Wait, are you actually asking for advice, or just venting?
If the former, I'd advise you to let it end UNLESS there is a definite time frame on one of crossing you the pond, and that timeframe is months, not years.
Put simply, long distance relationships don't work for indefinite time frames. Over the short term, yeah; a healthy relationship can handle a few months apart, as long as you know you're getting back together. However, this relationship? You've said it yourself, you're not hugely invested in it (I would be surprised if you were, after just 6 weeks). All you're doing is forcing exclusivity on yourself and her. While I'm sure neither of you are the cheating type, that just leads to resentment. Or, at the very least, a slow drifting apart with an awkward ending.
Then there's the fact that as months go by, you'll have less and less in common. You'll make different friends, get different interests, and one day find that you're each talking about stuff the other knows nothing about. A relationship thrives on communication, and lack of common ground just hinders that.
So, better to break it off neatly and cleanly now, and stay friends. If, sometime down the line, you meet again, you can always pick up where you left off.
Oh, one more thing;
...and think that physical contact is a necessity...
It is. Oh, I don't mean sex, I mean actual close contact; hugging, kissing, just spending time with each other. There's a reason we do them, you know; they reinforce the bonds between people. For example, when you kiss, your brain gets flooded with dopamine and oxytocin. The pleasurable sensations of this are a big part of what love is; chemically speaking, an all-natural crack addiction with your partner as your dealer
(well, in part; there's more to love than
just hormones, but denying they play a major role is demonstrably false).
Without the close contact that causes such bountiful highs, it gets harder and harder to keep the relationship actually alive.