Spacecraft and Aircraft Dynamics - Lecture 5 - Illinois Institute of ...

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The Orbital ElementsSo far, all orbits are parameterized by 3 parameters• semimajor axis, a• eccentricity, e• true anomaly, f• a and e define the geometry of the orbit.• f describes the position within the orbit (a proxy for time).M. Peet Lecture 5: Spacecraft Dynamics 20 / 26
The Orbital ElementsNote: We have shown how to use a, e and f to find the scalars r and v.Question: How do we find the vectors ⃗r and ⃗v?Answer: We have to determine how the orbit is oriented in space.• Orientation is determined by vectors ⃗e and ⃗ h.• We need 3 new orbital elements◮ Orientation can be determined by 3 rotations.M. Peet Lecture 5: Spacecraft Dynamics 21 / 26
Page 1 and 2: Spacecraft and Aircraft DynamicsMat
Page 3: Given t, find r and vFor elliptic o
Page 6 and 7: What are these Angles?Mean AnomalyM
Page 8 and 9: Relationships between M, E, and fM
Page 10 and 11: Solutions for Hyperbolic OrbitsRefe
Page 12 and 13: Hyperbolic Anomaly• Hyperbolic An
Page 14 and 15: Relationship between M and f for Hy
Page 16 and 17: Example: Jupiter FlybyM. Peet Lectu
Page 18 and 19: Example ContinuedWe need to find th
Page 22 and 23: Inclination, iAngle the orbital pla
Page 24 and 25: Argument of Periapse, ωAngle measu
Page 26: SummaryM. Peet Lecture 5: Spacecraf

Spacecraft and Aircraft Dynamics - Lecture 5 - Illinois Institute of ...

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