Anime is rather infamous for a number of rather cliched and frankly often disturbing things. One of the more infamous is the "panty shot," which of course is pretty much just a look at a girl's rear under a short skirt for no good reason.
Even fairly early in anime history (the late '70s), it appears that artists were prepared for this.
(The moment I'm pointing to happens at about 0:18 to 0:21.)
Sure, it's not actually especially revealing, but that's because the princess there has some kind of anime anatomy. It's also notable that her skirt is somehow blowing around in a vacuum. (Of course, the series was designed by Leiji Matsumoto, who is infamous for this kind of thing-he's well aware that it's impossible, but doesn't give an explosive decompression about it.)
It's little wonder that when they badly dubbed the series as Spaceketeers, they used the second, much more demure intro animation (which, other than the substitution of space pants for a short short skirt, was really similar in that part).
Gotta love Japan.