Advanced Electronic Communication Systems

Lecture 2Satellite Orbits

Assoc. Prof. Basem M. ElHalawany

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Satellite Orbits

➢ The orbital locations of the satellite vehicles (SV) in a satellitecommunication system play a major role in determining the coverageand operational characteristics of the services provided by that system.

➢ Artificial satellites that orbit the earth are governed by the same laws ofmotion that control the motions of the planets around the sun.

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Satellite orbit determination is based on the Laws of Motion

first developed by Johannes Kepplerand later refined by Newton

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➢ The laws that govern satellite motion are called “Kepler’s Laws”➢ These laws depends on laws of planetary motion that describe:

✓ The shape of the orbit, ✓ The velocities of the planet, ✓ The distance a planet is with respect to the sun.

➢ Kepler’s laws can be applied to any two bodies in space that interact through gravitation.

➢ The larger of the two bodies is called the primary, and the smaller is called the secondary.

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➢ The main competing forces that act on the satellite:

1. Gravity tends to pull the satellite in toward the earth2. Orbital velocity tends to pull the satellite away from the earth.

Satellite Orbits

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➢ The gravitational force

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➢ The angular velocity force (Inertia)

Satellite Orbits

➢ Notice that in order to maintain a satellite at the orbit radius r:

➢ Where the velocity needed to achieve that is given by:

Assuming all other forces acting on the satellite, such as the gravity forces from the moon, sun and other bodies, are neglected.

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What keeps the satellite in Orbit?

✓ If a satellite were launched vertically from the earth and then released, it would fall back to earth because of gravity.

✓ For the satellite to go into orbit around the earth, it must have some forward motion.

✓ The forward motion produces inertia, which tends to keep the satellite moving in a straight line .

If a satellite’s velocity is too high, the satellite will overcome the

earth’s pull and go out into space.

At lower speeds, gravity constantly pulls the satellite toward the earth.

The goal is to give the satellite theINITIAL SPEED

that will exactly balance the gravitational pull.

6For that reason, when the satellite is launched, it is given both vertical and forward motion.

https://www.youtube.com/watch?v=mbeoS0o_fNw

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➢Satellites are able to orbit around the planet because they

are locked into speeds that are fast enough to defeat the

downward pull of gravity.

➢Satellites are sent into space by a rocket launched from the

ground with enough energy (at least 25,039 mph!) to get

outside our atmosphere.

➢Once the rocket reaches its determined location it drops the

satellite into its orbit.

➢The initial speed of the satellite maintained as it detaches

from the launch vehicle is enough to keep a satellite on orbit for hundreds of years.

What keeps the satellite in Orbit?

8Is Fuel needed to keep Satellite speed in Orbit?

➢ Satellites do carry their own fuel supply, but unlike how a car uses gas, it is not needed to maintain speed for orbit.

➢ It is reserved for changing orbit, avoiding collision with debris, or sending it for decommission in “graveyard” orbit.

How Long Can Satellites Stay in Orbit?

➢ Satellites can sustain operations in their orbit for a long time.➢ NOAA’s GOES-3 Satellite for example had an operational life

spanning five different decades➢ It completed the decommissioning process on June 29, 2016 and

was carefully placed into a “graveyard” orbit above the geosynchronous orbit.

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1. The orbit of a planet is an ellipse with the Sun at one of thetwo foci.

2. A line segment joining a planet and the Sun sweeps out equalareas during equal intervals of time.

3. The square of the orbital period of a planet is proportional to thecube of the semi-major axis of its orbit.

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Kepler’s laws of planetary motion

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Kepler’s First law

➢ States that the path followed by a satellite around the earth will be an ellipse.

✓ Because the mass of Earth is substantially greater than that of the satellite, the center of mass of the two-body system will always coincide with the center of Earth (a.k.a. barycenter )

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✓ If no other forces are acting on the satellite, either intentionally by orbit control, or unintentionally, by gravity forces from other bodies, the satellite will eventually settle in an elliptical orbit, with the Earth as one of the foci of the ellipse.

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Kepler’s Second law ( the law of Areas)

➢ Kepler’s second law states that for equal intervals of time a satellite will

sweep out equal areas in the orbital plane, focused at the barycenter.

✓ for a satellite traveling distances D1 and D 2 meters in 1 second,✓ Areas A1 = A2 ✓ Because of the equal area law, distance D1 > distance D2 , and, therefore, Velocity

V1 must be greater than velocity V2 .

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Kepler’s Second law ( the law of Areas)

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➢ This result also shows that the satellite orbital velocity is not constant

➢ The satellite is moving much faster at locations near the earth, and slows down as it approaches apogee.

➢ This property can be used to increase the length of time a satellite can be seen from particular geographic regions of the earth.

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Kepler’s Third law (the harmonic law)

➢ The square of the orbital period (periodic time of orbit) of a planetis proportional to the mean distance between the two bodies(cube of the semi-major axis (α) of its orbit).

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➢ For ideal situation of a satellite orbiting a perfectly spherical earth of uniform mass, Kepler’s third law can be written as

✓ n: is the mean motion of the satellite in radians per second✓ µ: is the earth’s geocentric gravitational constant (Kepler’s Constant).

✓ The orbital period (P) in seconds is given by

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Kepler’s Third law (the harmonic law)

➢ This allows the satellite designer to select orbit periods, which best meet particular application requirements by locating the satellite at the proper orbit altitude.

➢ One very important orbit in particular, known as the geostationary orbit, is determined by the rotational period of the earth (almost 1 day)

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Kepler’s Third law (the harmonic law)

➢ Comparison between multiple orbiting objects:

(𝑃𝐴/𝑃𝐵)2 = (α𝐴/α𝐵)3

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Definitions of Terms for Earth-Orbiting Satellites

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➢ Notice that some references adds the radius of the earth to both perigee and apogee

➢ The satellite moves with minimum speed at apogee and with maximum speed at perigee

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Apogee/Perigee versus Semi-Major Axis

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➢ Notice that the semi-major axis is the average of both perigee and apogee➢ The semi-major axis determines the size of the orbit. What about the

shape?

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Eccentricity

Elliptical Orbit Eccentricity

✓ For a circle, e = 0✓ The range of values of the eccentricity for ellipses is 0 < e < 1✓ The higher the value of e, the longer, thinner, and flatter the ellipse

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➢ The eccentricity determines the shape of the orbit.➢ It tell us how round or flat the orbit is.

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Eccentricity

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Eccentricity in terms of Apogee and Perigee

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➢ Some references define Apogee and Perigee heights above the earth surface by subtracting the earth radius from ra and rb

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Eccentricity in terms of Apogee and Perigee

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✓ Using the following relation,

Prove the following .

22Inclination

➢ Inclination (i) is used to describe the tilt of the orbit➢ It is the angle between the equatorial plane to the orbital plane

Equatorial planeIs a plane that passes by the center of the earth and extends

out through the equator

Orbital planeIs a plane that flat on top of the orbit and passes through the center of the earth

23Inclination➢ A satellite rotating in orbit in the equatorial plane have i = 0 (Equatorial Orbit)➢ A satellite that has an inclination angle of 90 is in a polar orbit. ➢ A satellite that is in an orbit with some inclination angle is in an inclined orbit.

180o> i > 0o

24Inclination for Prograde and retrograde orbits

✓ The satellite rotates in the direction of the earth rotation (east/counter-clockwise)

✓ The satellite rotates opposite to the direction of the earth rotation

➢ Most satellites are launched in a prograde orbit, since the earth’s rotational velocity enhances the satellite’s orbital velocity, and reduces the amount of energy required to launch and place the satellite in orbit.

Retrograde or indirect orbit

180o> i > 90o

Prograde or direct orbit

90o> i > 0o

25References

1. Louis J. Ippolito, Jr., “Satellite Communications Systems Engineering: Atmospheric Effects, Satellite Link Design and System Performance”, Wiley, 2017

2. Dennis Roddy, “ Satellite Communications”, Fourth Edition

Chapter 2

Chapter 2

3. https://www.youtube.com/watch?v=2gAYqtmNJx8