Titan Beyond the Rings (APOD 2009 May 5)

[apodman]

http://antwrp.gsfc.nasa.gov/apod/ap090505.html

Cassini and curious Earthlings await the coming Saturnian equinox this summer when the ring plane will point directly at the Sun.

And so I wondered, is the ring plane necessarily in a planet's equatorial plane?

And here's an answer:

http://www.astronomycafe.net/qadir/q58.html

[bystander]

And so I wondered, is the ring plane necessarily in a planet's equatorial plane?

If true for rings, why not moons?

[Clint]

Another amazing photograph of Saturn's Rings, we need to get closer, much closer, I hope team scientists decide that towards the end of Cassini Mission they send it plunging through the ring complex to hopefully finally photograph the individual particles that make up these amazing rings...it'll even be more amazing if Cassini survives such a journey too.

Clint
Melbourne.

[rigelan]

The picture is very surreal with Epimethius being crystal clear in focus and Titan in the back (seemingly out of focus)

Though, I suspect this IS how titan looks when in focus - The image lengths are both pretty much the same at this point, infinity compared to the curvature of the camera. They should both be in focus.

[neufer]

And so I wondered, is the ring plane necessarily in a planet's equatorial plane?
And here's an answer: http://www.astronomycafe.net/qadir/q58.html

If true for rings, why not moons?

Perhaps, because this explanation is NOT TRUE for the ring plane?

<<The majority of Uranus's rings are opaque and only a few kilometers wide. The rings of Uranus are thought to be relatively young, at not more than 600 million years old. The Uranian ring system probably originated from the collisional fragmentation of a number of moons that once existed around the planet. After colliding, the moons probably broke up into numerous particles, which survived as narrow and optically dense rings only in strictly confined zones of maximum stability.

Since the rings of Uranus appear to be young, they must be continuously renewed by the collisional fragmentation of larger bodies. The estimates show that the lifetime against collisional disruption of a moon with the size like that of Puck is a few billion years. The lifetime of a smaller satellite is much shorter. Therefore all current inner moons and rings can be products of disruption of several Puck-sized satellites during the last four and half billion years. Every such disruption would have started a collisional cascade that quickly ground almost all large bodies into much smaller particles, including dust. Eventually the majority of mass was lost, and particles survived only in positions that were stabilized by mutual resonances and shepherding. The end product of such a disruptive evolution would be a system of narrow rings. However, a few moonlets must still be embedded within the rings at present. The maximum size of such moonlets is probably around 10 km.>>

[capjoe]

The picture looks photo-shopped.
Titan is quite a distance from Saturn, and the apparent size of the disk would be nowhere near what the picture shows.
Titan's apparent size in the picture seems to be about the size of Saturn itself!

My guess is that in reality, the apparent size of Titan would be closer to Epimetheus then what is shown.

[neufer]

The picture looks photo-shopped.
Titan is quite a distance from Saturn, and the apparent size of the disk would be nowhere near what the picture shows.
Titan's apparent size in the picture seems to be about the size of Saturn itself!

My guess is that in reality, the apparent size of Titan would be closer to Epimetheus then what is shown.

• 5151 km : Titan (radial distance 1,221,930 km.)
  0325 km : Encke Gap (radial distance 133,590 km.)
  0113 km : Epimetheus (radial distance 151,422 km.)

Titan is 16 times bigger than the Encke Gap but appears only 5+ times bigger in the photo
so the Cassini spacecraft must be about 600,000 km. from the Encke Gap.

Epimetheus is only ~ 70.000 km [=sqrt(151,422^2 - 133,590^2)] closer than the Encke Gap
so there is little perspective distortion there (from 600,000 km. away).

(Of course a good photo-shopping would take all this into account as well.)

[Indigo_Sunrise]

The picture looks photo-shopped.
Titan is quite a distance from Saturn, and the apparent size of the disk would be nowhere near what the picture shows.
Titan's apparent size in the picture seems to be about the size of Saturn itself!

My guess is that in reality, the apparent size of Titan would be closer to Epimetheus then what is shown.

From this site:

The view was acquired with the Cassini spacecraft narrow-angle camera on April 28, 2006, at a distance of approximately 667,000 kilometers (415,000 miles) from Epimetheus and 1.8 million kilometers (1.1 million miles) from Titan. The image captures the illuminated side of the rings. The image scale is 4 kilometers (2 miles) per pixel on Epimetheus and 11 kilometers (7 miles) per pixel on Titan.

Maybe that'll clear things up a bit.


Nice image, BTW.

[BMAONE23]

The picture looks photo-shopped.
Titan is quite a distance from Saturn, and the apparent size of the disk would be nowhere near what the picture shows.
Titan's apparent size in the picture seems to be about the size of Saturn itself!

My guess is that in reality, the apparent size of Titan would be closer to Epimetheus then what is shown.

Don't forget, we are only seeing a very small portion of the "A" ring around the Encke Gap in the foreground (although Titan is slightly more than twice the distance indicated to Rhea). The area covered would appear to be the cross section covered by the "E" in the Encke Gap label in This Image

[aristarchusinexile]

What a beautiful photo!!!

[apodman]

And so I wondered, is the ring plane necessarily in a planet's equatorial plane?
And here's an answer: http://www.astronomycafe.net/qadir/q58.html

If true for rings, why not moons?

Perhaps, because this explanation is NOT TRUE for the ring plane?

I was careful to write "an" answer (not "the" answer) because the link is just an arbitrary starting point, not the all-inclusive final word on the subject. There's actually a lot to consider that wasn't addressed in any of the links I found.

[neufer]

Perhaps, because this explanation is NOT TRUE for the ring plane?

I was careful to write "an" answer (not "the" answer) because the link is just an arbitrary starting point, not the all-inclusive final word on the subject. There's actually a lot to consider that wasn't addressed in any of the links I found.

I was careful to write "Perhaps....?" because I haven't the foggiest
idea what "the" answer is for super thin equatorial rings.

(If you do find out, be sure to let us know.)

[apodman]

(If you do find out, be sure to let us know.)

I was hoping to post a link that would beg the question and motivate someone else to answer it for me. I know that turnabout is fair play, but I did get my bid in first.

---

Living where we do, we get to see more than our share of Washington, D.C. postcards and such. It is very popular to show a long shot down the mall including the Washington Monument and the Capitol Building. They usually include the moon, which is "photoshopped" in more often than not. Sometimes you can tell by the impossible angle of the lit side. Other times it appears impossibly large, and I end up calculating how far back the camera would have to be for it to be real. The question you answered about the apparent size of Titan reminded me of that.

[neufer]

Living where we do, we get to see more than our share of Washington, D.C. postcards and such. It is very popular to show a long shot down the mall including the Washington Monument and the Capitol Building. They usually include the moon, which is "photoshopped" in more often than not. Sometimes you can tell by the impossible angle of the lit side. Other times it appears impossibly large, and I end up calculating how far back the camera would have to be for it to be real. The question you answered about the apparent size of Titan reminded me of that.

I didn't think that Washington yet knew how to photo shop:

http://features.csmonitor.com/politics/ ... ne-photos/

[BMAONE23]

Further along the line of Planetary Ring systems falling into apparent equitorial orbital paths, I think it would have something to do with the oblateness of gas planets and the concentrated equitorial gravity factor. I have often wondered if this is also why (in our solar system) all Gas Planets have ring systems and all Rocky planets do not.

[Pete]

(If you do find out, be sure to let us know.)

I was hoping to post a link that would beg the question and motivate someone else to answer it for me. I know that turnabout is fair play, but I did get my bid in first.

I'll try to answer. Grain of salt and all that!

First, why should a ring form at all? Ring particle collisions are not perfectly elastic, meaning that they conserve angular (and linear) momentum and do not conserve kinetic energy. Collisions reduce the relative velocity of the colliding bodies, so a collision between two bodies whose orbits are tilted relative to each other will decrease their tilt angle. Over the course of many collisions, a puffed up ring system will relax into a disk.

Why should the ring form in the equatorial plane? As stated in the link you provided (http://www.astronomycafe.net/qadir/q58.html), orbits inclined with respect to Saturn's equatorial plane precess (change orientation in space) due to the planet's oblateness. The extra mass around Saturn's equator pulls inclined bodies back toward the equatorial plane, so they cross the plane slightly sooner than they would in a perfectly spherical potential. This results in precession of the line of nodes; it rotates in the opposite direction of orbital motion. (The pericentre also precesses, but that's only relevant to eccentric orbits.) Here's a diagram of nodal precession due to an exterior planet. Different source of equatorial mass, same idea:

Omega: longitude of ascending node (see Keplerian Elements)
black: unperturbed orbits
green: inner planet's trajectory under the perturbing influence of the massive outer planet

Getting to my point: the nodal precession frequency is a function of distance from the planet. Imagine that Saturn's rings are instantly tilted to some nonzero inclination with respect to Saturn's equator. Each ring orbit undergoes nodal precession, but due to the rings' extent in semimajor axis, each particle orbit precesses at a slightly different rate. The initial rings eventually smear out, and we end up with a puffed up disk that settles into a thin ring (equatorial this time) through collisions, as described above.

Digression: in a spherically symmetric potential, inelastic collisions conserve angular momentum, and do not conserve kinetic energy. That's basic mechanics. Now, nodal precession of an orbit is the same as precession of the angular momentum vector, which projects out of the orbital plane according to the right-hand rule. Mentally tilt Saturn's rings again. Initially, the projection of the rings' total angular momentum vector onto the equatorial plane is nonzero. In a few nodal precession timescales, the equatorial component of angular momentum will average out to zero. This non-conservation of total angular momentum is a consequence of Noether's theorem, which links symmetries to conservation laws. In particular, rotational symmetry implies conservation of angular momentum. The laws of motion are not symmetric in the polar angle of an oblate planet's potential, so angular momentum is not conserved in any tilted plane.

(This is really pedantic, but that link begot, not begged, the question http://en.wikipedia.org/wiki/Begging_th ... uial_usage )

Living where we do, we get to see more than our share of Washington, D.C. postcards and such. It is very popular to show a long shot down the mall including the Washington Monument and the Capitol Building. They usually include the moon, which is "photoshopped" in more often than not. Sometimes you can tell by the impossible angle of the lit side. Other times it appears impossibly large, and I end up calculating how far back the camera would have to be for it to be real. The question you answered about the apparent size of Titan reminded me of that.

A telephoto lens can make the moon appear impossibly large. For example: http://apod.nasa.gov/apod/ap081212.html
...But photoshopped postcards wouldn't surprise me.

[neufer]

Further along the line of Planetary Ring systems falling into apparent equatorial orbital paths, I think it would have something to do with the oblateness of gas planets and the concentrated equatorial gravity factor.

Besides oblateness (e.g., Pete's mechanism), tides on the earth transport earth angular
momentum to our own moon forcing it to be ever more equatorial (as well as more distant).
Could this be an important factor vis-a-vis rings?

(I hesitate to mention magnetic field interactions for fear of stirring up Harry. )

I have often wondered if this is also why (in our solar system) all Gas Planets have ring systems and all Rocky planets do not.

Rhea may have rings.

Recent reports have suggested that the Saturnian moon Rhea may have its own tenuous ring system,
which would make it the only moon known to possess a ring system.

[apodman]

(This is really pedantic, but that link begot, not begged, the question http://en.wikipedia.org/wiki/Begging_th ... uial_usage )

I beg your pardon. John McIntyre is the first linguist to call my understanding "dim". Very entertaining.

I hesitate to mention magnetic field interactions for fear of stirring up Harry.

Better stirred than shaken.