Periodic Orbit Approach ~100 km Orbiters (Saturn+Enceladus Gravity) Orbit Insertion Costs Study on...
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Periodic Orbit Approach ~100 km Orbiters (Saturn+Enceladus Gravity) Orbit Insertion Costs Study on the Stability of Science Orbits of Enceladus Nathan J. Strange, Try Lam, Ryan P. Russell , Thomas R. Spilker Jet Propulsion Laboratory, California Institute of Technology Conclusions The Breath of Enceladus In mythology, Enceladus was a gigante who was buried buried under Mt. Aetna in Sicily by Athena. It is said his struggles to free himself cause Earthquakes, and his hot breath fuels eruptions of Aetna. How appropriate then that the moon Enceladus breathes its own icy plume. The images at right are a few of the many exciting observations made by the Cassini spacecraft of a very active cryovolcanic region near Enceladus’ south pole. Such discoveries hint that Enceladus is a prime target for future searches for liquid water and the possibilities associated with liquid water. Images of Enceladus courtesy NASA/JPL/Space Science Institute, images of Fountain of Enceladus courtesy wikipedia. Study Overview Enceladus will be a target for future solar system exploration and it is important to understand what types of Enceladus orbits are stable for future missions. This study is an early look at this question using two approaches: 1. Periodic Orbit Approach This approach finds periodic orbits in a time- independent, Saturn-Enceladus restricted three body problem + Enceladus gravity field model. In this system, the stability of a periodic orbit is determined from the eigenvalues of the full period state transition matrix. 2. Quasi-Periodic Orbit Approach This approach is a parametric search for long-life orbits in a full solar system gravity field. This a numerical approach where stability is defined as an orbit that neither escapes nor crashes in a 100 day interval. Polar orbits of Enceladus are the most desirable not only for global coverage of Enceladus, but also for providing good visibility of the active South polar region. Unfortunately, such orbits are highly unstable, primarily due to perturbations from Saturn’s gravity. A generic circular polar orbit of Enceladus will impact in about 2 days. Using repeat ground track (RGT) periodic orbits, the lifetime can be increased by an order of magnitude (assuming good knowledge of the full Enceladus gravity field) Quasi-Periodic Orbit Approach (Saturn System + Solar System Gravity) This approach is to propagate orbits for 100 days in the full N-body gravity of Saturn (with J2-J8), Saturn’s major moons, the planets, and the Sun. An initial guess is made based off of a family of distant retrograde orbits (DRO), a class of orbits known to have good stability characteristics in the restricted 3-body systems. [1,2], and then propagated for 100 days. The plot (top-right) shows the time until either impact or escape (as a color given by the scale) for a set of DRO orbits with various initial ranges from Enceladus and inclinations (defined in a rotating Enceladus- Saturn frame). The other plots at right are then generated from initial states where the DRO velocity is multiplied by a factor, k. The blue areas on the plots are relatively unstable, and the red areas are relatively stable (given that there is plenty of time to execute maneuvers before crashing or escaping). The white line on the plots denotes the orbits which have some visibility of the poles. The area to the right of the white line are orbits that can view the pole at some time. Most of this area is ‘blue,’ but there are a few ‘red’ orbits to be found some with relatively high inclinations. Two cases are shown below, propagated for 10 days. They are stable for 100 days, and offer oblique visibility of the poles. DRO, k=1.0 k=0.9 k=0.8 k=0.7 k = 0.7, r = 428 km, i = 50 deg k = 0.8, r = 500 km, i = 81 deg References [1] Lam, T., and Whiffen, G. J., “Exploration of Distant Retrograde Orbits Around Europa.” AAS/AIAA Spaceflight Mechanics Meeting, Paper AAS 05-110, Copper Mountain, Colorado, January 23-27, 2005. [2] Hénon, M., “Numerical Exploration of the Restricted Problem V. Hill’s Case: Periodic Orbits and Their Stability.” Astronomy & Astrophysics, Vol. I, 223-238, 1969. [3] Ocampo, C. A., and Rosborouigh, G. W., “Transfer Trajectory for Distant Retrograde Orbits of the Earth.” AAS/AIAA Spaceflight Mechanics Meeting, Paper AAS 93-180, Pasadena, California, February 22-24, 1993. [4] Lam, T., Hirani, A., and Kangas, J. A., “Characteristics of Transfers to and Capture at Europa.” AAS/AIAA Spaceflight Mechanics Meeting, Paper AAS 06-188, Tampa, Florida, January 22-26, 2006. Acknowledgment For the synchronously rotating Enceladus, periodic orbits in the restricted three body problem plus Enceladus J2,J3, and C22 model, repeat ground tracks (RGT) periodic orbits and represent higher order solutions to the frozen orbit problem. The plot at right shows that RGT orbits are unstable for inclinations from 50º to 145º and most unstable inclinations near 90º. The plot at left shows a stable 50 deg inclined 100 km orbit. This orbit is linearly stable. Although it does not over fly the pole directly, is does offer oblique viewing of the polar regions. This is not sufficient for instruments that require nadir pointing, but the distance is only ~250 km for instruments that can point off-nadir. The repeat ground track coverage of the surface of Enceladus is shown by the bottom-left plot. This orbit could be used for the early phase of a mission until the gravity field of Enceladus is known well enough to enable an excursion into an unstable polar orbit. For a Saturn arrival v-infinity similar to Cassini, the ∆V cost is ~1.1 km/s or a Cassini style Saturn Orbit Insertion (SOI) (after passing through the gap in the F-G rings) followed by a Periapsis Raise Maneuver (PRM) to target a Titan flyby with the appropriate v-infinity for a Hohmann transfer to Enceladus. A Titan flyby would be targeted rather than one of Enceladus because it is more efficient to target Titan initially and then use multiple Titan Flybys to reach Enceladus. The lowest energy way to reach Enceladus from Titan is to use a Hohmann transfer. If the PRM targets Titan with a v-infinity of ~2.4 km/s, Enceladus may be reached with a v-infinity of ~3.7 km/s. This is the most energy efficient way to reach Enceladus without using many time consuming flybys of Saturn’s other moons. With a v-infinity of 3.7, km/s the Enceladus orbit insertion ∆V would be ~3.5 km/s to reach a 100 km circular orbit. It would require maneuvers of about 4.6 km/s from Saturn Arrival to Enceladus Orbit. This is a very large ∆V cost and would probably only allow for a small orbiter, unless an innovative way is found to reach orbit. stable unstable stable Average inclination (deg) ~50 o ~145 o 2:15 RGT Family References [1] Russell, R. P., Lara, M., "Repeat Ground Track Lunar Orbits in the Full-Potential Plus Third-Body Problem," Paper AIAA-2006-6750, Aug. 2006. [2] Lara, M., Russell, R. P., "On the Design of a Science Orbit about Europa," Paper AAS 06-168, Jan. 2006. • Polar orbits are highly unstable. • Many stable orbits exist that give oblique visibility of the poles. • Brief excursions from stable orbits into unstable polar orbits are possible. • Getting into Enceladus orbit is very expensive. The work described on this poster was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). The authors would like to thank Kim Reh and James Cutts for their support of this study.
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Transcript of Periodic Orbit Approach ~100 km Orbiters (Saturn+Enceladus Gravity) Orbit Insertion Costs Study on...
Periodic Orbit Approach~100 km Orbiters (Saturn+Enceladus Gravity)
Orbit Insertion Costs
Study on the Stability of Science Orbits of EnceladusNathan J. Strange, Try Lam, Ryan P. Russell , Thomas R. Spilker
Jet Propulsion Laboratory, California Institute of Technology
Conclusions
The Breath of EnceladusIn mythology, Enceladus was a gigante who was buried buried under Mt. Aetna in Sicily by Athena. It is said his struggles to free himself cause Earthquakes, and his hot breath fuels eruptions of Aetna.
How appropriate then that the moon Enceladus breathes its own icy plume. The images at right are a few of the many exciting observations made by the Cassini spacecraft of a very active cryovolcanic region near Enceladus’ south pole. Such discoveries hint that Enceladus is a prime target for future searches for liquid water and the possibilities associated with liquid water.
Images of Enceladus courtesy NASA/JPL/Space Science Institute, images of Fountain of Enceladus courtesy wikipedia.
Study OverviewEnceladus will be a target for future solar system exploration and it is important to understand what types of Enceladus orbits are stable for future missions.
This study is an early look at this question using two approaches:
1. Periodic Orbit ApproachThis approach finds periodic orbits in a time-independent, Saturn-Enceladus restricted three body problem + Enceladus gravity field model. In this system, the stability of a periodic orbit is determined from the eigenvalues of the full period state transition matrix.
2. Quasi-Periodic Orbit ApproachThis approach is a parametric search for long-life orbits in a full solar system gravity field. This a numerical approach where stability is defined as an orbit that neither escapes nor crashes in a 100 day interval.
Polar orbits of Enceladus are the most desirable not only for global coverage of Enceladus, but also for providing good visibility of the active South polar region. Unfortunately, such orbits are highly unstable, primarily due to perturbations from Saturn’s gravity.
A generic circular polar orbit of Enceladus will impact in about 2 days. Using repeat ground track (RGT) periodic orbits, the lifetime can be increased by an order of magnitude (assuming good knowledge of the full Enceladus gravity field)
Quasi-Periodic Orbit Approach (Saturn System + Solar System Gravity)
This approach is to propagate orbits for 100 days in the full N-body gravity of Saturn (with J2-J8), Saturn’s major moons, the planets, and the Sun. An initial guess is made based off of a family of distant retrograde orbits (DRO), a class of orbits known to have good stability characteristics in the restricted 3-body systems. [1,2], and then propagated for 100 days.
The plot (top-right) shows the time until either impact or escape (as a color given by the scale) for a set of DRO orbits with various initial ranges from Enceladus and inclinations (defined in a rotating Enceladus-Saturn frame). The other plots at right are then generated from initial states where the DRO velocity is multiplied by a factor, k.
The blue areas on the plots are relatively unstable, and the red areas are relatively stable (given that there is plenty of time to execute maneuvers before crashing or escaping). The white line on the plots denotes the orbits which have some visibility of the poles. The area to the right of the white line are orbits that can view the pole at some time.
Most of this area is ‘blue,’ but there are a few ‘red’ orbits to be found some with relatively high inclinations. Two cases are shown below, propagated for 10 days. They are stable for 100 days, and offer oblique visibility of the poles.
DRO, k=1.0
k=0.9
k=0.8
k=0.7
k = 0.7, r = 428 km, i = 50 deg
k = 0.8, r = 500 km, i = 81 deg
References[1] Lam, T., and Whiffen, G. J., “Exploration of Distant Retrograde Orbits Around Europa.” AAS/AIAA Spaceflight Mechanics Meeting, Paper AAS 05-110, Copper Mountain, Colorado, January 23-27, 2005.
[2] Hénon, M., “Numerical Exploration of the Restricted Problem V. Hill’s Case: Periodic Orbits and Their Stability.” Astronomy & Astrophysics, Vol. I, 223-238, 1969.
[3] Ocampo, C. A., and Rosborouigh, G. W., “Transfer Trajectory for Distant Retrograde Orbits of the Earth.” AAS/AIAA Spaceflight Mechanics Meeting, Paper AAS 93-180, Pasadena, California, February 22-24, 1993.
[4] Lam, T., Hirani, A., and Kangas, J. A., “Characteristics of Transfers to and Capture at Europa.” AAS/AIAA Spaceflight Mechanics Meeting, Paper AAS 06-188, Tampa, Florida, January 22-26, 2006.
Acknowledgment
For the synchronously rotating Enceladus, periodic orbits in the restricted three body problem plus Enceladus J2,J3, and C22 model, repeat ground tracks (RGT) periodic orbits and represent higher order solutions to the frozen orbit problem.
The plot at right shows that RGT orbits are unstable for inclinations from 50º to 145º and most unstable inclinations near 90º.
The plot at left shows a stable 50 deg inclined 100 km orbit. This orbit is linearly stable.
Although it does not over fly the pole directly, is does offer oblique viewing of the polar regions. This is not sufficient for instruments that require nadir pointing, but the distance is only ~250 km for instruments that can point off-nadir.
The repeat ground track coverage of the surface of Enceladus is shown by the bottom-left plot.
This orbit could be used for the early phase of a mission until the gravity field of Enceladus is known well enough to enable an excursion into an unstable polar orbit.
For a Saturn arrival v-infinity similar to Cassini, the ∆V cost is ~1.1 km/s or a Cassini style Saturn Orbit Insertion (SOI) (after passing through the gap in the F-G rings) followed by a Periapsis Raise Maneuver (PRM) to target a Titan flyby with the appropriate v-infinity for a Hohmann transfer to Enceladus.
A Titan flyby would be targeted rather than one of Enceladus because it is more efficient to target Titan initially and then use multiple Titan Flybys to reach Enceladus.
The lowest energy way to reach Enceladus from Titan is to use a Hohmann transfer. If the PRM targets Titan with a v-infinity of ~2.4 km/s, Enceladus may be reached with a v-infinity of ~3.7 km/s. This is the most energy efficient way to reach Enceladus without using many time consuming flybys of Saturn’s other moons.
With a v-infinity of 3.7, km/s the Enceladus orbit insertion ∆V would be ~3.5 km/s to reach a 100 km circular orbit.
It would require maneuvers of about 4.6 km/s from Saturn Arrival to Enceladus Orbit. This is a very large ∆V cost and would probably only allow for a small orbiter, unless an innovative way is found to reach orbit.
stable unstable stable
Average inclination (deg)
~50o ~145o
2:15 RGT Family
References[1] Russell, R. P., Lara, M., "Repeat Ground Track Lunar Orbits in the Full-Potential Plus Third-Body Problem," Paper AIAA-2006-6750, Aug. 2006.
[2] Lara, M., Russell, R. P., "On the Design of a Science Orbit about Europa," Paper AAS 06-168, Jan. 2006.
• Polar orbits are highly unstable.• Many stable orbits exist that give oblique visibility of the poles. • Brief excursions from stable orbits into unstable polar orbits are possible.• Getting into Enceladus orbit is very expensive.
The work described on this poster was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). The authors would like to thank Kim Reh and James Cutts for their support of this study.
