How big was the closest approach between the launched New Horizons and Moon?

See this post for an estimate.

Thanks!

C/A was 185,000 km or so to Luna. Had we launched 21 Jan, it would have been about
10x closer. And yes, our modeling takes lunar gravity into account when computing
the launch targets.

-Alan

In fact, IIRC, lunar perturbations factored into computing a new launch date for Cassini, which was delayed from the originally scheduled launch date due to Huygens-related work on the pad. Due to tight pre-launch estimates of propellant margins, mission planners were worried that too close a lunar flyby would have perturbed the trajectory outbound to Venus-1, requiring a propellant expenditure. And there was a point during the launch period when the Moon was in "the wrong position," so, from what I understand, the new launch date was scheduled when the Moon was no longer "in the way." Of course, virtually perfect navigation during VVEJGA/cruise has given more than adequate margin at Saturn.

Mariner 10 (to Venus and Mercury) was deliberately launched to pass fairly close to the moon on its' departure to check out its' cameras.

{Mariner 10 had a major upgrade in camera technology over prior spacecraft}

Yep -- and they ended up using those lunar photos for more than they had planned, since the initial failure of the camera heaters led them to think that the cameras would soon go permanently out of focus and they'd have to make the launch of Mariner 10's twin that they had planned in the event of a Mariner 10 launch failure. They examined the lunar photos very carefully for evidence of such defocusing, and found that -- while the cameras were teetering on the very brink of it -- they hadn't quite gone over, and would soon warm up as the craft approached the Sun. So Mariner 11 instead sits in the Air and Space Museum, near the third Voyager and the third Viking lander (which makes for a melancholy viewing experience).