AERO423 HW5 Solution-2

AERO 423 Homework #5 Monday, October14, 2019, 11:59pm 1. AEROSAT is to be placed in an repeat ground track orbit that repeats every 10 days and every 127 orbits. The inclination is 66 degrees. a) Find the mean semi-major axis for the orbit. Provide a Table showing the iterations. b) Find the eccentricity for the frozen orbit. Term1 Term2 N0 R0 D Ro Height 1 1 0.000926097 7745.9561 1367.8211 1.005684246 1.000372227 0.000931708 7714.8269 -31.12926 1336.6919 1.005764927 1.000375237 0.000931785 7714.3988 -0.42806 1336.2638 1.005766047 1.000375279 0.000931786 7714.3929 -0.00594 1336.2579 1.005766063 1.000375279 0.000931786 7714.3928 -0.00008 1336.2578 b) 2. A satellite is in a circular orbit at an inclination of 60 deg. and an altitude of 800 km and it has a conical sensor, which operates with a minimum grazing angle of 15 degrees. a) Plot the curve of percent of latitude coverage as a function of latitude. b) Determine the swath width. Based on the swath width does the satellite see every point on the Earth each day. What area may not be seen? c) Then using STK select four points at 0 ° , 30 ° N, 55 ° N and 70 ° N and determine the percent of time each day each of these points are in coverage (in view of the satellite and above the 15 deg. grazing angle). What is the difference between this number and that calculated in a). A run time of two days should be sufficient. Solution d ω dt = 3 J 2 n 4 R e p ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 4 − 5sin 2 i ( ) 1 + J 3 2 J 2 R e p ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ sin i sin ω e ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = 0 1 + J 3 2 J 2 R e p ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ sin i sin ω e ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = 0, ω = π / 2 e = − J 3 2 J 2 R e p ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ sin i sin ω e = 0.000884 ε = 15deg, η = 59.12deg, λ = 15.88deg T = 2 π R 3 μ = 6052sec

a) b) Since SW>2807 every point from will be seen every day. c) 3. A satellite system for observing the Earth has been proposed. The requirement is that all points on the Earth between 75 ° N and 75 ° S should be in view of at least one satellite all the time. The sensor on the satellite has a grazing angle of 15 degrees. The system will have an inclination of 62 deg. a) Determine the minimum allowable altitude of the system that will satisfy the above requirement. b) Using an altitude of 700 km and using the class notes determine the minimum # of satellites that will satisfy the requirement. c) Based on your answer in b) propose a constellation (# of sats, and # of planes) d) Select points along a longitude line at latitudes 0, 20, 40, 60 and 80 degrees and then run STK to determine the # of satellites in view at all times for one day for each point. Did your proposed system satisfy the requirement? If it does not what change would you make to your constellation? Solution a) With i =62 then to see all points to 75 degree latitude With , 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 0 10 20 30 40 50 60 70 80 90 % Coverage Latitude-deg Percent Coverage i = 60 e = 15 Alt =800 SW = 2 R e λ max = 3534.7 km Distance between equator crossings= R e T hrs ( ) 15 deg/ hr ( ) π /180 = 2807 km 0 < θ < i + λ max ( ) λ max = 75 − i = 13deg ε = 15deg