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Unformatted text preview: MAE 453 Intro to Space Flight Dr. Scott Ferguson Note Set 3A Page 1 of 9 Note Set 3A Examining Circular and Elliptical Orbits The purpose of this note set is to build upon the orbital equation introduced in Note Set 2 for the special cases of circular and elliptical orbits. For each of these cases, equations for key geometric elements, velocities, and the period at introduced. Additionally, corresponding Keplers Laws are identified. Introduction In Note Set 2B, we established the orbit equation and derived the mechanical energy per unit mass The orbit equation has an eccentricity factor It defines the shape of the orbit or trajectory In this note set, we are going to investigate the properties (velocity, period, etc.) of the different orbits Circular Orbits (e = 0) As a refresher, we defined the orbit equation as: ( ) cos 1 1 2 e h r + = ( 2- 2 1 ) If e = 0 , this equation reduces to: 2 h r = ( 3- 1 ) o Reminder: this describes the orbit of mass m 2 around mass m 1 o What do we see about the value of r ?? Does it change? Lets figure out some properties of a circular orbit Why can the velocity of a circular orbit be given by Equation (3-2)?? r v circular = ( 3- 2 ) o Does the speed in a circular orbit change?? MAE 453 Intro to Space Flight Dr. Scott Ferguson Note Set 3A Page 2 of 9 The time, T , required for one orbit is called the period: 2 / 3 2 r T circular = ( 3- 3 ) o How did we get this?? We can determine the specific energy of the orbit by setting e = 0 in Equation (2-31): ( ) 2 2 2 1 2 1 e h = ( 2- 3 1 ) 2 2 2 1 h = o Substituting in Equation (3-1) gives: r circular 2 = (3-4) o Is the energy of a circular orbit positive or negative??...
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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.
- Spring '08