Morehead State University Morehead, KY Prof. Bob Twiggs RJTwiggs@gmail

1. Understanding Orbits Orbit Facts Morehead State University Morehead, KY Prof. Bob Twiggs RJTwiggs@gmail.com

2. Understanding Orbits This aircraft is flying across the country. The ground controller radios the pilot and wants to get all of the parameters that determine it’s flight, what are they? • Longitude • Latitude • Altitude • Horizontal velocity • Heading ( north, south, etc.) • Velocity (ascending or descending) Page 105-6 SSE-120

3. Understanding Orbits Understanding Longitude and Latitude SSE-120

4. Understanding Orbits Understanding Longitude and Latitude Greenwich, UK SSE-120

5. Understanding Orbits Understanding Longitude and Latitude Greenwich, UK SSE-120

6. Understanding Orbits Understanding Longitude and Latitude SSE-120

7. Understanding Orbits Understanding Longitude and Latitude Morehead ~= W 840, N 37.50 Page 105-6 SSE-120

8. Understanding Orbits Satellite Launch Ports SSE-120

9. Understanding Orbits Launch directions from launch ports 57.50 Vandenberg AFB ISS 51.60 Cape Kennedy 28.50 Polar Polar French Guiana Polar Near Equatorial SSE-120

10. Understanding Orbits Understanding Longitude and Latitude r = 6378 km What additional orbit launch velocity would be needed to launch to 500 km circular orbit from the equator to the east? What additional orbit launch velocity would be needed to launch to 500 km circular orbit from the equator to the west? SSE-120

11. Understanding Orbits Understanding Longitude and Latitude r = 6378 km 50 40 Q = 300 30 20 10 q 0 r’ = 6378*cos (q) r’ Now can calculate throw velocity at any latitude SSE-120

12. Understanding Orbits What must be the velocity of the launch vehicle to put a spacecraft into a given orbit? Orbital Velocity - v Altitude - h Altitude - h Page 308 SSE-120

13. Understanding Orbits Page 273 SSE-120

14. Understanding Orbits What determines the velocity of spacecraft in a circular orbit? Fc Altitude: given v Velocity of spacecraft Vcir = 631.3481 r-1/2 km/sec r - is from center of the earth – 6378 + alt km Orbit Vesc = 892.8611 r-1/2 km/sec Fg Orbit Period Circumference = 2pr Time to orbit = distance/velocity Orbit Period = Time to orbit (minutes) Page 181 SSE-120

15. Understanding Orbits Understanding Longitude and Latitude SSE-120

16. Understanding Orbits Eccentricity e = 2c/2a Relationship between conic sections Conic Sections Eccentricity Circle e = 0 Ellipse 0 < e < 1 Parabola e =1 Hyperbola e >1 Page 157 SSE-120

17. Understanding Orbits Spacecraft orbit definition • Orbital size, use the semimajor axis, a • Orbital shape, is defined by eccentricity, e • Orientation of the plane in space, uses • inclination, i X • right ascension of the ascending node, Ω X • Orientation of the orbit within the plane is defined by the argument of perigee, v X • Spacecraft’s location in the orbit is represented by true anomaly, u Page 155-156 SSE-120

18. Understanding Orbits Page 155-156 SSE-120

19. Understanding Orbits X X X

20. Understanding Orbits • Classic Orbital Elements (COEs) Checklist • Orbit’s size • Orbit’s shape • Orbit’s orientation • Orbit plane in space • Orbit within the plane • Spacecraft’s location Page 159 SSE-120

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29. Understanding Orbits For a zenith pass. A What is the distance d in km? d B What is the time it takes the spacecraft to go from A to B? r h SSE-120

30. Understanding Orbits What is maximum latitude that a geostationary spacecraft can be seen? SSE-120

31. Understanding Orbits Assessment Time SSE-120