Orbital burn timings

[Punk]

So I have been watching a few KSP vids on youtube and came across the 'burn when you see the Mun rise over Kerbin' technique. I was wondering if that is just a happy coincidence or does that work both for other transfer burns in KSP (Mun to Kerbin, Kerbin to Minmus) as well as in the real world (Earth to Moon)?

It seems like it would just depend on the radius of the initial body and the orbital radius and hence speed of the target body, but maybe there is some unavoidable relationship between the two?

Cheers

[Trebuchet-Launch]

Yes, but it only works when flying from a low orbit around the primary body (in this case, Kerbin) to something orbiting it... in a circular orbit. This does accurately describe the situation with the two moons, or Earth and its moon... or the future planets to be added and THEIR moons. It's because of Kepler's 3rd law: the squares of orbital periods are equal to the cubes of the semimajor axis of their orbits. From a low orbit around Kerbin (or whatever planet), the semimajor axis of the transfer burn is always going to be roughly half of the semimajor axis of the target, meaning that the targeted moon, regardless of distance, will always make about the same angular movement during the course of the transfer.

The happy part is that this brute-force-and-massive-ignorance piloting method gets you something reasonably close to a minimum energy transfer.

[maltesh]

It works for Kerbin to Distant Object with decent-sized SOI in a circular orbit around Kerbin.

If you're doing a Hohmann Transfer from a low orbit to a high orbit, and the initial, low orbit is far, far lower than the final high orbit is, an object in a circular orbit whose radius is that of the high orbit will move about 63° in the time it takes you to complete the transfer.

If you are in orbit over Kerbin at 100km altitude, the angular distance between the center of Kerbin and its visible edge is about 59°.

The two angles are close enough to allow the Munrise/Minmusrise burn methods to work, when departing LKO to one of Kerbin's moons.

It's also close enough to get you near the Moon when departing from LEO. Doesn't work for orptimally timing any other transfer. (Well, technically, if Kerbol had a visible surface, you could use it to time transfes to its planets, but you would need a spacecraft capable of several dozen kilometers per second of delta-V to get to a starting orbit where it would work.)

[Punk]

Thanks both for your explanations. I have learnt something today, ill have to read it through a couple times and look up some parts but ill get it in the end.

I like hard sci-fi space stuff (no awkward but convienient ignoring the light speed barrier) and its amazing how elegant and brutally simple physics can be. In most places it behaves and can be used to advantage but if you dont get the maths right it can tear you to bits on an atomic scale or just put you into the side of a moon at 2000 k a second.