STKAstrogator training

1
Mars Libration Point Missions
Major Paul E. Damphousse, USMC Captain Joshua M.
Kutrieb, USAF Captain Jon D. Strizzi, USAF
2
Overview

• Naval Postgraduate School / Analytical Graphics
• Sun-Mars Libration Point Orbits
• Communications System at Mars L1, L2
• Desktop Computer Simulation and Analysis
• 2016 Earth - Mars Transfer

3
Conferences

• AAS / AIAA Spaceflight Mechanics Meeting, Feb 01
• AAS / AIAA Astrodynamics Specialists Conference,
  Jul 01
• Mars Society International Convention, Aug 01

4
Motivation

• NASAs vision is to focus more of our energy
  on going to Mars and beyond. - Dan Goldin,
  AWST, Jan 2001
• NASA is seeking innovation to attack the
  diversity of Marsto change the vantage point
  from which we explore - CNN, 25 June 2001

5
PATCHED CONIC APPROACH

• 4-Body Motion for Interplanetary Travel
• Sun, Earth, Mars, Spacecraft
• Approximated in 3 Phases ( Each simplified as a
  2-body problem )
• Departure Phase
• Cruise Phase
• Arrival Phase

6
PATCHED CONIC APPROACH

• Patched Conic App w/ Spheres of Influence
• (Generic Earth-to-planet example)

7
Libration Points
8
Libration Points

• History -- Analytical solution for 3-Body Problem
• Newton - computed lunar orbit 8 error (1687)
• Euler - problem of 2 fixed force centers (1760)
• Euler - rotating/synodic coord system (1772)
• Jacobi - created his integral from Euler
  restricted 3-body system (1772)
• Lagrange - equilibrium pts of restricted 3-body
  system (1772)
• Confirmed 134 yrs later with discovery of Trojan
  asteroids

9
Libration Points

• Derivation
• 2 large bodies / primaries rotate about c.m.
• Produce 5 equilbrm pts where forces balance in
  synodic frame - lagrange (libration) points
• 3 colinear pts - L1, L2, L3 (unstable)
• 2 triangular pts - L4, L5 (stable)

Earth-Moon example
10
Earth - Mars Communications

• Challenges
• Lander -- added weight, cost, power, risk
• Blackout periods of over 12 hours
• Solutions
• Low-Medium Orbiting Relay Satellites
• Draim Constellation (common period, inclined)
• Aerosynchronous Constellation
• Phobos / Deimos Martian Moons
• L1 L2 Orbit Constellation
• only 2 satellites required for operations

11
Proposed Comm System
(ref. Pernicka, 1992)
12
Sun-Mars Libration Point Orbits

• L1, L2 Libration Point Orbits
• 2 satellites one in orbit about each point
• Near-continuous coverage of Mars surface / orbit
• Near-continuous link to Earth
• Mission Considerations
• Efficient Maintenance of 180 offset
• insertion maneuvers, station-keeping
• Solar Exclusion Zone
• T gt 0.9 yrs
• Orbit Geometry

13
Sun-Mars Libration Points

• L4, L5 Lagrange Points
• Stable Points
• very little station-keeping
• collecting Trojans for billions of yrs /
  collision risk
• 5261 Eureka, 1998 VF31 (1-2 km range)
• Communication Distance
• equil ?, Lagrange pt to Mars ? 227.9x106 km
• req power of Goldstone DSN station (California)

14
Sun-Mars Libration Point Orbits

• Libration Orbit Constellation Advantages
• 2 spacecraft required - minimum cost
• L1 spacecraft can always see Sun, Earth
• Long orbit period - simple tracking from Martian
  landers
• Observation platforms solar monitoring
• Small DV maneuvers required
• Disadvantages
• 1 million km distance - satellite to lander
• Solar radiation interference
• Loss of one satellite significant

15
Historical Missions

• Proposal Earth-Moon L2 point
• communications to the dark side (1966)
• John Breakwell, Robert Farquhar
• satellite oscillated around L2 pt, sporadic
  operations
• periodic, out-of-plane solution developed ? Halo
  orbit
• International Sun-Earth Explorer-3 (ISEE-3)
• launched Aug 1978
• mission in vicinity of Sun-Earth L1 point

16
(No Transcript)
17
Historical Missions

• Solar and Heliospheric Observatory Sat (SOHO)
• launched Dec 95, unobstructed view of Sun from
  S-E/M L1 pt

18
What is Astrogator?

• Interactive orbit maneuver and space mission
  planning tool
• Fully integrated within STK
• For Earth orbiting, Lunar, libration point, and
  interplanetary missions
• Key features
• User-defined gravity fields, propagators,
  coordinated systems
• Targeted trajectory design
• Online Help

19
Astrogator History

• Swingby (CSC) built for GSFC, 1989
• Commercialized as Navigator (CSC, 1994)
• Navigator purchased by AGI
• GSFC requests COTS solution
• Astrogator developed (1997)
• Uses some Swingby / Navigator algorithms
• Developers helped us on this effort
• Don Dichmann and John Carrico

20
Specific to Libration Orbit Missions

• Rotating Libration Point (RLP) Coordinate System
• Vehicle Local Coordinate Axes
• Propagators
• Targeting
• Differential Corrector
• manual iterations for 1st maneuver
• X-Z plane targeting

21
Rotating Libration Point CoordinateSystem (RLP)

• Used for missions to the libration points
• Defined for a system of primary and less-massive
  secondary gravitating bodies

Place origin (libration point) X-axis primary to
secondary Y-axis orthogonal to X-axis in the
plane and direction of secondarys motion
about primary Z-axis orthogonal to X Y
22
Vehicle Local Coordinate Axes

• VNC Frame
• In the VNC (Velocity - Normal - Co-normal)
  coordinate frame
• the X axis is along the velocity vector
• the Y axis is along the orbit normal
• the Z axis completes the orthogonal triad

23
Targeting

• Target Sequence allows Astrogator to define
  maneuvers in terms of goals they are to achieve
• Basic targeting problem
• Given a set of orbital goals, how can control
  parameters be perturbed to meet them?
• Differential Corrector is the robust Astrogator
  tool
• Libration point orbits require multiple segments
  and phased targeting approach

24
Mission Simulations and Analysis

• 2003 Direct Insertion About L1 (Pernicka study)

25
Mission Simulations and Analysis

• 2003 Transfer with Braking Maneuver

26
Mission Simulations and Analysis

• 2016 Transfer with Braking Maneuver

27
Mission Simulations and Analysis

• 2016 Transfer with Braking Maneuver
• TOF comparison for L1 insertion
• Comm constellation trajectories (2 s/c)

28
Mission Simulations and Analysis

• 2016 Transfer with Varying Z Amplitude

29
Mission Simulations and Analysis

• Braking maneuver at periapsis
• Small change in elevation angle yields large
  change in Z-Amplitude

30
Mission Simulations and Analysis

• Relative 180 deg Phasing Selection for S/C
• Achieve by
• Separate Launches
• Relative phasing control via on-board propulsion
• Three methods to control phasing with propulsion
• Midcourse Correction (MCC) Maneuver
• Time of Flight (TOF) Adjustment from Mars
  Periapsis to Libration Orbit Insertion (LOI)
• Martian Phasing Loop

31
Mission Simulations and Analysis

• Midcourse Correction (MCC) Maneuver
• Change time of arrival at periapsis Mars, LOI
• (Solid line)

32
Mission Simulations and Analysis

• TOF Adjustment from Mars Periapsis to LOI
• B-plane correlates with Z-amplitude
• Amplitude correlates with TOF

33
Mission Simulations and Analysis

• Martian Phasing Loop
• Phasing orbit period lt LOI epoch difference due
  to periapsis rotation and transfer TOF

34
Scenario
35
Targeting Methods with STK Astrogator

• Direct Transfer

36
Targeting Methods with STK Astrogator

• Libration Orbit Insertion (LOI)

37
Targeting Methods with STK Astrogator

• Braking Maneuver at Mars Periapsis

38
Targeting Methods with STK Astrogator

• Z Amplitude Variations

39
Phasing Loop Targeting

• Modified Target Procedure
• After one phasing loop by L1 s/c, LOI matches L2
  s/c
• Two simultaneous differential corrector targeting
  schemes
• Inner Targeter
• Transfer from phasing loop to LOI
• Outer Targeter
• Retrograde maneuver at first Mars periapsis

40
Communication Coverage

• Use properly phased
• system to
• determine gaps
• Max revisit time
• gap duration over interval
• Start at LOI
• propagate for 674 days
• determine visibility
• latitude points at
• one longitude

41
Stationkeeping (SK)

• History
• ISEE-3
• ACE
• SOHO
• Tight vs. Loose Control Techniques
• SK Frequency/Magnitude Dependencies
• Insertion maneuver
• Orbit error
• Time since burn
• Accuracy of burn
• SK Timing

42
Stationkeeping Sensitivity

• Initial study
• 0.1 mm/sec error causes deviation after ¾ rev.
• Sun-Earth deviations after 1½ rev.
• Deviations after same duration

43
Stationkeeping (part 2)

• Monte Carlo Analysis
• Uncertainties modeled as uncorrelated errors
• 100 m in position
• 10 cm/s in velocity
• 10 uncertainty in area of spacecraft
• DV error of 10 cm/s
• Vary these parameters propagate L2 s/c for 90
  days
• SK maneuver to return trajectory to periodic
  propagate for 1 year
• Gather statistics for this correction
• 100 runs
• Mars L2 DV 0.044 m/s (0.003 std dev)
• Earth L2 DV 0.45 m/s (0.03 std dev)
• Earth L2 (45 days) DV 0.43 m/s (0.03)

44
Conclusions

• Innovative Communications Concept Explored
• Revisit earlier work for 2003 mission
• Full trajectories for 2016 2 s/c in Sun-Mars
  libration orbits
• Use of phasing loop achieves 180 degree offset
• Communications coverage explored
• Poles experience few gaps, but longer (up to 6
  days)
• Monte Carlo analysis for stationkeeping
• Require order magnitude less than similar Earth
  orbits
• Successful NPS / Industry Partnership!

45
Acknowledgements

• Drs. Robert Farquhar and David Dunham (JHU/APL)
• Professor Henry Pernicka (SJSU)
• John Carrico and Roger Martinez (AGI)
• Dean Rudy Panholzer and Professor Don Danielson
  (US NPS)

46
Backup B-Plane
NASA, Mission Analysis and Design Tool (Swingby)
Mathematical Principles, Rev 1, Sept 1995
(Draft), Sect 4.4.1.