Jupiter & Saturn phases?

I've observed Mars (gibbous), Venus and Mercury (crescent & gibbous) gone through phases.

However, it just occurred to me I've never seen Jupiter and/or Saturn going through phases. At first I thought oh because they are outer planets, but wait Mars is beyond Earth as well! So can you guys assist me by bringing the phase to full in helping me understand why the gas giants don't have phases? Or perhaps I've never looked early enough (I admit I've never pushed my weary bones out of bed in the early morning hours for the gas giants as I've done on the Red Planet ;-). But wait, I've never see photos of the gas giants with phase either (except one photo of Saturn from space probe which showed very nice gibbous phase).

Thanks in advance.
Ron B[ee]

Hi Ron. Hope my attempt doesn't furrow your brow too much...

A superior (outer) planet's phase -- relative to Earth view -- occurs at quadrature (planet and Sun at 90 degs. "separation," relative to Earth; planet near zenith at sunrise/sunset). Imagine the Earth as being the 90-deg. vertex of a right triangle; the Sun and outer planet at the other two vertices.

Now imagine the sides of that right triangle, using Earth and Mars:
Assume length of Sun-Earth side = 1.
Sun-Mars length: ~1.5 (mean ~141 million miles)
Mars-Earth: ~1.2
*Sun/Mars/Earth vertex (this is the key): ~51 degs.

Now, let's replace Mars with Jupiter (again, in a right triangle):
Sun-Jupiter length: ~5.2 (mean ~483 million miles)
Jupiter-Earth: ~5.3
*Sun/Jupiter/Earth vertex: ~11 degs.

Theoretically, this might allow for a ~96% illuminated gibbous phase for Jupiter. However, Jupiter's not a terrestrial planet. Factor in it's gasseous nature (and corresponding diffusion of sunlight along its terminator), and we're lucky to "see" a 99% illuminated Jove (which is what Jupiter's gibbous phase *does* present to us, under favorable conditions). Discerning a 99% gibbous phase on an ellipse such as Jupiter... sounds pretty-darn subjective, to me!

How about Saturn?
Sun-Saturn length: ~9.5 (mean ~887 million miles)
Saturn-Earth: ~9.8
*Sun/Saturn/Earth vertex: ~5.9%

Under ideal conditions, Saturn's gibbous phase would be in the realm of ~99.7% illuminated.

Shall we give Jupiter a try? It's around 99.2% illuminated, these days. :-)

Best wishes.
-Dan