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MAE2_Lecture11

# MAE2_Lecture11 - Space Flight Mechanics I The Two-Body...

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Space Flight Mechanics I The Two-Body Problem Orbit Equation Orbital Trajectories Energy Equation Orbit Geometry MAE 2 NASA Image

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2 MAE 2 The Two-Body Problem Motion of a spacecraft in the solar system is generally dominated by one central body at a time. The trajectory of the spacecraft relative to the central body (Earth, sun, moon, etc.) represents a solution to the two-body problem. Assumptions for the two-body problem include: The motion of the spacecraft is governed by attraction to a single central body. The mass of the spacecraft is negligible compared to the central body. The bodies are spherically symmetric, with mass concentrated at the center of each body. Only gravitational forces act on the bodies.
3 MAE 2 Circular Orbit Newton's law of universal gravitation states that the gravitational force between two masses is inversely proportional to the square of the distance beteen them. F = G m M r 2 F = gravitational force m = spacecraft mass M = central body mass G = 6.67 × 10 11 m 3 / kg.s 2

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