1. ASEN 5519: Interplanetary Mission Design Monday, September 25th, 2006
Jeffrey S. Parker
2. Lecture Overview Pork Chop Plots
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
3. Interplanetary Mission Design Why do we go?
Science, Exploration, Survival
What is the cost?
Excess arrival energy
Time of transfer
Planetary Quarantine concerns
How do we get there?
Optional: Gravity Assists
Optional: Resonant Orbits
Optional: Deep Space Maneuvers
Choose an itinerary that optimizes cost vs. benefit!
4. Terminology Quick review of terminology:
C3: Launch Energy (km2/s2)
V8: Hyberbolic excess velocity (km/s). It is the velocity you have arriving/departing a planet’s 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.
5. Lambert’s Problem Formulation of Lambert’s Problem:
Given: t0, R0, tf, Rf
Find: V0, Vf
Basic limitations: 2-body equations of motion
Determines an approximate ?V budget for Planet A – Planet B transfers for many different dates.
Pork Chop Plots
6. Application of Lambert’s Problem Trajectories that all depart the Earth at the same date, but arrive at Mars at different dates
7. Application of Lambert’s Problem More Mars arrival dates
Remember: Earth and Mars are not coplanar! Real Hohmann transfers rarely exist
8. Application of Lambert’s Problem More Mars arrival dates
Type II Trajectories
9. Application of Lambert’s Problem Summarizing the results
Departure date constant
Arrival date variable
10. Varying Departure Dates Now, let us allow the Earth-Departure time to vary
11. Pork Chop Plots (PCP’s) 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.
12. Pork Chop Plots (PCP’s)
13. Pork Chop Plots (PCP’s)
14. Resulting Trajectories
15. What happens if we miss our launch date?
16. Pork Chop Plots (PCP’s)
17. 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.
Produce a PCP for each segment in the itinerary!
18. Review: The Hyperbola
19. Hyperbola Toolbox (See Handout on Website)
20. Launch Parameters
21. Launching from Earth Earth’s pole is tilted with respect to the ecliptic. This obliquity angle is approximately 23.45°
Additionally, launch vehicles have a limited available azimuth-range.
22. Definition of the B-Plane
23. B-Plane Toolbox (Handout on Web)
24. B-Plane Targeting Advantage of B-Plane targeting: well-linearized system!
Example: constructing a TCM enroute to Mars
25. 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).
26. On to the Mars Odyssey Example! (Click here to directly link)