Saturn's rings at different phase angles
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The montage above shows the changing appearance of Saturn's rings with changing phase angle. The solar elevation angle relative to the ring plane is the same in all of the renderings. The rendering at upper left shows Saturn when the phase angle is 0 degrees. In the one at top right the phase angle is 4.5 degrees. Notice how much darker the rings appear. The brightening of the rings as the phase angle drops to 0 degrees is known as the opposition effect and is very pronounced in the case of Saturn's rings. What's happening is that as the phase angle increases we start 'seeing' shadows within the rings - they are composed of "billions and billions" of icy chunks (together with some dust) and these can cast shadows on each other. At lower left the phase angle has increased to 45 degrees and the rings are even darker. This is a somewhat similar viewing geometry to the one the Cassini spacecraft has on its approach to Saturn. At very high phase angles (126 degrees at lower right) the rings become very dark. In fact they should probably be even darker than here. Notice also the changing appearance of features within the rings. In particular the contrast within the B ring has increased and a contrast reversal is evident in the A ring: The outer part which was darkest at low phase angles is now the brightest part of the A ring.
In addition to the above, note that with increasing phase angle the rings not only darken but also get slightly redder.
These renderings are rendered with my new PT3RT renderer using a photometric model of Saturn's rings based on my own measurements of Earth based and Hubble Space Telescope (HST) images Saturn and on theoretical articles on the photometric behavior of the rings. In particular, I used this HST image, it is processed to appear very close to what Saturn looks like to the human eye. My measurements are not particularly accurate but I used a fairly large number of images and the accuracy was adequate for my purposes. The model of Saturn's rings is also fairly new. Last but not least, my own visual observations of Saturn also had a considerable influence on the final appearance of the renderings, especially the color and contrast. They were done with an MN61 telescope which is a 6" Maksutov-Newtonian.
One problem when doing something like this is that from Earth the phase angle never exceeds 6 degrees so the single image at 45 degree phase obtained by the Cassini spacecraft in October 2002 provided a very valuable data point. Many more images should be obtained in the coming months/years when Cassini nears Saturn and then starts orbiting the planet. It is known that as the phase angle increases from 0 to 6 degrees the brightness of the rings drops substantially (20-25%). Not unexpectedly, in the Cassini image the brightness had fallen further. I also made crude estimates from the Voyager spacecraft images but for various reasons the Voyager images are rather difficult for me to utilize for this purpose.
All of this is still under development and these renderings might change slightly in the future. In particular I suspect that in these renderings the rings start to get reddish too quickly when the phase angle becomes non-zero.
The opposition effect in new light
A very interesting consequence of the behavior of Saturn's rings described above is how they should appear when we get close to the planet. As seen from Earth the entire rings system has the same phase angle, thus the brightness of the rings at a particular distance from Saturn is more or less the same everywhere. When we get close to Saturn this is no longer the case.The area within the rings that lies on a line from the sun through our location and towards the rings is 'at opposition' and therefore appears brighter than other parts of the rings. The two renderings below are an attempt to simulate this.
Click the images for higher resolution versions.
In the rendering at left the phase angle is at minimum at the left edge of the ring system. Therefore the rings appear brighter there than to the right where the phase angle is higher. The point where the phase angle is 0 degrees is not visible in this rendering since it falls beyond the ring system at left. Usually I have seen the brightness of the rings depicted with constant intensity in similar viewing geometries as here.
In the rendering at right the point where the phase angle is 0 degrees is prominent; as indicated above the brightness of the rings increases by 20-25% when the phase angle drops from 6 degrees to 0 degrees. Whether the bright area really appears as symmetric as here is uncertain. The reason is that few or no measurements of brightness as a function of phase angle are available when it changes due to changes in elevation above the ring plane; they are only available in the horizontal direction as seen in these renderings. This is due to the Earth's movement around the Sun. This means that in the renderings the brightness variations should be correct in the horizontal direction but perhaps inaccurate in the vertical direction. So these renderings might happen to be correct but they also may be giving just a crude idea of what the rings look like at close range with this lighting geometry. Knowledge of the rings' photometric behavior should be revolutionized once the Cassini spacecraft reaches Saturn.
Incidentally, the Moon also exhibits strong opposition brightening. It's very prominent in some images taken by astronauts on the Moon's surface and also in images from lunar orbit. Many nice examples can be seen in images at The Project Apollo Image Gallery website, for example this image from lunar orbit (notice the bright mountain/area near the top) and this image from the surface (notice how much brighter the surface appears near the astronaut's shadow than elsewhere).
Animations of the changing appearance of Saturn's rings
I prepared two animations depicting the rings' behavior. One of these is a flight around Saturn; in it the phase angle varies between 0 and 155 degrees. The other one shows the opposition brightening; in it the phase angle varies between 0 and 11 degrees.
around_saturn.mpg : Flight around Saturn illustrating
variations in ring brightness with varying phase angle
oppos_effect.mpg : The brightening of Saturn's rings caused by the opposition effect
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