Lunar Flight Dynamics Mark Beckman July 12, 2012

1. Lunar Flight Dynamics Mark Beckman July 12, 2012 Mark Beckman - Flight Dynamics

2. LRO Mission Minimum Energy Lunar Transfer: ~ 4 days 30 x 216 km Quasi-frozen Orbit: up to 60 days Lunar Orbit Insertion Sequence (4): 2-5 days 50 km Polar Mapping Orbit: at least 1 year • Lunar Reconnaissance Orbiter (LRO) mission launched on June 18, 2009 • It is still orbiting the moon today Mark Beckman - Flight Dynamics

3. LRO Mapping Orbit Mark Beckman - Flight Dynamics

4. How do you get to the Moon? • Need a really big rocket to shoot you from the Earth to the Moon • But it’s not that simple… • You must lead the Moon or when you arrive at the Moon 3-5 days later, the Moon won’t be there anymore (must know the precise time-of-flight to get to the Moon) • Remember that you are on a spinning sphere, so you only have one (sort of) opportunity per revolution (day) to shoot in the right direction • You want to shoot with the minimum amount of energy that will get you there because when you get there you will have to put on the brakes to enter lunar orbit (no refueling options in space!) Mark Beckman - Flight Dynamics

5. Further Complications • To complicate things, the Moon’s orbit is not circular - it’s elliptical or elongated so the distance from the Earth to the Moon is not constant • So your minimum energy to get to the Moon is a function of how far away the Moon is at arrival • Additionally, this is not a 2D problem, it’s 3D • The Earth spins on an axis tilted 23.5 degrees from the ecliptic plane • The Moon’s orbit is inclined 5 degrees from the ecliptic plane • You launch from a fixed latitude on the Earth Mark Beckman - Flight Dynamics

6. Opportunities to Get to the Moon • When you solve all that, you get one fixed location per day you can insert onto your cislunar trajectory • You actually get two launch opportunities per day, both of which put you at the same location above • Now you have your two solutions per day to get to the Moon but there might be other constraints • You might have shadows – the spacecraft flies into the Earth’s shadow. You might have to discard these opportunities. • The cost to insert at the Moon is a function of orbital geometry at arrival. You might have to discard days that are too expensive fuel-wise. • You might have restrictions on your final orbit. Lighting restrictions (ala LRO) would limit you to two chances per month, each chance being three consecutive days. Mark Beckman - Flight Dynamics

7. TLI Quadrants Launch MECO-1 Short coast solutions for northern latitude TLIs Two TLI locations Short/Long coast Long coast solutions for northern latitude TLIs Short coast solutions for southern latitude TLIs Long coast solutions for southern latitude TLIs Mark Beckman - Flight Dynamics

8. Short & Long Coast Mark Beckman - Flight Dynamics

9. LRO Images Mark Beckman - Flight Dynamics

10. Shackleton Crater Mark Beckman - Flight Dynamics

11. Launch Window Overview Insertion Plane Moon Earth 1 month Orbit Plane 1 year Moon • Beta-earth at insertion is relatively fixed (~80 deg) • Beta-sun at insertion is function of lunar phase • Sun circles moon system once/year after insertion • Two (2) extreme lighting conditions (the solstices) • Prime opportunities for looking at permanently light/shadowed regions • Need to be near beta-sun-0 at each of the solstices (South Pole Views) Mark Beckman - Flight Dynamics

12. Lunar Orbit Insertion • You have now planned how to GET TO the Moon, now you have to get into orbit about it • Lunar Orbit Insertion (LOI) is a retrograde maneuver (braking) that removes a lot of energy • Your spacecraft’s thrusters are limited in how much braking they can apply • This might affect your trajectory design since LOI maneuver is not anywhere near instantaneous (called finite maneuver modeling) • Now that you are at the Moon, the Moon itself causes problems … • Depending on your transfer trajectory, your LOI may not be visible to Earth • Depending on the time of year, LOI may not be in sunlight (spacecraft are almost all solar powered) • Lastly, what do you do if something goes wrong? The entire mission success depends on achieving lunar orbit Mark Beckman - Flight Dynamics

13. LRO LOI Mark Beckman - Flight Dynamics

14. 10 Day Recovery Maneuver • Deep Space Maneuver (DSM) must be performed within 10 days of lunar swingby • Approximately 90 day transfer to 2nd lunar encounter • Additional ΔV cost: 300 m/sec • Polar orbit can be achieved Mark Beckman - Flight Dynamics

15. LOI Interrupted Late Burn Time (min) 0 5 10 15 20 25 30 35 40 Anything > 20 min: Successful LOI Small overall ΔV penalty No impact to primary mission Mark Beckman - Flight Dynamics

16. You’re at the Moon now … but there’s more • Once you get into a low lunar orbit, you’d think you might be done • There is no atmosphere to slow the spacecraft down • There is no oblateness which causes orbital precession around the Earth • But low lunar orbits are not stable, they drift • The drift is in the eccentricity or elongation of the orbit • The drift is periodic but eccentricity generally increases • Eventually, the periapsis (or closest approach to the Moon) will impact the surface and your mission is over • So, you must routinely control your spacecraft (stationkeeping) to maintain your orbit Mark Beckman - Flight Dynamics

17. Stationkeeping Mark Beckman - Flight Dynamics

18. Stationkeeping Phase Plot Point every ascending node Lunar longitude labeled SK ΔV 1 SK ΔV 2 Mark Beckman - Flight Dynamics

19. LRO Low Periapsis Cycle Mark Beckman - Flight Dynamics

20. LRO-LCROSS Mark Beckman - Flight Dynamics

21. Lunar CA Mark Beckman - Flight Dynamics

22. LRO MOC Mark Beckman - Flight Dynamics

23. References • http://lunar.gsfc.nasa.gov/ • http://nssdc.gsfc.nasa.gov/planetary/lunar/ • http://lcross.arc.nasa.gov/ • http://www.nasa.gov/mission_pages/LADEE/main/ • http://science.nasa.gov/missions/grail/ Mark Beckman - Flight Dynamics