Dorrie Byford Week 5: February 15 th , 2007

1. Dorrie ByfordWeek 5: February 15th, 2007 Communications Group Leader / Autonomous Rendezvous Team Member / Website Designer Satellite Selection and Optimization Dorrie Byford

2. Satellite Location Scenarios • One in Gangale orbit leading Mars • Mars sats capable of transmitting to Earth during blockage • Two in Gangale orbit (one leading, one trailing) • Mars sats solely relay from Gangale sat to Mars • One at L4 • Mars sats capable of transmitting to Earth during blockage • One at L4 & one at L5 • Mars sats solely relay from L4/L5 to Mars • One leading Mars in same orbit • Mars sats capable of transmitting to Earth during blockage • One leading Mars and one trailing Mars • Mars sats solely relay from leading/trailing to Mars • All scenarios have 3 satellites orbiting Mars Dorrie Byford

3. Optimal Scenario • Two Satellites in Gangale orbit • ±8 deg from Mars • ±20 mil km z amplitude • Satellite Requirements: • Leading/Trailing Gangale sats • 2 satellites • 7 m dishes • 15.75 kW each • Mars sats • 3 satellites • 7 m dishes • 1 kW each km km km Dorrie Byford

4. Back-up Slides Dorrie Byford

5. Comm Statistics Dorrie Byford

6. Code Description • The code begins by setting all necessary variables for the locations and conditions of all bodies. Next the path of each body is calculated on a daily basis for a period of at least 7 Earth years. This accounts for every possible scenario since the positions repeat after this amount of time. Dorrie Byford

7. Code Assumptions • Earth travels on a perfect ellipse • Mars travels on a perfect ellipse with the Sun offset from the center Dorrie Byford

8. Comm Statistics • The code next checks to see if each satellite has direct line of sight with Earth. The equation for a line between the sat’s current location and Earth is created. Now all y values tested for: – radius of Sun <= x <= radius of sun • If any value falls inside the Sun, line of sight is not available and that satellite can not be used on that day • For the Gangale satellites, the line of sight problem is 3D. To handle this, the same procedure is followed three times – xy, yz, and zx. If the line goes through the Sun from all three directions, then the signal is blocked. Dorrie Byford

9. Gangale Orbit km km km *All figures output from attached Matlab code Dorrie Byford

10. Note on the Sun • While the sun may seem large compared to the orbits, it is actually to scale. Instead of just making the sun it’s actual size, I included the 3 deg that transmissions must be away from the sun. Dorrie Byford

11. Earth-Mars Orbits km Dorrie Byford km

12. L4/L5 Locations km Dorrie Byford km

13. Comm Blockage • When the program finds a position where both satellites are blocked by the Sun, the code aborts and a plot is made of the current location of all applicable bodies. The following slides show the boundary of the complete comm blockage situations. Dorrie Byford

14. Comm Blockage w/ 1 Gangale • <= 16 deg b/t Mars and sat km km km Dorrie Byford

15. Comm Blockage w/ 2 Gangale • <= 7 deg b/t Mars and sats km km km Dorrie Byford

16. Comm Blockage w/ 1 Leading • <= 18 deg b/t Mars and sat km km Dorrie Byford

17. Comm Blockage w/ Leading & Trailing • <= 9 deg b/t Mars and sats km Dorrie Byford km

18. Satellite Usage Optimization • If only one satellite has line of sight, then that satellite is used. However, if both satellites can be used, the program chooses the satellite with the shortest transmission distance. The program also keeps track of which satellite was selected for each day so that usage statistics can be calculated. Dorrie Byford

19. Program Output • Once all 7 years have been evaluated, the program outputs stastistical analysis. It computes max and min distances, corresponding transmission times, % of time each sat is used, and % of time (throughout 7 years) that comm could be maintained if one sat was lost. The following slides list the output for each scenario. Dorrie Byford

20. 1 Gangale Output • No comm blackouts. • Maximum transmit distance using Gangale sat: 4.0082e+008 km • Maximum transmit distance using Mars sat: 3.9851e+008 km • Maximum transmit distance from sat to Mars: 6.7504e+007 km • Maximum transmit time: 25.807 min • Minimum transmit time: 2.9383 min • Mars sat is prime: 94.47 percent • Gangale sat is prime: 5.53 percent • Maximum total transmit distance: 4.6452e+008 km • Minimum total transmit distance: 5.289e+007 km • Comm avail if Gangale sat is lost: 94.47 percent • Comm avail if Mars sat is lost: 97.312 percent Dorrie Byford

21. 2 Gangale Output • No comm blackouts. • Maximum transmit distance using Gangale Sat1: 3.9406e+008 km • Maximum transmit distance using Gangale Sat2: 3.9443e+008 km • Maximum transmit distance from sat to Mars: 3.4925e+007 km • Maximum transmit time: 23.848 min • Minimum transmit time: 4.898 min • Sat1 is prime: 46.198 percent • Sat2 is prime: 53.802 percent • Maximum total transmit distance: 4.2927e+008 km • Minimum total transmit distance: 8.8163e+007 km • Comm avail if Sat2 is lost: 96.928 percent • Comm avail if Sat1 is lost: 97.504 percent Dorrie Byford

22. L4 Output • No comm blackouts. • Maximum transmit distance using L4 sat: 3.2125e+008 km • Maximum transmit distance using Mars sat: 3.9851e+008 km • Maximum transmit time: 30.514 min • Minimum transmit time: 2.9383 min • L4 sat is prime: 5.53 percent • Mars sat is prime: 94.47 percent • Maximum total transmit distance: 5.4925e+008 km • Minimum total transmit distance: 5.289e+007 km • Comm avail if L4 sat is lost: 94.47 percent • Comm avail if Mars sat is lost: 93.971 percent Dorrie Byford

23. L4/L5 Output • No comm blackouts. • Maximum transmit distance using L4 sat: 3.5093e+008 km • Maximum transmit distance using L5 sat: 3.3043e+008 km • Maximum transmit time: 32.163 min • Minimum transmit time: 15.644 min • L4 sat is prime: 54.762 percent • L5 sat is prime: 45.238 percent • Maximum total transmit distance: 5.7893e+008 km • Minimum total transmit distance: 2.8159e+008 km • Comm avail if L4 sat is lost: 94.47 percent • Comm avail if L5 sat is lost: 93.971 percent Dorrie Byford

24. Leading Output • No comm blackouts. • Maximum transmit distance using A sat: 3.8406e+008 km • Maximum transmit distance using Mars sat: 3.9851e+008 km • Distance from Leading Sat to Mars sat: 6.7888e+007 km • Maximum transmit time: 25.108 min • Minimum transmit time: 2.9383 min • A sat is prime: 5.53 percent • Mars sat is prime: 94.47 percent • Maximum total transmit distance: 4.5194e+008 km • Minimum total transmit distance: 5.289e+007 km • Comm avail if A sat is lost: 94.47 percent • Comm avail if Mars sat is lost: 94.163 percent Dorrie Byford

25. Leading/Trailing Output • No comm blackouts. • Maximum transmit distance using A sat: 3.9245e+008 km • Maximum transmit distance using T sat: 3.9558e+008 km • Maximum transmit distance from sat to Mars: 3.9743e+007 km • Maximum transmit time: 24 min • Minimum transmit time: 5.0221 min • A sat is prime: 52.535 percent • T sat is prime: 47.465 percent • Maximum total transmit distance: 4.32e+008 km • Minimum total transmit distance: 9.0398e+007 km • Comm avail if A sat is lost: 94.432 percent • Comm avail if T sat is lost: 94.355 percent Dorrie Byford

26. Power Calculations • To find the necessary power requirements, I ran all of the distances with the Link Budget Analysis spreadsheet. The results for all six scenarios follow. Dorrie Byford

27. 1 Gangale Dorrie Byford

28. 2 Gangale Dorrie Byford

29. L4 Dorrie Byford

30. L4/L5 Dorrie Byford

31. Leading Dorrie Byford

32. Leading and Trailing Dorrie Byford