An analytic orbital model of Saturn’s F ring strands
Nicole Albers Miodrag Sremčević
Larry W. Esposito
European Planetary Science Congress
Rome, Italy, September 2010
University of Colorado at Boulder
PIA09806 (Image Credit: NASA/JPL/Space Science Institute)
The F ring strands in Voyager ISS
Murray et al. (1997)
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
The F ring strands in Cassini ISS
Charnoz et al. (2005)
=> F ring strands reveal a kinematic spiral that tightens up in time
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
The F ring strands in Cassini UVIS
no inner strand
one inner strand
Strands in occultations (see left side) are individual detections of potentially different physical strands. ● Multiple strands in a single occultation could denote a wrapped­around spiral structure.
● Residuals to the F ring core (above) suggest general properties of strand kinematics.
●
two inner strands
one inner strand
+ core­like strand
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Modeling the F Ring Strands' Kinematics (1/2)
(a) Strand is an ensemble of F ring particles
(b) Individual particles move on freely precessing, inclined ellipses after being ejected from the F ring core in a scattering or collision event
(c) Collective strand motion is described based on continuous distributions of individual particle orbits
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Modeling the F Ring Strands' Kinematics (1/2)
(a) Strand is an ensemble of F ring particles
(b) Individual particles move on freely precessing, inclined ellipses after being ejected from the F ring core in a scattering or collision event
(c) Collective strand motion is described based on continuous distributions of individual particle orbits
The strand's distribution of orbital elements translates into a phase­space distribution, providing insights into the ejecta's formation event. Although Prometheus' gravitational influence is taken into account, local perturbations during close encounters are not modeled by this approach.
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Modeling the F Ring Strands' Kinematics (2/2)
Semimajor axis a is the only independent parameter
∞
(1) Eccentricity and inclination are functions of a: X a =∑i c i a−a0 i
(2) Mean motion, apsidal and nodal precession are directly calculated including additional accelerations due to gravitational influences by the Sun and the Saturnian satellites, predominantly Prometheus and Pandora (3) Mean longitude, longitude of pericenter, and longitude of ascending X t , a= X 0 Ẋ a t−t X 
node are modeled as using the above frequencies (4) In the most general case: t ≠t ≠t 
t  : Epoch of apsidal alignment
t  : Epoch of strand formation
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Modeling the F Ring Strands' Kinematics (2/2)
Semimajor axis a is the only independent parameter
∞
(1) Eccentricity and inclination are functions of a: X a =∑i c i a−a0 i
(2) Mean motion, apsidal and nodal precession are directly calculated including additional accelerations due to gravitational influences by the Sun and the Saturnian satellites, predominantly Prometheus and Pandora (3) Mean longitude, longitude of pericenter, and longitude of ascending X t , a= X 0 Ẋ a t−t X 
node are modeled as using the above frequencies (4) In the most general case: t ≠t ≠t 
t  : Epoch of apsidal alignment
t  : Epoch of strand formation
Minimal strand model has ten orbital parameters: 0, t  ,0, t  , 0, t  , e i , i i 
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
System Snapshot (unobtainable): ●
Assume having a camera with a 360° FOV hovering above Saturn that could take an instantaneous image of the entire F ring “Panorama” Observations:
●
Camera staring at constant inertial longitude allowing the ring material to pass through the FOV at its mean motion; images taken in succession are then “stichted” together in the co­rotating longitude frame
● Particle­Tracking Observations:
Camera following a ring stretch at its mean motion on Keplerian orbit; images taken in succession are then “stitched” together in the mean anomaly frame
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Radius – 140220 km
System Snapshot
Inertial Longitude
Shows the strands' true nature
The system after ~143 days Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
System Snapshot (unobtainable): ●
Assume having a camera with a 360° FOV hovering above Saturn that could take an instantaneous image of the entire F ring “Panorama” Observations:
●
Camera staring at constant inertial longitude allowing the ring material to pass through the FOV at its mean motion; images taken in succession are then “stichted” together in the co­rotating longitude frame
● Particle­Tracking Observations:
Camera following a ring stretch at its mean motion on Keplerian orbit; images taken in succession are then “stitched” together in the mean anomaly frame
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Panorama
Inertial Longitude
Corotating Longitude
Radius – 140220 km
System Snapshot
Shows the strands' true nature
Almost any form will create a straight line!
After ~143 days
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
System Snapshot (unobtainable): ●
Assume having a camera with a 360° FOV hovering above Saturn that could take an instantaneous image of the entire F ring “Panorama” Observations:
●
Camera staring at constant inertial longitude allowing the ring material to pass through the FOV at its mean motion; images taken in succession are then “stichted” together in the co­rotating longitude frame
● Particle­Tracking Observations:
Camera following a ring stretch at its mean motion on Keplerian orbit; images taken in succession are then “stitched” together in the mean anomaly frame
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Panorama
Particle­Tracking
Inertial Longitude
Corotating Longitude
Mean Anomaly
Shows the strands' true nature
Almost any form will create a straight line!
Reveals the underlying Keplerian orbits
Radius – 140220 km
System Snapshot
After ~143 days
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Radius – F ring core
System Snapshot
Panorama
Particle­Tracking
­2 deg Inertial Longitude
Corotating Longitude
Mean Anomaly
Apparent slope depends on observation time and true anomaly.
Illustrates the relative eccentricity of core and strand
Relative to the F ring core
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Radius – F ring core
System Snapshot
Panorama
Particle­Tracking
­160 deg Inertial Longitude
Corotating Longitude
Mean Anomaly
Apparent slope depends on observation time and true anomaly.
Illustrates the relative eccentricity of core and strand
Relative to the F ring core
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Panorama
Particle­Tracking
Inertial Longitude
Corotating Longitude
Mean Anomaly
Radius – 140220 km
System Snapshot
The system after ~605 days Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Three visualizations of the F ring system
Panorama
Particle­Tracking
Inertial Longitude
Corotating Longitude
Mean Anomaly
Radius – F ring core
Radius – 140220 km
System Snapshot
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Summary – Model implications (1/2)
●
Radial extent of the strand is determined at formation
1st order may be missing due to immediate interactions with the F ring core, known to wiggle on +/­ 50 km
●
Radial distances between different strand orders are nearly constant at the same true anomaly
●
●
Brightness/Equivalent Depth of strand diminishes in time ●
Constraints on the strand formation scenario
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Summary – Preliminary Results (2/2)
Residual scatter of about 50 km consistent with that of the F ring core
● Multiple inner strand detections indicate the “spiral” is tightening up
● Other than expected the equivalent depth appears unchanged in time
●
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy
Summary – Preliminary Results (2/2)
Residual scatter of about 50 km consistent with that of the F ring core
● Multiple inner strand detections indicate the “spiral” is tightening up
● Other than expected the equivalent depth appears unchanged in time
●
Cassini UVIS has most likely seen two physical inner strands since SOI;
Core­like inner strand seemingly has active material sources embedded.
Nicole.Albers@lasp.colorado.edu EPSC 2010, Rome, Italy