ASEN 5519: Interplanetary Mission Design

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ASEN 5519Interplanetary Mission Design

• Monday, September 25th, 2006
• Jeffrey S. Parker

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Lecture Overview

• Pork Chop Plots
• Launch Windows
• Launch Parameters
• B-Plane Targeting
• Planetary Quarantine Requirements
• Mars Odyssey Example
• Spacecraft observations and Orbit Determination
• Using the B-Plane to Target a Planetary Arrival
• Next Week B-Plane Targeting applied to Gravity
  Flybys

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Interplanetary Mission Design

• Why do we go?
• Science, Exploration, Survival
• What is the cost?
• Launch energy
• Excess arrival energy
• Time of transfer
• Planetary Quarantine concerns
• How do we get there?
• Launch
• Optional Gravity Assists
• Optional Resonant Orbits
• Optional Deep Space Maneuvers
• Optional Low-thrust
• Choose an itinerary that optimizes cost vs.
  benefit!

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Terminology
Outbound

• Quick review of terminology
• C3 Launch Energy (km2/s2)
• V8 Hyberbolic excess velocity (km/s). It
  is the velocity you have arriving/departing a
  planets sphere of influence (SOI) w.r.t. the
  planet.
• V8 VS/C VPlanet
• V8in The excess velocity when arriving at a
  planet.
• V8out The excess velocity when departing from a
  planet.

VSCHelio
V8out
SOI
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Lamberts Problem

• Formulation of Lamberts Problem
• Given t0, R0, tf, Rf
• Find V0, Vf
• Basic limitations 2-body equations of motion
• Practical Implementation
• Determines an approximate ?V budget for Planet A
  Planet B transfers for many different dates.
• Pork Chop Plots

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Application of Lamberts Problem

• Trajectories that all depart the Earth at the
  same date, but arrive at Mars at different dates

Type I Transfers
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Application of Lamberts Problem

• More Mars arrival dates
• Remember Earth and Mars are not coplanar! Real
  Hohmann transfers rarely exist

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Application of Lamberts Problem

• More Mars arrival dates
• Type II Trajectories

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Application of Lamberts Problem

• Summarizing the results
• Departure date constant
• Arrival date variable

Type II
Type I
Type I
Type II
Minimum V8
Minimum C3
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Varying Departure Dates

• Now, let us allow the Earth-Departure time to vary

TD June 6, 05
TD June 26, 05
TD July 16, 05
TD Aug 5, 05
TD Aug 25, 05
Best Type I TD Aug 5, 2005, C3 16.15
km2/s2 Best Type II TD Aug 25, 2005, C3 15.6
km2/s2
Best Type I TD Aug 25, 2005, V8 2.47
km/s Best Type II TD June 26, 2005, V8 2.47
km/s
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Pork Chop Plots (PCPs)

• Add full trade-space of departure/arrival dates
• Building-block of basic interplanetary mission
  design
• Example shown is a PCP for Earth-Mars in 2005.

Mars Arrival Dates
Earth Departure Dates
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Pork Chop Plots (PCPs)
Type II Transfers
180 over-the-top Transfers (The Ridge)
Type I Transfers
C3 Local Minima
V8 Local Minima
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Pork Chop Plots (PCPs)
Type II Transfer C3 19.5 km2/s2 V8 2.8
km/s TOF 350 days
Type I Transfer C3 18 km2/s2 V8 2.65 km/s TOF
220 days
Nominal Mars Arrival July 14th, 2006
Nominal Mars Arrival March 26th, 2006
Nominal Earth Departure July 31st, 2005
Nominal Earth Departure Aug. 21st, 2005
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Resulting Trajectories
Type II
Type I
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What happens if we miss our launch date?
Type I Transfer
Type II Transfer
23.3 day window
24.0 day window
Example The Launch Vehicle can provide a C3 of
21 km2/s2
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Pork Chop Plots (PCPs)
Acceptable C3 and V8 ranges
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Distant Planets

• A single Pork Chop Plot analysis will generally
  be sufficient for a mission to a local planet.
• For distant planets, it is usually desirable to
  swing by nearby planets enroute to the distant
  planet to save energy.
• Implications
• Produce a PCP for each segment in the itinerary!

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Review The Hyperbola
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Hyperbola Toolbox(See Handout on Website)
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Launch Parameters
z
RLA Right-Ascension of Launch Asymptote DLA
Declination of Launch Asymptote C3 Launch
Energy
Ecliptic Axes (NOT Equatorial)
V8
x
y
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Launching from Earth

• Earths pole is tilted with respect to the
  ecliptic. This obliquity angle is approximately
  23.45
• Additionally, launch vehicles have a limited
  available azimuth-range.

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Definition of the B-Plane
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B-Plane Toolbox (Handout on Web)
Positions and velocities may be used at periapse
or at the SOI.
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B-Plane Targeting

• Advantage of B-Plane targeting well-linearized
  system!
• Example constructing a TCM enroute to Mars

Well-behaved and very linear relationships
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Planetary Quarantine Requirements

• Planetary Quarantine Requirements (PQRs) enforce
  that a spacecraft shall have a very low chance
  of impacting a planet if at any time during its
  mission all of its propulsion capabilities fail.
• Especially important in the cases of Venus,
  Earth, Mars, Europa, and various other moons in
  the solar system.
• In some cases, that means there has to be a 99
  chance of missing the planet at any time during a
  trajectory leg.
• In other cases, e.g., Cassini flying over Earth
  carrying radioactive materials, the chances of
  miss must be better than 99.9999 (literally).

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On to the Mars Odyssey Example!

• (Click here to directly link)