453 Note_set_2a

453 Note_set_2a - MAE 453 Intro to Space Flight Dr. Scott...

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Dr. Scott Ferguson Note Set 2A Page 1 of 7 Note Set 2A – Formulating the Two-Body Problem The purpose of this note set is to formulate the foundation behind the two-body problem. The equations of motion in an inertial frame, and within a relative frame, will be developed to depict the motion of two bodies moving solely because of gravitational attraction. This material will form the foundation for establishing orbital equations. Introduction We’ll start with a vector-based approach of determining the motion of two bodies ± Motion is due solely to the mutual gravitational attraction ± The motion of one relative to another is a conic section (circle, ellipse, parabola, hyperbola) Provide the basis of developing the equations of motion associated with an orbit Equations of Motion in an Inertial Frame We are going to look at the “two-body problem.” Here we’ll consider two point masses acted on only by the gravitational force between them ± Let’s identify the center of mass for each mass with respect to an inertial frame of reference XYZ o The frame can translate, but the axes do not rotate o We can also identify the position vector G R r of the system’s center of mass, G : 2 1 2 2 1 1 m m R m R m R G + + = r r r (2-1) o r r is a vector that goes from m 1 to m 2
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This note was uploaded on 05/19/2010 for the course MAE 453 taught by Professor Mazzoleni,a during the Spring '08 term at N.C. State.

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453 Note_set_2a - MAE 453 Intro to Space Flight Dr. Scott...

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