lecture04 - Circular orbit special case For circular orbits...

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Unformatted text preview: Circular orbit special case For circular orbits e = 0, there is no perigee, so is undefined. Argument of latitude is the angle from the ascending node n to the satellite position vector r , and is defined even for circular orbits. Argument of latitude is defined for all or- bits and if the orbit is non-circular, u = + . It is defined for non-circular orbits because the node, perigee, and satellite po- sition vector all lie in the same plane. It is common to say for circular orbits = 0 and = u , i.e., true anomaly is measured from the ascending node, even though they arent strictly speaking true. This works in many formulas. L. Healy ENAE404 Spring 2007 Lecture 4 (Feb. 6) 1 Equatorial orbit special case For equatorial orbits i = 0, there is no node, so is undefined. True longitude (right ascension) of periap- sis true which is the angle between I and perigee e . For non-equatorial orbits, note the plane that has the vernal equinox I and the perigee is in general neither the equatorial nor the orbital plane. Defining this angle in the general case in terms of the other angles therefore requires spherical trigonometry. It is thus not widely used outside of the context of equatorial orbits. It is common to say for equatorial orbits = 0 and = true , i.e., the argument of perigee is measured from I , even though they arent strictly speaking true. L. Healy ENAE404 Spring 2007 Lecture 4 (Feb. 6) 2 Circular and equatorial orbit special case For circular equatorial orbits, both and are undefined. True longitude (right ascension) true is the angle from I to the satellite. For non- circular, non-equatorial orbits, these vec- tors define a plane that is neither the equa- torial nor orbital plane, which again means defining this in terms of the other angles requires spherical trigonometry. It is thus not widely used outside of the context of circular, equatorial orbits. It is common to say for circular equatorial orbits that = 0, = 0, and = true i.e., true anomaly is measured from I , even though strictly speaking these things arent true. L. Healy ENAE404 Spring 2007 Lecture 4 (Feb. 6) 3 Satellite state representation We now have a representation in terms of the state, the Classical or Kepler orbital elements, a , e , i , , , and motion in time parameter ( t )....
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lecture04 - Circular orbit special case For circular orbits...

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