Planetary Rings

Planetary Rings#

Planetary Rings#

  1. Planetary Rings

  2. Formation

    1. Roche Limit

    2. Formation of Saturn’s Rings

  3. Flatness of Ring*

    1. Flatness Timescale

  4. Planetary Gaps

    1. Spiral Waves

    2. Shepherding

      1. Moonlets

    3. Ring Survival

  5. Saturn’s Rings

    1. E Ring - The Blue Ring

Formation#

The formation of planetary rings are caused by the creation of small particles around the ring called dust:

  1. Circumplanetary disk (the debris when the planet was formed).

  2. Asteroid impact with moon.

  3. Tidal disruption by passing through the Roche Limit.

Roche Limit#

The main theory for the formation of planetary rings is due to tidal forces breaking apart large bodies orbiting the planet (e.g., moons, planetesimals). Any objects would lose its gravitational influence if it passes the Roche Limit given by:

\[\begin{split} \begin{aligned} a_\text{R} &= 1.44\left(\frac{M}{m}\right)^{\frac{1}{3}}R_m\\ a_\text{R} &= 1.44\left(\frac{\rho_M}{\rho_m}\right)^{\frac{1}{3}}R_M \end{aligned} \end{split}\]

Formation of Saturn’s Rings#

While Saturn’s rings are the most prominent, its formation is much less understood than Jupiter, Uranus, and Neptune. The three proposed formation are:

  1. Unaccreted remnants of Saturn’s protosatellite disk.

  2. Debris from a destroyed moon.

  3. Debris from a tidally disrupted comet.

Flatness of Ring*#

The same mechanics that makes galaxies and solar system flat plays the role in the ring. A ring is flat because the particle cloud first whiz around each other and eventually collide with on another resulting in cancelation of one of the spacial dimensions. This cancellation is due to the conservation of angular momentum such that the cloud is actually spining so it creates a plane that spins along the canceled axis.

See secular mechanics for better explanation on why inclinations changes due to orbital precession.

Flatness Timescale#

The time it takes for a cloud of particles around the planet to flatten depends on the optical depth \(\tau\) and vertical oscillation frequency \(\mu\),

\[t_\text{flat} = \frac{\tau}{\mu}\]

Planetary Gaps#

Spiral Waves#

There are two spacial waves (\(\frac{dN}{dV}\)) one horizontal (spiral density waves) and vertical (spiral bending waves) are caused by orbital resonance with the moon. Spiral waves are affected throughout the ring system however are not considered gaps due to the weak gravitational affects of the moons.

Shepherding#

We begin the formation of the gaps by a process called shepherding – moon repels ring material on nearby orbits. This is due to the transfering of angular momentum from the ring material to the moon effectively increasing the ring material’s eccentricity (\(L\propto \sqrt{1-e^2}\)).

  • One moon will push the ring material of two sides clearing the path for itself.

  • Two moons will push the ring material together creating a narrow band.

Moonlets#

Moonlets has a radius of several kilometers causing gaps several times its radius. The moonlets are porous with a low density of about \(\rho\le 500 \rm{\ kg\ m^{-3}}\)

Ring Survival#

The ring its material very fast due to either sputtering, gas drag, Poynting-Robertson drag, or re-accretion. The replenishment of rings are caused by the same reason they were formed see Formation

Saturn’s Rings#

E Ring - The Blue Ring#

The E-ring is unique due to its blue color. The E-ring is blue due to the size of the grains on the order of a micrometer

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