located between 700km- 1,500km from the Earth, • MEO satellites are located at 10,000km from the Earth
  • 61. • LEO' is a small non-geostationary satellite which operates in Low Earth Orbit, providing mainly mobile data services. • A 'MEO' is a non-geostationary satellite which operates in Medium Earth Orbit, again providing mobile telephony services. • Polar orbiting satellites orbit the earth in such a way as to cover the north and south polar regions.
  • 64. Station Keeping • A geostationary satellite should be kept in its correct orbital slot. • The orbit control process required to maintain a stationary orbit is called station- keeping. • https://www.youtube.com/watch?v=6SLYos 1VNpU • https://www.youtube.com/watch?v=YcfitG oip2g
  • 66. • A geostationary satellite also will drift in latitude. • https://www.youtube.com/watch?v=toyuU6Q 1IW8 • The main perturbing forces being the gravitational pull of the sun and the moon. • These forces cause the inclination to change at a rate of about 0.85°/year.
  • 69. • Satellite altitude also will show variations of about 0.1 percent of the nominal geostationary height • The total variation in the height is 72 km. • Thus both the latitude and longitude sides of the box are 147 km. • This 30m dia antenna beam does not encompass the whole of the box and therefore could miss the satellite. • Such narrow-beam antennas therefore must track the satellite of the box and therefore could miss the satellite. • The diameter of the 5-m antenna beam at the satellite will be about 464 km, and this does encompass the box, so tracking is not required. • By placing the satellite in an inclined orbit, the north- south station keeping maneuvers may be reduced
  • 71. • The satellite is placed in an inclined orbit of about 2.5° to 3°, in the opposite sense to that produced by drift. • Over a period of about half the predicted lifetime of the mission, the orbit will change to equatorial and then continue to increase in inclination.