lecture09 - Satellite centered coordinate systems The final...

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Unformatted text preview: Satellite centered coordinate systems The final two coordinate systems we’ll discuss, RSW and NTW, are satellite-centered, • Type: usually Cartesian. • Center: satellite position. • Orientation: polar axis ˆ W = ˆ h perpendic- ular to orbital plane, RSW principal axis ˆ R = ˆ r , NTW second axis ˆ T = ˆ ˙ r . RSW is satellite radial , NTW is satellite normal coordinates. RSW is sometimes called Local Vertical Local Horizontal (LVLH) though it’s not precisely gravitationally horizontal. For circular orbits, they are the same, but ex- cept at perigee and apogee for non-circular or- bits they are not, because r and ˙ r are not per- pendicular. L. Healy – ENAE404 – Spring 2007 – Lecture 9 (Feb. 22) 1 In-track, cross-track When describing the position of a satellite, one often hears the terms • in-track : ˆ T direction, • along-track : ˆ S direction, • cross-track : ˆ W direction, usually in the context of errors. In-track and along-track are usually timing errors, because they are basically the velocity vector direction. Cross-track errors are either positioning or per- turbation computation errors, and are usually much smaller than cross track errors. L. Healy – ENAE404 – Spring 2007 – Lecture 9 (Feb. 22) 2 Flight-path angle Ref.: Curtis Sec. 2.4, pp. 48–50 Related to the RSW/NTW distinction is the concept of flight-path angle , γ . This is the angle that the velocity vector ˙ r makes with the local horizontal, the perpendicular to position vector. See Figure 2.11. In other words, it is the angle between ˆ S and ˆ T , note positive is clockwise. • For a circular orbit, the flight-path angle is always zero, because the velocity vec- tor is always perpendicular to the position vector. • For an elliptical (non-circular) orbit, it is positive from perigee to apogee, and neg- ative from apogee to perigee. L. Healy – ENAE404 – Spring 2007 – Lecture 9 (Feb. 22) 3 Picture of RSW vs. NTW R S N T Note that the positive sense of the flight-path angle from ˆ S to ˆ T is clockwise, but positive rotation about ˆ W (out of plane towards you) is counterclockwise. L. Healy – ENAE404 – Spring 2007 – Lecture 9 (Feb. 22) 4 Flight-path angle computation The tangent of the flight-path angle is the ratio of velocity along the radial vector v r , and perpendicular to it, v ⊥ . The prependic- ular component is the speed times the angular rate, and the radial speed is the time rate of change of the distance, both computed pre- vously (Lecture 8, p. 13) v r = ˙ r = s...
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lecture09 - Satellite centered coordinate systems The final...

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