I caught the shortest glimpse of a clip from a film I loved when I saw it as a kid and would dearly love to see again. It’s an animation I’d guess made in the '60s (maybe earlier, maybe even in the '70s either) and from what I recall it described the solar system. The main thing I recall about the film was that it had a beautifully animated scene with Saturn and its rings depicted I think. I believe it was American or maybe Canadian, a short animated film about the planets. I’ve tried googling but nothing has come up.
Probably Cosmic Zoom 1969, Canada.
No I found that thinking I’d hit the jackpot but it’s not the film I saw years ago. The film I saw was confined to the solar system.
Hmm. Okay then. I guess you’re not talking about the CGI animations by NASA (from the early 80s), but that’s the only Saturn animation I know of.
That’s a beautiful animation but this one was definitely older, more traditionally animated. It may not have been Saturn that was depicted, it may have been Jupiter. I remember individually animated debris that was either forming a ring or maybe it was just depicting the asteroid belt. It’s at least 20 years since I saw it in its entirety. I think it also had a section on Earth’s moon.
Not this by any chance? 
Before he did the effects for Stanley Kubrick’s 2001, Douglas Trumbull did a short film for (I believe) Canada entitled Universe. He also did a film for the Travel and Transportation pavoilion for the 1964-65 World’s Fair entitled To the Moon and Beyond (Which I saw, but it was almost 50 years ago, so my memory’s a bit hazy). I know that both films depicted flybys of the planets in what was (still is, in fact) pretty realistic imagery (You can see a behind-the-scehnes shot of them “touching up” Jupiter for one of these in the book The Making of Kubrick’s 2001). Might you have seen scenes from either of these?
I’ve looked, but I couldn’t find any clips from them. Or even stills.
I vote for Satellites of the Sun (1974), by the National Film Board of Canada. It’s available online here, from their website. Fast forward to 09:15 - amirite? Or amirite? 'cause I remember seeing the thing you describe in a classroom in the UK when I was young, and it had some multiplane animation of Saturn’s rings, with parallax. Only a tiny clip but it made an impression.
I knew what parallax was because of Moon Buggy on the Atari 2600. So computer games were educational after all!
Although my first thought was the Douglas Trumbull films mentioned by Mr Meacham above. There’s an interview with Trumbull here where he describes To the Moon and Beyond in a way that perhaps explains why clips are hard to find:
“To the Moon and Beyond was basically a space film, similar in some ways to what many people know as Powers of Ten, the film Charles and Ray Eames made, because it was the universe from the Big Bang to the microcosm in 15 minutes. It started out with a huge explosion, it was projected on to a hemispherical planetarium screen and it was photographed and projected in this process called Cinerama 360, which was 65mm negative film, ten perforations high, so it was a circular image on 70mm film projected into a dome with fish eye lenses.”
Elsewhere he seems to imply that he didn’t actually work on Universe at all. (“I think it was [To the Moon and Beyond] and another called Universe, made by the National Film Board of Canada, that – Kubrick saw Universe any number of times, I frankly don’t know how many times he saw To the Moon and Beyond – were really the validating influence on Kubrick’s belief that it was feasible to make 2001.”). Universe is also available on the NFB’s website, here. It was in black and white. Saturn’s rings pop up at 10:20 - similar footage, but not as vivid.
“I am vivid… vivisection”, Bjork said that when she won a Brit award.
YES! YES! YES! That’s it! A detail I left out that just confirmed that it’s the film I saw is a reference to Earth’s “2nd moon” something I’ve never seen or heard referred to since. I had found a tiny clip of the film from an Africa Bambaataa promo so was sure it existed but my inability to find it was frustrating me. Thanks. It’s funny I may have seen that when I was as young as five but I can remember lots of it so vividly.
I definitely saw that film you linked to Ashley but if you look at - YouTube and go to 38.45 you’ll find the clip I found. It’s very brief but it seems to depict a similar but not identical scene to the one at 9.15 in Satellites of the Sun.