Applied Technology Institute (ATIcourses.com) Stay Current In Your Field • Broaden Your Knowledge • Increase Productivity 349 Berkshire Drive • Riva, Maryland 21140 888-501-2100 • 410-956-8805 Website: www.ATIcourses.com • Email: [email protected] Boost Your Skills With ATIcourses.com! ATI Provides Training In: • Acoustic, Noise & Sonar Engineering • Communications and Networking • Engineering & Data Analysis • Information Technology • Radar, Missiles & Combat Systems • Remote Sensing • Signal Processing • Space, Satellite & Aerospace Engineering • Systems Engineering & Professional Development Check Our Schedule & Register Today! The Applied Technology Institute (ATIcourses.com) specializes in training programs for technical professionals. Our courses keep you current in stateof-the-art technology that is essential to keep your company on the cutting edge in today's highly competitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presented On-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our training increases effectiveness and productivity. Learn From The Proven Best! Satellite Communication Systems Engineering A comprehensive, quantitative tutorial designed for satellite professionals March 16-18, 2009 Boulder, Colorado June 15-17, 2009 Beltsville, Maryland $1740 (8:30am - 4:30pm) "Register 3 or More & Receive $10000 each Off The Course Tuition." Instructor Dr. Robert A. Nelson is president of Satellite Engineering Research Corporation, a consulting firm in Bethesda, Maryland, with clients in both commercial industry and government. Dr. Nelson holds the degree of Ph.D. in physics from the University of Maryland and is a licensed Professional Engineer. He is coauthor of the textbook Satellite Communication Systems Engineering, 2nd ed. (Prentice Hall, 1993) and is Technical Editor of Via Satellite magazine. He is a member of IEEE, AIAA, APS, AAPT, AAS, IAU, and ION. Additional Materials In addition to the course notes, each participant will receive a book of collected tutorial articles written by the instructor and soft copies of the link budgets discussed in the course. Testimonials “Great handouts. Great presentation. Great real-life course note examples and cd. The instructor made good use of student’s experiences." “Very well prepared and presented. The instructor has an excellent grasp of material and articulates it well” “Outstanding at explaining and defining quantifiably the theory underlying the concepts.” “Fantastic! It couldn’t have been more relevant to my work.” “Very well organized. Excellent reference equations and theory. Good examples.” “Good broad general coverage of a complex subject.” Course Outline 1. Mission Analysis. Kepler’s laws. Circular and elliptical satellite orbits. Altitude regimes. Period of revolution. Geostationary Orbit. Orbital elements. Ground trace. 2. Earth-Satellite Geometry. Azimuth and elevation. Slant range. Coverage area. 3. Signals and Spectra. Properties of a sinusoidal wave. Synthesis and analysis of an arbitrary waveform. Fourier Principle. Harmonics. Fourier series and Fourier transform. Frequency spectrum. 4. Methods of Modulation. Overview of modulation. Carrier. Sidebands. Analog and digital modulation. Need for RF frequencies. 5. Analog Modulation. Amplitude Modulation (AM). Frequency Modulation (FM). 6. Digital Modulation. Analog to digital conversion. BPSK, QPSK, 8PSK FSK, QAM. Coherent detection and carrier recovery. NRZ and RZ pulse shapes. Power spectral density. ISI. Nyquist pulse shaping. Raised cosine filtering. 7. Bit Error Rate. Performance objectives. Eb/No. Relationship between BER and Eb/No. Constellation diagrams. Why do BPSK and QPSK require the same power? 8. Coding. Shannon’s theorem. Code rate. Coding gain. Methods of FEC coding. Hamming, BCH, and ReedSolomon block codes. Convolutional codes. Viterbi and sequential decoding. Hard and soft decisions. Concatenated coding. Turbo coding. Trellis coding. 9. Bandwidth. Equivalent (noise) bandwidth. Occupied bandwidth. Allocated bandwidth. Relationship between bandwidth and data rate. Dependence of bandwidth on methods of modulation and coding. Tradeoff between bandwidth and power. Emerging trends for bandwidth efficient modulation. 10. The Electromagnetic Spectrum. Frequency bands used for satellite communication. ITU regulations. Fixed Satellite Service. Direct Broadcast Service. Digital Audio Radio Service. Mobile Satellite Service. 11. Earth Stations. Facility layout. RF components. Network Operations Center. Data displays. 12. Antennas. Antenna patterns. Gain. Half power beamwidth. Efficiency. Sidelobes. 13. System Temperature. Antenna temperature. LNA. Noise figure. Total system noise temperature. 14. Satellite Transponders. Satellite communications payload architecture. Frequency plan. Transponder gain. TWTA and SSPA. Amplifier characteristics. Nonlinearity. Intermodulation products. SFD. Backoff. 15. The RF Link. Decibel (dB) notation. Equivalent isotropic radiated power (EIRP). Figure of Merit (G/T). Free space loss. WhyPower flux density. Carrier to noise ratio. The RF link equation. 16. Link Budgets. Communications link calculations. Uplink, downlink, and composite performance. Link budgets for single carrier and multiple carrier operation. Detailed worked examples. 17. Performance Measurements. Satellite modem. Use of a spectrum analyzer to measure bandwidth, C/N, and Eb/No. Comparison of actual measurements with theory using a mobile antenna and a geostationary satellite. 18. Multiple Access Techniques. Frequency division multiple access (FDMA). Time division multiple access (TDMA). Code division multiple access (CDMA) or spread spectrum. Capacity estimates. 19. Polarization. Linear and circular polarization. Misalignment angle. 20. Rain Loss. Rain attenuation. Crane rain model. Effect on G/T. Register online at www.ATIcourses.com or call ATI at 888.501.2100 or 410.956.8805 Vol. 97 – 53 Satellite 2001 Daily What Is the Radius of the Geostationary Orbit? by Robert A. Nelson Most communications satellites operate from the geostationary orbit, since from this orbit a satellite appears to hover over one point on the equator. An Earth station antenna can therefore be pointed at a satellite in a fixed direction and tracking of the satellite across the sky is not required. The basic question to be discussed is, “What is the radius of the geostationary orbit?” The geostationary orbit must satisfy three conditions: (1) the velocity must be in the direction and sense of the Earth’s rotation; (2) the velocity must be constant; and (3) the period of revolution must exactly match the period of rotation of the Earth in inertial space. The first condition implies that the orbit must be a direct orbit in the equatorial plane. The second condition implies that the orbit must be circular. To satisfy the third condition, the radius of the orbit must be chosen to correspond to the required period given by Kepler’s third law. According to this law, the square of the orbital period is proportional to the cube of the semimajor axis.1 The problem reduces to determining the value of the orbital period. However, it is not simply 24 hours, or one mean solar day. The mean solar day is equal to the average time interval between successive transits of the Sun over a given meridian and is influenced by both the rotation of the Earth on its axis and the motion of the Earth along its orbit. Instead, the appropriate period of the geostationary orbit is the sidereal day, which is the period of rotation of the Earth with respect to the stars. One sidereal day is equal to 23 h 56 m 4.0905 s of mean solar time, or 86 164.0905 mean solar seconds. Using this value in Kepler’s third law, we compute the orbital radius as 42 164.172 km. Relationship between the sidereal day and the mean solar day. Yet even this value for the orbital period is not quite correct because the Earth’s axis precesses slowly, causing the background of stars to appear to rotate with respect to the celestial reference system. The Earth’s axis is tilted by 23.4° with respect to a line perpendicular to the orbital plane and executes a conical motion with a precessional period of about 26 000 years. Therefore, the sidereal day is less than the true period of the Earth’s rotation in inertial space by 0.0084 seconds. On this account, the period of the geostationary orbit should be 86 164.0989 mean solar seconds. The corresponding orbital radius is 42 164.174 km. There is also a correction due to the unit of time itself. The mean solar second is defined as 1/86 400 of a mean solar day. However, in terms of the second of the International System of Units (SI), defined by the hyperfine transition of the cesium atom, the present length of the mean solar day is about 86 400.0025 seconds. The mean solar day exceeds a day of exactly 86 400 seconds by about 2.5 milliseconds due to slowing of the Earth’s rotation caused by the Moon’s tidal forces on the shallow seas. This extra time accumulates to nearly one second in a year and is compensated by the occasional insertion of a “leap second” into the atomic time scale of Coordinated Universal Time (UTC). Adding this increment to the orbital period, we obtain 86 164.1014 seconds. The corresponding orbital radius is 42 164.175 km. The analysis so far has assumed that the Earth can be regarded as a perfect sphere. However, in reality the Earth’s shape is more nearly oblate. The equatorial radius is 6378.137 km, while the polar radius is 6356.752 km. The gravitational perturbation due to oblateness causes the radius to be increased by 0.522 km.2 The resulting geostationary orbital radius is 42 164.697 km. In practice, once the satellite is operational in the geostationary orbit, it is affected by a variety of perturbations that must be compensated by frequent stationkeeping maneuvers using thrusters onboard the spacecraft. These perturbations are caused by the gravitational attractions of the Sun and the Moon, the slightly elliptical shape of the Earth’s equator, and solar radiation pressure. Because the orbit is constantly changing, it is not meaningful to define the orbit radius too precisely. By comparison, using recent data for 16 Intelsat satellites, we obtain a semimajor axis with a mean of 42 164.80 km and a standard deviation of 0.46 km. A perfectly geostationary orbit is a mathematical idealization. Only the distinction between the mean solar day and the sidereal day needs to be taken into account. Therefore, it is customary to quote a nominal orbital period of 86 164 seconds and a radius of 42 164 km. The height above the equator is 35 786 km and the orbital velocity is 3.075 km/s. _________________________________ 1 Mathematically, Kepler’s third law may be expressed as T 2 = (4 π 2 / GM) a 3, where T is the period, a is the semimajor axis, and GM is the gravitational constant for the Earth, whose value is 398 600.5 km3 / s2. For a circular orbit, the semimajor axis a is equal to the radius r. 2 The correction is ∆r = ½ J2 ( RE / r )2 r, where r is the orbital radius, RE is the Earth’s radius, and J2 is the Earth’s oblateness coefficient, 0.001 083.

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