ASEN 5050 SPACEFLIGHT DYNAMICS Orbit Transfers

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ASEN 5050SPACEFLIGHT DYNAMICSOrbit Transfers

• Prof. Jeffrey S. Parker
• University of Colorado Boulder

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Announcements

• Homework 4 is due Friday 9/26 at 900 am
• Youll have to turn in your code for this one.
• Again, write this code yourself, but you can use
  other code to validate it.
• Concept Quiz 8 is active after this lecture due
  before Wednesdays lecture.
• Mid-term Exam will be handed out Friday, 10/17
  and will be due Wed 10/22. (CAETE 10/29)
• Take-home. Open book, open notes.
• Once you start the exam you have to be finished
  within 24 hours.
• It should take 2-3 hours.
• Todays office hours are at 200.
• Reading Chapter 6 (SIX, we jumped a few)

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Space News

• Sunday MAVEN arrived at Mars!

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Space News
Today Cassini is flying by Titan for the 106th
time. 1400 km altitude, 5.6 km/s Vp
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Space News

• Then Tuesday MOM arrives at Mars!
• MOI Tuesday at 2000 Mountain
• It will enter occultation at 2004
• MOI will end at 2024
• Well know if its successful around 2030
• Notice that I write Tuesday here. Itll be
  Wednesday in India and that keeps throwing me off
  ? Aw, time conversions!
• Not sure if there will be media coverage. Try
  http//www.spaceflightnow.com/ or NASA TV.

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ASEN 5050SPACEFLIGHT DYNAMICSOrbital Maneuvers

• Prof. Jeffrey S. Parker
• University of Colorado - Boulder

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Orbital Maneuvers

• Hohmann Transfer Walter Hohmann (1880-1945)
  showed minimum energy transfer between two orbits
  used two tangential burns.

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Hohmann Transfer

• Can also be done using elliptical orbits, but
  must start at apogee or perigee to be a minimum
  energy transfer.

(Algorithm 36, Example 6-1)
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Hohmann Transfer

• We just argued that the Hohmann Transfer is
  (usually) the most energy-efficient orbital
  transfer.
• Why?
• Consider EllipticalElliptical transfer
• Tangential Burns
• Energy efficiency considerations

V is highest at perigee, thus energy-changing
maneuvers are the most efficient at perigee!
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Energy Changes
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Hohmann Transfer

• Example LEO to GEO
• LEO altitude 185 km, radius 6563.136 km
• GEO altitude 35,786 km, radius 42,164 km
• VLEO 7.7932 km/s VGEO 3.0747 km/s
• VpT 10.2521 km/s VaT 1.5958 km/s
• ?V1 2.4590 km/s ?V2 1.4788 km/s
• Total ?V 3.9378 km/s

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Hohmann Transfer
GEO
Moon Radius
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Hohmann Transfer
GEO
Moon Radius
General radii transfers
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Orbital Maneuvers

• Bi-elliptic Transfer Uses two Hohmann
  transfers. Can save Dv in some cases. rb must
  be greater than rfinal, but can otherwise be
  optimized.

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Bi-elliptic Transfer

• Equations you need

SIMPLE, because all maneuvers are tangential,
co-planar.
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Bi-elliptic Transfer

• Much longer flight times for bi-elliptic
  transfer, but sometimes less energy.

(Algorithm 37, Example 6-2)
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Bi-elliptic Transfer

• LEO GEO via 100,000 km altitude ?V
• ?V1 2.903 km/s
• ?V2 0.799 km/s
• ?V3 0.605 km/s
• Total ?V 4.307 km/s
• More than Hohmann!

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Bi-elliptic LEO-GEO
Moon Radius
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Bi-elliptic LEO-GEO
Hohmann
Moon Radius
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Bi-elliptic Transfer

• LEO 250,000 km via 2.4 million km altitude ?V
• ?V1 3.192 km/s
• ?V2 0.329 km/s
• ?V3 0.327 km/s
• Total ?V 3.849 km/s
• More than Hohmann (4.058 km/s)!

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Bi-elliptic 185 km 250,000 km
Hohmann
Moon Radius
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Hohmann vs Bi-elliptic
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One-Tangent Burns
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Orbit Transfer Comparison
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Changing Orbital Elements

• ?a ? Hohmann Transfer
• ?e ? Hohmann Transfer
• ?i ? Plane Change
• ?O ? Plane Change
• ?? ? Coplanar Transfer
• ?? ? Phasing/Rendezvous

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Changing Inclination

• ?i ? Plane Change
• Inclination-Only Change vs. Free Inclination
  Change

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Changing Inclination

• Lets start with circular orbits

Vf
V0
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Changing Inclination

• Lets start with circular orbits

Vf
V0
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Changing Inclination

• Lets start with circular orbits

Are these vectors the same length? Whats the
?V? Is this more expensive in a low orbit or a
high orbit?
Vf
V0
?i
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Changing Inclination

• More general inclination-only maneuvers

Where do you perform the maneuver? How do V0 and
Vf compare? What about the FPA?
Line of Nodes
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Changing Inclination

• More general inclination-only maneuvers

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Changing The Node
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Changing The Node
Where is the maneuver located?
Neither the max latitude nor at any normal
feature of the orbit!
There are somewhat long expressions for how to
find uinitial and ufinal in the book for circular
orbits. Lamberts Problem gives easier solutions.
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Changing Argument of Perigee
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Changing Argument of Perigee
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Changing Argument of Perigee
Which ?V is cheaper?
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Circular Rendezvous (coplanar)

• Target spacecraft interceptor spacecraft

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Circular Rendezvous (coplanar)
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How do we build these?

• Determine your phase angle, f
• Determine how long you want to spend performing
  the transfer
• How many revolutions?
• Build the transfer
• Compute the ?V

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How do we build these?

• Compute the ?V

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Example 6-8
This should be 20
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Example 6-8
Should be positive
This should really be an absolute value (one
maneuver is in-track, one is anti-velocity)
This should really be an absolute value (one
maneuver is in-track, one is anti-velocity)
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Conclusions

• Better to use as many revolutions as possible to
  save fuel.
• Trade-off is transfer duration
• If you perform the transfer quickly, be sure to
  check your periapse altitude.

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Circular Coplanar Rendezvous (Different Orbits)
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Circular Coplanar Rendezvous (Different Orbits)

• Use Hohmann Transfer
• The wait time, or time until the interceptor
  and target are in the correct positions

p aL
Synodic Period
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Example 6-9
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Example 6-9
I think this should be pi alpha, not alpha pi
(see Fig 6-17)
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Announcements

• Homework 4 is due Friday 9/26 at 900 am
• Youll have to turn in your code for this one.
• Again, write this code yourself, but you can use
  other code to validate it.
• Concept Quiz 8 is active after this lecture due
  before Wednesdays lecture.
• Mid-term Exam will be handed out Friday, 10/17
  and will be due Wed 10/22. (CAETE 10/29)
• Take-home. Open book, open notes.
• Once you start the exam you have to be finished
  within 24 hours.
• It should take 2-3 hours.
• Todays office hours are at 200.
• Reading Chapter 6 (SIX, we jumped a few)