MA 4362 Astrodynamics

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MA 4362Astrodynamics
The Bi-Elliptic Orbital Transfer Homework 10
Solution Vallado, Chapter 6, Sections 6.3.1,
6.3.2, 6.3.3
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Bi-Elliptic "Lunar-Boost" Transfer used to
Salvage HughesCommunication Satellite, 1998
Exploited Energy Gains from Bi-Elliptic Transfer
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Homework 10
Lets do some calculations on this problem
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Orbit Parameters
Radius!
Altitude!
44,250 km
Intercept At Lunar Perigee
Radius!
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Initial Orbit Parameters
Semi Major Axis and Eccentricity
(
Normalizing Velocity
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First Compute HohmannTransfer DV
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Calculate DV1 for Hohmann Transfer
Energy (Magnitude) of Initial orbit
Initial Orbit Outside Final Orbit
Burn 1 at Apogee
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Calculate DV2 for Hohmann Transfer
Energy (Magnitude) of Initial orbit
Initial Orbit Outside Final Orbit
Burn 2 at Perigee
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DV1, DV2, DVTotal Hohmann Transfer
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Next Compute DV Required toInsert Spacecraft
ontoElliptical Lunar Trajectory
Altitude!
Burn at Perigee Why?
Radius!
44,250 km
Intercept At Lunar Perigee
Radius!
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Compute DV1 forElliptical Lunar Trajectory
a1 , e1 -gt Initial (Useless) orbit Semi-Major
Axis, eccentricity aT -gt Lunar Trajectory
Semi-Major Axis
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Parameters of Trans-Lunar Orbit
DV1
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Compute DV2 Requiredby Lunar Gravity Assist
Well learn more about This later when we study
Three-body problems
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due
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DV2 Requiredfrom Lunar Gravity Assist
aT , eT -gt Lunar Trajectory Semi-Major Axis,
eccentricity aT -gt Earth-Return
Trajectory Semi-Major Axis
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1
2
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Parameters of Earth-Return Orbit
DV2 gravity assist
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Calculate DV required to Circularize Final orbit
aT -gt Earth-Return Trajectory Semi-Major
Axis Rc -gt Final Orbit Radius, 42241 km
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final
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Finally,Compare Total DV requiredfor Hohmann
Transferto DV Required for Bi-EllipticLunar
Gravity Assist Transfer
Assume that DV due to Gravity Assist is
Free .. I.e. dont count it
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Total DV Comparison
Hohmann Transfer
DVTotal DV1 DV2 5.468 km/sec
Bi-Elliptic (including DV2 gravity assist)
Transfer
DVTotal DV1 DV2 DVfinal 1.88184
km/sec
Bi-Elliptic (excluding DV2 gravity assist)
Transfer
DVTotal DV1 DV2 DVfinal 1.61726
km/sec
70.4 DV savings, WOW!
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Postscript
So Thats how they were able to salvage the
satellite!