So far out of all the posts here no one has yet seemed suprised about the mind boggaling goofyness of the entire plot concept. EuroSec spends Millions of dollars to send a probe to see the other side of the sun. Why not just wait six months then look up? We do go Around the sun. That and all the other goofy plots. I still have to say I love this movie. It is precicly the reason that the idea is so dumb that I always have to smile and chukel and watch it again.
For starters, the sun doesnt stand still, it spins at about 1 rotation every 25-35 days or so (depending on which area of the sun, similar to Jupiter), on a tilted axis like earth as well, however thats only the surface, the core could be spinning in the opposite direction for all we know... but it wouldnt take 6 months, as the sun is spinning counter-clockwise, and the earth is orbiting counter-clockwise... I dont feel like doing the math, but there would be periods where it would take longer, and periods where it would be shorter.
As for why you may want to see whats on the other side, there are a few reasons, #1: you are monitoring a specific solar flare/storm, #2: you need to see a star thats on the other side of ours at that time #3: you sent a probe, and it just happened to get there (intentionally or not) when the earth wasn't also on that side. I'm sure there are more reasons.
Im not saying that they actually bothered to think about that, I think they were mostly riding on the "dark side of the moon" wagon when they came up with it, but its still legitimate.
Well, it is not the "dark side of the sun", which of course doesn't exist. Anyway the plot is not in the slightest realistic. As the orbits of the planets are not circular but elliptical no object could stand undetected for being on the "far side of the sun". Moreover, no ballistic flight (as seems the case) to this new planet could last only three weeks. But those are details compared to the core of the plot, which is that everything which happens on one planet takes place at the same very moment on the other planet, in a mirrored way. It is alluded to by the Ross character but unfortunately not elaborated upon.
As the orbits of the planets are not circular but elliptical no object could stand undetected for being on the "far side of the sun".
A body following the same elliptical orbit around the sun as the earth but at the exact opposite point would not be detectable from the earth. Your other criticisms are valid but I still think the story is an interesting idea if you don't get bogged down in the iffy science.
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Of course it's not realistic. You have to look at this, and other dated scifi films, like a Twilight Zone episode. Anything is possible there. I love 50s and 60s scifi movies. I never view them and think ... this can't be possible today. Too many people look at these movies and expect everthing to be from the "here and now". I'm not sure if some people can train themselves to appreciate these dated movies, but you'll be much more articulate in the world if you can.
I don't think the idea of another planet on the opposite side of the is goofy, even though we now know that it wouldn't be possible. What I think was goofy was the idea that everything on this planet would be a mirror image of everything on our planet--people objects, cultures, history, etc. That's much more metaphysical than science fiction.