Morehead State University Morehead, KY Prof. Bob Twiggs Understanding Orbits Orbit Facts 1

SSE-120 Understanding Orbits Page Longitude Latitude Altitude Horizontal velocity Heading ( north, south, etc.) Velocity (ascending or descending) 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?

SSE-120 Understanding Orbits 3 Understanding Longitude and Latitude

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

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

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SSE-120 Understanding Orbits Page Understanding Longitude and Latitude Morehead ~= W 84 0, N

SSE-120 Understanding Orbits 8 Satellite Launch Ports

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

SSE-120 Understanding Orbits 10 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 Understanding Orbits 11 Understanding Longitude and Latitude  r = 6378 km r’ r’ = 6378*cos (  ) Now can calculate throw velocity at any latitude  

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

SSE-120 Understanding Orbits Page

SSE-120 Understanding Orbits Page What determines the velocity of spacecraft in a circular orbit? v FgFg FcFc Velocity of spacecraft Altitude : given Orbit Period V cir = r -1/2 km/sec r - is from center of the earth – alt km V esc = r -1/2 km/sec Circumference = 2  r Orbit Time to orbit = distance/velocity Orbit Period = Time to orbit (minutes)

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

SSE-120 Understanding Orbits Page Orbital size, use the semimajor axis, a Orbital shape, is defined by eccentricity,  Orientation of the plane in space, uses  inclination, i  right ascension of the ascending node, Ω Orientation of the orbit within the plane is defined by the argument of perigee,  Spacecraft’s location in the orbit is represented by true anomaly,  Spacecraft orbit definition X X X

SSE-120 Understanding Orbits Page

Understanding Orbits X X X 19

SSE-120 Understanding Orbits Page 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

SSE-120 Understanding Orbits Page

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SSE-120 Understanding Orbits Page

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SSE-120 Understanding Orbits r h d For a zenith pass. 1.What is the distance d in km? 2.What is the time it takes the spacecraft to go from A to B? B A 29

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

SSE-120 Understanding Orbits Assessment Time 31