Slide 0 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED The Two-body Equation of Motion Newton’s Laws gives us: The solution is an orbit described by a conic section (circle, ellipse, parabola, or hyperbola) that is fixed in space The satellite will trade kinetic energy for potential energy (speed for altitude) as it moves around in orbit We need six initial conditions to solve this equation –The six Classical Orbital Elements (a, e, i, , , ) are often used to visualize the location and motion of the satellite

Slide 1 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Orbit Size: Semi-major Axisa Orbit Shape: Eccentricity e Orbit Tilt: Inclination i Orbit Twist: Right Ascension of Ω the Ascending Node Orbit Rotation: Argument of Perigeeω Satellite Location: True Anomaly Classical Orbital Elements

Slide 2 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Size: Semi-Major Axis (a) How big is an orbit? We measure the length of the longest side of the ellipse and, by convention, divide it in half Orbit size depends on how fast we “throw” our satellite into orbit –The faster we throw it, the more energy its orbit has and the bigger its orbit is US: Fig. 5-2

Slide 3 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Shape: Eccentricity (e) e = 0 (circular) e =.5 e =.7 US, Fig. 5.3 Circle e =0.0 Ellipse e = 0.0 to 1.0 Parabola e = 1.0 Hyperbola e >1.0 e =.8

Slide 4 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Tilt: Inclination (i) Equatorial Plane Angular momentum vector h Inclination i K

Slide 5 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Tilt: Inclination (i) Inclination, iOrbit Type 0 o or Equatorial 90 o Polar 0 o  i  90 0 Direct or prograde (satellite moves in same direction as Earth’s rotation) 90 o  i  Indirect or retrograde (satellite moves in opposite direction of Earth’s rotation) US: Table 5-2

Slide 6 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Twist: Right Ascension of the Ascending Node (  ) We measure how an orbit is twisted by locating its ascending node relative to the vernal equinox direction (in the equatorial plane) Equatorial Plane Vernal Equinox Direction (Originally pointed to the constellation Aries, the Ram) Ascending Node Right Ascension of the Ascending Node (Also called the Longitude of the Ascending Node) 

Slide 7 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Rotation: Argument of Perigee (  ) We locate perigee relative to the ascending node (in the orbit plane) Equatorial Plane Ascending Node Perigee (Point Closest to the Earth) Argument of Perigee 

Slide 8 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Satellite Location: True Anomaly ( ) Finally, we locate the satellite relative to perigee, (in the orbit plane) Equatorial Plane Perigee (Point Closest to the Earth) True Anomaly

Slide 9 SP200, Block III, 1 Dec 05, Orbits and Trajectories UNCLASSIFIED Classical Orbital Elements i 2a e =.8 Ascending Node Vernal Equinox Direction Perigee   K h