Chpt. 5: Describing Orbits By: Antonio Batiste 5.1 Orbital Elements: If you’re flying an airplane and the ground controllers call you on the radio to ask where you are and where you’re going, you must tell them six things: 1. Latitude 2. Longitude 3. Altitude 4. Horizontal velocity 5. Heading (I.e. north, south, etc.) 6. Vertical velocity (ascending or descending Johannes Kepler developed a method for describing and defining the six orbital elements. Classic Orbital Elements (COEs) • • • • Orbit’s size Orbit’s shape Orbit’s orientation Spacecraft’s location Orbit’s size – uses the semimajor axis, a ε = - μ /2a ε = specific mechanical energy (km2/s2) μ = gravitational parameter of the central body (km3/s2) a = semimajor axis (km) Orbit’s shape – Eccentricity (specifies the shape of an orbit by looking at the ratio of the distance between the two foci and the length of the major axis) e = 2c / 2a Eccentric Shapes 0<e<1.0 e =1 e > 1.0 ellipse parabola hyperbola NOTE: e = 0 is a circle Orbit’s orientation divides into 2 main parts: Orbit’s plane in space - Inclination, I -Right ascension of the ascending node (swivel), Ω Orbit within the plane -Argument of perigee, ω Orbit’s plane in space -Inclination, i – describes tilt of the orbital plane with respect to the fundamental plane (or equatorial plane) ranges: 0o to 180o degrees Refer to pg. 158 Fig. 5-5 -Right ascension of the ascending node, is the angle we measure along the equator Note: Right ascension is similar to longitude except its reference point is the vernal equinox. Orbit within the plane -Line of nodes – the intersection of the orbital plane and the fundamental plane. Ascending Node – where the spacecraft goes from below equator to above equator. (south to north) Descending Node – when the spacecraft goes from above equator to below equator. (north to south) Other Types of Orbits: Equatorial: Polar: 0 or 180 90 Direct(Prograde): 0 < i < 90 Indirect (Retrograde): 90< i <180 -Moves in direction of Earth’s rotation. (ascending node) -Moves against direction of Earth’s rotation. (ascending node) Argument of perigee, ω - the angle along the orbital path between the ascending node and perigee. (measure in direction of spacecraft motion) 0o < ω < 360o True anomaly, v – the angle along the orbital path from perigee to the spacecraft’s position vector, R More types of orbits: Geostationary orbit – a circular orbit with a period of about 24 hours and inclination 0o. (ex: comm. Satellites) Geosynchronous orbits – inclined orbits with a period of about 24 hours. Semi-synchronous orbit – has a period of 12 hours. Sun-synchronous orbits – are retrograde, low-Earth orbits (LEO), typically inclined 95o to 105o. (ex: remote-sensing) Molniya orbit – a semi synchronous, eccentric orbit. (ex; some specific comm. Missions)