lecture5 - MECH 6521/498D Space Flight Performance Basic...

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MECH 6521/498D Space Flight Performance Gemini 3 - Titan II • Basic space flight and orbital mechanics •Circular and elliptical orbits •Orbit maneuvers • Hohmann transfer • plane and altitude changes • Perturbation Reading: Sutton and Biblarz Chapter 4 and Chapter 3
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• First and upper stage propulsion • Orbit injection or transferring from one-orbit to another • Velocity vector adjustments and minor in-flight corrections • Re-entry and landing • Rendezvous and docking • Plane change of flight trajectory • Simple rotation • De-orbiting and disposal of used/spent SC • Emergency or alternative mission •…etc. Space Flight To find the velocity increment required for various maneuvers, we must calculate trajectories and orbits . Common operations ¾ The engineering applications of orbital mechanics
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¾ Kepler’s laws ¾ Newton’s Law of Gravitation J.E. Prussing and B.A. Conway, Orbital Mechanics, Oxford University Press, 1993 Two approaches to understand orbital mechanics: Basic Orbital Mechanics Orbital mechanics (or flight mechanics) - study of the motions of artificial satellites and space vehicles moving under the influence of forces such as gravity, atmospheric drag, thrust, etc. - a modern development of celestial mechanics which is the study of the motions of natural celestial bodies such as the moon and planets.
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Johannes Kepler (1571-1630) • German mathematician, astronomer, astrologer, and natural philosopher • Born in Weil der Stadt and moved to Leonberg as a boy where he attended the local Latin school • Studies theology and philosophy at University of Tubingen • Professor of mathematics and astronomy, later become Imperial Mathematician to the Holy roman Emperor (1609 and 1619) • Grave Inscription in German: “The heavens I have measured, now I measure the shadows of the Earth. Towards the heavens strived the spirit, the body’s shadow rests here” Keplerian Orbits
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Johannes Kepler (1571-1630) • Keplerian Laws of planetary motion • Root of orbital mechanics • Reasonable approximation of the dynamics of a small body orbiting around much larger body in a 2-body universe • Interesting to note that Kepler derived his laws by observation only. He did not have calculus , which was only available 100 years later. (by Sir Isaac Newton)!! Keplerian Orbits
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For earth orbit: • the earth’s gravitational attraction is so much stronger than the sun and moon • can approximate most orbital dynamics by considering only the effects of the earth on the satellite. (clearly the effect of the satellite on the earth is negligible) the so-called restricted two-body universe • gravitational attraction of sun and moon are considered as perturbations to the two-body problem • in the two-body universe, if the effect of drag ignored the motions of the satellite are exactly described by Kepler’s laws. The Two-Body Problem
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lecture5 - MECH 6521/498D Space Flight Performance Basic...

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