This year Santa has decided to try a new strategy to deliver presents which he hopes will require less physics-defying magic, since magic is in short supply these days. Instead of personally flying gifts to every child in the world in one night, Santa would like to launch one or more rockets from the North Pole that enter into an orbit around the Earth and then drop presents over each country in the world. From there locally stationed elves will distribute the presents to each house.

Don't worry about the propulsion, weight, or distribution. Santa has those aspects covered. You can assume that the payload starts out at a miraculous 195 kg. A kilo is dropped for each country. If you require multiple rockets, the payload must be appropriately divided between them (1 kg per drop). You can drop anywhere over the country. You don't really have any time constraints. Santa wants all the drops done before the first country experiences midnight December 25, but that shouldn't be a problem.

Optimizing for both number of orbits and number of burns (Santa wants to minimize $orbits \times burns$), what is the minimum number of orbits required to perform all 195 drops, where an orbit is one revolution of one rocket around the Earth?

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    $\begingroup$ As in previous years, this is meant to be a bit of light-hearted fun for the season. Feel free to vote to close if y̶o̶u̶'̶r̶e̶ ̶a̶ ̶g̶r̶i̶n̶c̶h̶ you don't think it is appropriate for the site. $\endgroup$ – called2voyage Dec 21 '16 at 22:05
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    $\begingroup$ ONE giant extremely drawn out dogleg maneuver causing ONE rocket to spiral from one pole to the other over many revolutions whose ends don't meet and thus are technically ONE orbit! HAHAHAHAHA... /alt-grinch end $\endgroup$ – kim holder Dec 21 '16 at 22:16
  • $\begingroup$ @kimholder Remember Santa's in a short supply of magic. ;) $\endgroup$ – called2voyage Dec 21 '16 at 22:18
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    $\begingroup$ gee, that does cover all the cheats rather well... $\endgroup$ – kim holder Dec 21 '16 at 22:21
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    $\begingroup$ You might get some ideas for how to answer it from this xkcd $\endgroup$ – Cody Dec 22 '16 at 16:49

Okay, gonna cheat. Launch way early, nearly vertically, into suborbital trajectory with apogee near Hill sphere, that way maybe 10% of an orbit is elapsed, and only one burn is needed.

Near apoapsis, lob the presents out of the airlock in such a way that each enters suborbital trajectory hitting a different latitude - at these speeds, altitudes and distances, you can change the point of landing to an arbitrary spot on Earth, pretty much with muscle power alone. Keep tossing for 24h to cover all longitudes; time it such that the presents arrive early on december 24th of local time of the destination; they will differ less than half an hour between latitudes anyway.

Let's just hope they don't burn up on reentry.

  • $\begingroup$ Oh if we're going to cheat I can do way better. All-digital presents this year. Zero orbits. $\endgroup$ – Schlusstein Mar 23 '17 at 18:40
  • $\begingroup$ Creative and efficient. Hard to quantify how much magic is used, but doesn't seem too extravagant. $\endgroup$ – called2voyage Mar 23 '17 at 18:53
  • $\begingroup$ @Schlusstein How do you get digital presents to weigh 195 kg? $\endgroup$ – called2voyage Mar 23 '17 at 18:56
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    $\begingroup$ @called2voyage one 195 kg couch delivered to a poor family in Longyearbyen and digital presents for everyone else. $\endgroup$ – Schlusstein Mar 23 '17 at 19:27
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    $\begingroup$ I wonder what the african children will think of the Steam coupons. $\endgroup$ – SF. Mar 23 '17 at 21:11

Yes, Santa's sleigh in a semi geosynchronous in 1 long orbit. A sleigh big enough to carry all the presents and each present dropped with GPS controls, airbag heat shielding, parachutes and some form of minor propulsion like an arm. Sure, like clockwork.

  • $\begingroup$ So, wait...you're assuming the sleigh is already in space? How do the presents get there? Are they assembled in space? $\endgroup$ – called2voyage Mar 23 '17 at 18:54
  • $\begingroup$ @called2voyage No just accumulated over a year from launches. $\endgroup$ – Muze Mar 23 '17 at 19:49
  • $\begingroup$ Each of those separate launches counts as a burn for the purpose of my question, also when dropping the presents you will need more burns to position them to drop on each country. This doesn't conserve burns very much. $\endgroup$ – called2voyage Mar 23 '17 at 20:00
  • $\begingroup$ @called2voyage Each present having its own propulsion would be more practical by having the mass of the presents in 1 single orbit then burning fuel to make drops directly over head the targets with the total sum of combined weight. You will need some type of targeting system on the para-shuts at least even if you are directly over head to account for drift. might as well use the same system to guide presents independently to each target using the sleigh as a mother-ship.. $\endgroup$ – Muze Mar 24 '17 at 5:40
  • $\begingroup$ @called2voyage presents are build over the north pole using a levitron type space station. and air guided parachutes to pinpoint, $\endgroup$ – Muze Feb 20 '18 at 18:37

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