MA 4362 Astrodynamics

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MA 4362Astrodynamics
The Bi-Elliptic Orbital Transfer Vallado,
Chapter 6, Sections 6.3.1, 6.3.2, 6.3.3
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The Hohmann Transfer
Always Optimal For Two-burn Transfer
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Something to Think About?
Can we exploit this region To design a transfer
maneuver that is more Efficient than a Hohmann
Transfer?
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Answer Yes! Sometimes?
The Bi-elliptic Three-burn Transfer
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Calculating the Transfer Orbits
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Calculating the Transfer Orbits (contd)
Free parameter
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Calculate DV1
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Calculate DV1 (contd)
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Calculate DV1 (contd)
Normalizing Dimensions by Rc1
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Calculate DV1 (concluded)
Defining
Normalized formula for DV1
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Calculate DV2
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Calculate DV2 (contd)
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Calculate DV2 (contd)
Simplifying
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Calculate DV2 (contd)
Simplifying
Defining
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Calculate DV2 (contd)
Normalized formula for DV2
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Calculate DV3
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Calculate DV3 (contd)
Simplifying
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Calculate DV3 (contd)
Normalized formula for DV3
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Total Delta V
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Total Delta V (contd)
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Total Delta V (contd)
Simplifying
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Problem Constraints
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Problem Constraints(Contd)
Transfer orbit(s) apogee Outside of final orbit
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Problem Constraints(Contd)
We build Constraint into DV equation by making
substitution
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Finally . Whew!
Comparison of Bi-ellipticand Hohmann Transfer
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Comparison of Bi-ellipticand Hohmann Transfer
What Happens when B ?????????????????????????
?????
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
What Happens when B ?????????????????????????
???? ?????????? simplifying and
?????????????????
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
What Happens when B ?????????????????????????
???? ?????????? finally
Not surprisingly you get a Hohmann transfer
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
What Happens when B-gt ????????????????????????
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
Find the Break Even Point
DVbi-elliptic? DVHohmann
hohmann
Bi-elliptic Best energy
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
Find the Break Even Point
DVbi-elliptic? DVHohmann
Simplify
R 11.938
Solution
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
For R lt 11.938 Hohmann Transfer is Superior
Beyond GTO
GTO
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
Finite Orbits
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
Finite Orbits
R60 Thats a pretty Big orbit
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Comparison of Bi-ellipticand Hohmann Transfer
(contd)
R60 Thats a pretty Big orbit
Rmax
km
about the same distance as the moon so is
the Bi-elliptic orbit of any practical use?
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Bi-Elliptic "Lunar-Boost" Transfer used to
Salvage Hughes HGS-1Communication Satellite, 1998
http//www.hsc.com/hsc_pressreleases/98_06_05_hgs1
.html
Exploited Energy Gains from Bi-Elliptic Transfer
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Bi-Elliptic Lunar-Assist Rescue Mission
Well learn more about This later when we study
Three-body problems