Name:GTID:ECE 6390: Satellite Communications and Navigation SystemsTEST 1 (Fall 2006)• Please read all instructions before continuing with the test.• This is a closed notes, closed book, closed friend, open mind test. On your desk you shouldonly have writing instruments and a calculator.• Show all work. (It helps me to give partial credit.) Work all problems in the spaces below theproblem statement. If you need more room, use the back of the page. DO NOT use or attachextra sheets of paper for work.• Work intelligently – read through the exam and do the easiest problems first. Save the hardones for last.• All necessary mathematical formulas are included either in the problem statements or the lastpage of this test.• You have 80 minutes to complete this examination. When the proctor announces a “last call”for examination papers, he will leave the r oom in 5 minutes. The fact that the proctor doesnot have your examination in hand will not stop him.• I will not grade your examination if you fail to 1) put your name and GTID number in theupper left-hand blanks on this page or 2) sign the blank below acknowledging the terms of thistest and the honor code policy.• Have a nice day!Pledge Signature:I acknowledge the above terms for taking this examination. I have neither given nor received unau-thorized help on this test. I have followed the Georgia Tech honor code in preparing and submittingthe test .11. Short Answer Section (19 points)(a)(1) (2)List two methods for attitude control on board a satellite.(b)All electronics must be space- Answer before launch to test their ability to withstandthe harsh temperatures and radiation of outer space.(c)The type of space propulsion system that has the best thrust-to-weight ratio is anAnswer drive.(d)In a simple medium, Maxwell’s equations can be simplified and combined into the scalarorAnswer wave equation, which describes radio wave propagation.(e) Famous Dates: Match the dates below to the events.1630a) First satellite Sputnik launched by USSR1945b) Georgia Tech last won the college football championship1957c) Arthur C. Clarke publishes “Extra-Terrestrial Relays”1958d) Telestar I and I I launched by Bell Labs1962e) Explorer I, first US satellite is launched1969f) First mobile satellite telephone networks launched1980sg) Johannes Kepler born2000h) Moon landing1990i) Global Positioning System launched22. Satellite Transponder: Label the components in the bent-pipe transponder diagram be-low. Be as specific as possible. (16 points)3. LO Leakage: Standard X-band radar guns in the US operate at 10.525 GHz. If all con-sumer electronics working in this portion of the spectrum use a similar superhetero dyne RFfront end with low-side local oscillators (LOs) to mix down the carrier to a common 10 MHzintermediate frequency, what would be the LO frequency used in a radar detector detectordetector detector. (5 points)34. Deep Space Orbits: A “gravitational slingshot” is a method for propelling a spacecraft toouter planets without using extraordinary amounts of fuel, cost, and propulsion complexity.Under most circumstances, the orbit of a satellite around the solar system is an ellipse withthe massive sun at one of the focii. The sun provides the principle gravitational forces tomaintain the orbit, unless the spacecraft approaches very close to a planet. For a brief timeperiod, the spacecraft can get a “free” boost in its relative velocity with respect to the sun bygetting “slung forward” by the nearby gravity well of a planet in motion. This will transferthe satellite to a higher orbit without firing thrusters. Conservation of energy still holds – thespacecraft is simply borrowing some of the momentum of the massive, moving planet.Below is a series of slingshots and orbits approximately used by the NASA to send the Cassinispacecraft to Saturn, originally launched on 15 October 1998. The spacecraft was first sentto Venus in a half-orbit to receive its first slingshot. After the first boost, the spacecraftcompleted an entire elliptical orbit whose aphelion (furthest point from the sun) was slightlypast Mars (the distance Raphin the diagram below). Venus had made several revolutions andwas nearly back at the same point in space when Cassini completed a full orbit and returnedfor its second slingshot boost. It was this final boost that placed the spacecraft in a half-orbitthat would set a rendezvous with Saturn. Clearly, this is a very effective albeit time-consumingmethod for traveling to distant planets.Below is a diagram of Cassini’s approximate path through the solar system, as well as all thepertinent planetary data. Estimate the year and month that the spacecraft first arrived at Sat-urn. Show all the steps in your calculation, using the back of this page if necessary. (30 points)RVenus=1.08 m10x11REarth=1.52 m10x11Raph=2.40 10 mx11Msun=1.98 10kgx30G =6.67 10 Nmkgx-11 2 -2RaphSaturnRSaturn=1.43 10mx12EarthCassiniSpacecraftJupiterSunMarsVenus45. Link Budget for a Deep Space Communications: Below are the specifications for thedigital downlink of a deep s pace probe. Assuming an ideal (Shannon limit) communicationsystem, calculate the maximum distance from earth that this satellite is capable of maintainingcommunications. (30 points)Communications LinkKu-band Downlink Frequency 14.0 GHzRF Signal Bandwidth 200.0 kHzTarget Data Rate 100.0 kbpsSatellite Transmitter HardwareSatellite Transmit Power (Amplifier Output) 800 WSatellite Transmit Antenna Gain 40 dBiEarth Station Receiver HardwareEarth Station Receiver Antenna 55 dBiReceiving Antenna Noise Temperature 30 KLow-Noise Amplifier Device Noise Temperature 70 K5Cheat Sheetλf = c c = 3 × 108m/sPR= PT+ GT+ GR− 20 log104πλ− 20 log10(r) − Additional Loss in dB¨r = r˙θ2−GMPr2¨θ = −2 ˙r˙θrT2=4π2a3µµ = GMpG = 6.672 × 10−11Nm2/kg2ME= 5.974 × 1024kgb = ap1 − e2perigee = (1 − e)a apogee = (1 + e)aCircular Orbit: V =rµRShannon Limit: C = B log2(1 + SNR) (bits/sec)Logarithmic Link Budget: PR= PT+ GT+ GR− 20 log104πλ− 20 log10(r)PN= kT B k = 1.3807 × 10−23J