BACKGROUND Traffic engineers use the Poisson (pronounced pwa-sso) probability distribution function (pdf) to forecast the number (traffic) of vehicles passing through a certain point in a highway per time unit. We will use the Poison pdf to calculate the current and future satellite traffic in the geosynchronous/geostationary orbit (GSO). According to the current GSO satellite list, there are 446 satellites orbiting the earth on this orbit. Hence, in the average, there is a separation of 360/446 = 0.8072 between a satellite and the next. In other words, the satellite frequency is 446/1440 = 0.31 satellites/minute, or 3.23 minutes between satellite and satellite. With the satellite frequency and the Poisson pdf, we can estimate the probability of, for instance, observing 2 consecutive GSO satellites within a time period.

The Poisson pdf is defined as: (,) = t () ! , for t 0, > 0, and k = 0, 1, 2,

Where, (lambda) is the measured mean frequency of a sample or population, 0.31 satellites/minute k is the number of events happening within a time t

For example, the Poisson probability of observing 2 consecutive satellites within 3 minutes is: (2, 3) = 0.313 (0.31 3) 2 2! P (2, 3) = 0.170, or 17%

REQUIREMENTS Develop a C++/Fortran program that will prompt the user for a stream/file containing the GSO satellite list, open the file, calculate the mean frequency, close the file, and prompt for different combinations of k and t, while the user wish. End the program with an entry of x or X at the appropriate prompt. The code should consist of, at least, a main function/program and two functions: one for calculating Poisson probabilities and another called from the latter to calculate factorials. The output(s) must be formatted. Note: Use the Developing a C++/Fortran Program handout as a guide. In addition, apply the Divide-and-Conquer principle. The submitted code should comply with all requirements for projects set forth in the Projects and Labs Rubric document. A sample binary code will be available for you to experiment and see how your own program must work.

Below is a sample of the input data

Name Common name Orbit inc

12061B YAMAL 300K -177.0 0.0

09008A NSS-9 -176.9 0.0

02055A TDRS 10 -174.3 5.5

13004A TDRS 11 -171.1 5.0

91054B TDRS 5 -167.5 14.5

17047A TDRS 13 -149.7 6.7

00081B AMC-8 (GE-8) -139.0 0.0

06054B AMC-18 -139.0 0.0

10008A GOES 15 -135.0 0.1

00054B AMC-7 (GE-7) -135.0 0.1

04003A AMC-10 (GE-10) -135.0 0.0

99060A AMC-4 (GE-4) -134.9 0.1

05041A GALAXY 15 (G-15) -133.0 0.0

04017A AMC-11 (GE-11) -131.0 0.0

96054A AMC-1 (GE-1) -130.9 2.2

17026A SES-15 -129.1 0.0

03013B GALAXY 12 (G-12) -129.0 0.0

08063A CIEL-2 -128.8 0.0

03044A GALAXY 13 (HORIZONS-1) -127.0 0.0

05030A GALAXY 14 (G-14) -125.0 0.0

08038B AMC-21 -124.9 0.0

08024A GALAXY 18 (G-18) -123.0 0.0

03034A GALAXY 23 (G-23) -121.0 0.0

04016A DIRECTV 7S -119.0 0.0

10010A ECHOSTAR 14 -118.9 0.0

02006A ECHOSTAR 7 -118.8 0.0

07009A ANIK F3 -118.7 0.0

16038B EUTELSAT 117 WEST B -117.0 0.0

13012A EUTELSAT 117 WEST A -116.8 0.0

13058A SIRIUS FM-6 -116.1 0.0

06049A XM-4 (BLUES) -115.2 0.0

11059A VIASAT-1 -115.1 0.0

15010B EUTELSAT 115 WEST B -114.9 0.0

12075B MEXSAT 3 -114.8 0.0

15056A MORELOS 3 -113.1 6.0

06020A EUTELSAT 113 WEST A -113.0 0.0

06054A WILDBLUE-1 -111.2 0.0

04027A ANIK F2 -111.1 0.0

09035A TERRESTAR-1 -111.0 2.7

06003A ECHOSTAR 10 -110.2 0.0

02023A DIRECTV 5 (TEMPO 1) -110.1 0.0

08035A ECHOSTAR 11 -110.0 0.0

99059A TELSTAR 12 (ORION 2) -109.2 1.6

96022A MSAT M1 -107.4 8.2

05036A ANIK F1R -107.3 0.0

00076A ANIK F1 -107.3 0.0

13014A ANIK G1 -107.3 0.0

12035A ECHOSTAR 17 -107.1 0.0

04041A AMC-15 -105.1 0.0

17063A SES-11 (ECHOSTAR 105) -104.9 0.0

09033A GOES 14 -104.3 0.1

95019A AMSC 1 -103.3 10.4

11035A SES-3 -103.0 0.0