Does someone tweak the orbital mechanics to hit these anniversary?
I very much doubt they planned it. It just worked out that way. How do I know this? Well, there were delays in the construction of New Horizon, and there were delays in the launch of New Horizon back in 2006. Or basically when you’re designing/launching a payload to anywhere. Doing so while hitting a specific date is tricky.
As for orbital mechanics? From launch onward, New Horizon was being shot out of the solar system. There is not much you can control about that. You just hope your launch went OK, and that nothing gets in your way because the traditional way of getting around the solar system so far is gravity and momentum. Or basically New Horizon was flying in the direction the rocket sent it, which took it by Jupiter and thus New Horizon sped up.
Dawn meanwhile is one of the first missions where you have control of where you are going really after the launch. The majority of missions launched in the past 50 years, you do not. You do all the maths before launch, and hope the launch goes OK for the most part (though, even ion thrusters have their limitations. So again mostly you’re at the mercy of how the launch goes). Sure, you have retrorockets on some of these spacecrafts but considering fuel is heavy/you don’t take much with you. So you can only do small corrections. Mostly you just use very clever math to get where you’re going. Cassini is probably one of the most complicated missions ever from an orbital mechanics standpoint.
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