There is no analytical solution for multi-body problem. But one can still use numerical solution to simulate. Though the error will become bigger and bigger and not reflect the real world scenario.
This is a great news. Before that, if you start with a small instance, there is no way to upgrade to higher instance since they exclusively support 64-bit. Now you can upgrade smoothly from micro to any instance.
Yeah, you need some luck to make it to the front page. If I recall correctly, one vote can be enough, but it has to be done soon after submission time.
Once you get past that threshold, karma skyrockets.
It gets worse because not many "interesting" people dedicate some time to /newest. I used to go there once every day. The main problem is HN doesn't discriminate by topic combined with lack of downvote. The noise to signal ratio is too high. There are way too many spam, blogspam and metoo articles against a few actual interesting submissions. And most times a blogspam article gets to the frontpage instead of the original source. It's a shame.
In reddit the people doing the honorable job of upvoting new stories are called "Knights of New". This effect is notable on good communities like /r/programming. Trash submissions quickly get downvoted.