Exploration of Distant Retrograde Orbits Around Europa AAS 05-110 Try Lam Gregory J. Whiffen 2005 AAS/AIAA Space Flight Mechanics Meeting Copper Mountain, Colorado 23-27 January 2005
Agenda 1/24/2005 Motivation and Introduction Stability of DROs around Europa Applications of DROs in Designing Missions Transfers to and from DROs Conclusion 2005 AAS/AIAA Space Flight Mechanics Meeting TL-2
Motivation With the potential of water under Europa s icy surface, going to Europa has been a key mission objective for many scientists and engineers An important element in designing a mission to Europa is safety, more specifically, the stability of the trajectories around Europa were it can be very chaotic Due to Jupiter s massive size, Europa s unknown gravity field, and perturbations from the other neighboring moons, transferring safely to Europa and remaining in a stable orbit around Europa is a challenge. Distant Retrograde Orbits (DROs) may be a solution 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-3
Introduction Distant Retrograde Orbits (DROs) are stable periodic orbits around a body with 3 rd body perturbation In the Jupiter-Europa System DROs are retrograde and near elliptical relative to Europa in the rotating frame, inertially the orbit spirals around Europa DROs are continuation of circular orbits in the retrograde direction Inertial Frame: 35,000 km DRO Jupiter-Europa Rotating Frame: 35,000 km DRO 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-4
Extremely stable in the planar case, but can exist for wide range of inclinations (approx. +/- 45 from planar) Introduction Size of a DRO is classified by the minor axis in the rotating frame Inclination for an out-of-plane DRO is defined by its angle at the right crossing of the rotating x- axis Europa Vy Varying the y-velocity at the right crossing of the x-axis we can show the stability for planar DROs at different distances from Europa Jupiter-Europa Rotating Frame: 10,000 to 50,000 km DRO 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-5
Stability of DROs around Europa Planar DROs are found to be stable for a wide range of distances (near Europa s surface to those near Jupiter) Stable - not impacting or escaping Europa for at least 200 days Stability for out-of-plane DROs can be analyzed by varying the z-velocity -0.40 3 Examle -0.45 Cases -0.50 L2 Distance unstable Y Velocity at Y=0 Crossing [km/sec] -0.55-0.60-0.65-0.70-0.75 stable -0.80-0.85 unstable -0.90 5000 10000 15000 20000 25000 30000 35000 40000 5:2 Resonance 3:2 Resonance 4:3 Resonance X Distance From Europa [km] near periodic DROs 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-6
Stability of DROs around Europa Stability of Out-of-Plane DROs: (Case 1 and 2) Stability of a 11,000 km and a 13,200 km DRO by varying both the Y-velocity and the Z-velocity - represent a simple periodic DRO Colorbar represents orbital lifetime in days near the 5:2 instability neck stable 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-7
Stability of DROs around Europa Stability of Out-of-Plane DROs: (Case 3) Stability of a 35,000 km DRO by varying both the Y-velocity and the Z-velocity - represent a simple periodic DRO Colorbar represents orbital lifetime in days stable 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-8
Mission Design Applications Another way to view stability of out-of-plane DROs is to rotate the velocity vector of a simple periodic DRO at right crossing The result Whiffen s Red Sea Plot stable orbital lifetime in days unstable Europa s Science Orbit - Near Stable Transfer - Unstable Transfer 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-9
Transfers Between DROs and Low Alt. Orbits Unstable Optimized Transfers on the Red Sea Plot Delta V from Europa Science Orbit (1,665 km 110 deg) to 35,000 km DRO [m/sec] Delta V from 35,000 km DRO to Circular Orbit (5,000 km 125 deg) [m/sec] 1800 1750 1700 1650 1600 1550 1500 1450 1400 1350 1300 1100 1050 1000 950 900 850 800 750 700 650 600 Europa Science Orbit (1,665 km & 110º) to 35,000 km DRO 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Coast Time / Total Flight Time 35,000 km DRO to 5,000 km Circular Orbit at 125º accel = 0.4069 mm/s^2 accel = 0.6103 mm/s^2 accel = 1.2207 mm/s^2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Coast Time / Total Flight Time Next Slide accel = 0.35 mm/s^2 accel = 0.25 mm/s^2 accel = 0.20 mm/s^2 accel = 0.15 mm/s^2 accel = 0.60 mm/s^2 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-10
Transfers Between DROs and Low Alt. Orbits Example Trajectory: Europa Science Orbit to 35,000 km DRO Rotating Frame accel = 0.4067 mm/s 2 V = 1.458 km/sec TOF = 59.66 Inertial Frame 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-11
Other Mission Design Applications DRO-Type Captures and Escapes DRO-Type Escape DRO-Type Capture 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-12
Conclusion and Future Work Conclusion: DRO are ideal quarantine orbits or intermediate orbits if stability is desired DROs provide a near continuous stable path from very distant orbits to low altitude orbits and vice versa DRO-type escapes and captures allow for high V escapes and distant captures around Europa Future work: Investigate the design trade between safe and unsafe transfers to Europa (navigating in the Red Sea Plot) Flight Time, V, and Minimum Orbital Lifetime Investigate long term stability of DROs (1000 years) 1/24/2005 2005 AAS/AIAA Space Flight Mechanics Meeting TL-13