An intriguing question regarding orbital mechanics and time.

[windows_x_seven]

Hello there.

I'd like to know how does one calculate how long a trip will take, for example Kerbin -> Mun (how long does it take to reach it, from Kerbin Orbit to Mun Orbit), or Kerbin -> Duna, or even better, Jool -> Moho using Dres as a gravitational slingshot (actually, ignore the Jool -> Moho one, I think it would be better to keep things simple for now)

Please reply. This will be important to me. Thank you.

Edited July 1, 2015 by windows_x_seven
I shall now call this an ANSWERED QUESTION.

[AlexinTokyo]

The time taken will depend on what kind of transfer you perform.

For an ideal Hohmann transfer, the formula for transfer time is:

t_H = À√[(r₁ + r₂)³ / 8μ] where r_1|2 are the radii of the starting and target orbits, and μ is the standard gravitational parameter of the central body.

You can find the orbital radii of KSP's celestial bodies in the tracking station in game, or on the wiki.

Alternatively, you can use alexmoon's KSP Interplanetary Transfer Window Planner or the ITWP mod to generate pork-chop plots allowing you to calculate almost any transfer you need.

If you're interested in more maths related to spaceflight, I recommend OhioBob's site at http://www.braeunig.us/space/index.htm

[Sharpy]

As you prepare a route using maneuver nodes, clicking anywhere on the route, as you see "Add Waypoint" or something like that, below that there's a "T: +3d 2h" or something like this - that's the time to reach that place by following the waypoints.

It's a bit trickier for routes from places where you are not. If you want Jool-Moho, you need first to plot a route to Jool (may be quite bogus, millions of dV), then note down your time to Jool, then continue plotting the route to Moho, write down the final time and substract the two.

oh, but how can you plan so far ahead? Well, open the game directory and edit settings.cfg, increasing CONIC_PATCH_LIMIT from the default 3 to some 7...

[windows_x_seven]

Thanks for both answers, although AlexinTokyo's was the one I really was looking for. Rep for everyone.

[Sharpy]

Note that's for optimal Hohmann transfer from a circular orbit. In KSP, unless you're a perfectionist (and probably use MechJeb) that's rarely the case at least for Kerbin-> its moons, as after launch your orbit will likely be quite elliptic, so you don't have a neat r1, and transfer dV - and time, as result - will strongly depend on the point where you start.

And similarly, the time can be reduced *a lot* by spending only a little more dV. If instead of dV-optimal Hochmann transfer where your transfer orbit is tangent to the target orbit, you exceed it, the travel time drops drastically - with strongly elongated orbits the speed around the apoapsis drops to a crawl, and it takes long days for your target body to catch up. By moving the periapsis away, you proceed to the rendezvous point still at a brisk pace, but then you both need to get the extra speed initially and lose it during the meet-up. (but seriously, measly 100m/s can make a difference of a week in case of Minmus.) The same applies to travel to the ouiter planets.

[Chaos_Klaus]

  Quote

Note that's for optimal Hohmann transfer from a circular orbit. In KSP, unless you're a perfectionist (and probably use MechJeb) that's rarely the case at least for Kerbin-> its moons, as after launch your orbit will likely be quite elliptic, so you don't have a neat r1, and transfer dV - and time, as result - will strongly depend on the point where you start.

Starting from LKO, it really does not matter if your initial orbit around kerbin is perfectly shaped. The only thing that matters here is the shape of the transfer orbit. And that will have a very specific periapse and apoapse.

Also ... you don't need to be a wizard to get a nice circular orbit after launch. It just takes the right technique and some practise. Actually, I don't really get how people come up with elliptical orbits, while they propably do a circularization burn. Are they not doing that maneuver accurately? Or maybe people have a strange definition of an elliptic orbit, because 100km x 105km is not very elliptic really.

[FancyMouse]

  Chaos_Klaus said:

Actually, I don't really get how people come up with elliptical orbits, while they propably do a circularization burn. Are they not doing that maneuver accurately?

With extremely low TWR (e.g. Ions) you need to burn for multiple times to achieve a high dV change. You need to plan for a lot of elliptical orbits in this case (last one most important for getting the right ejection). Nothing strange here.

[Sharpy]

  Chaos_Klaus said:

Also ... you don't need to be a wizard to get a nice circular orbit after launch. It just takes the right technique and some practise. Actually, I don't really get how people come up with elliptical orbits, while they propably do a circularization burn. Are they not doing that maneuver accurately? Or maybe people have a strange definition of an elliptic orbit, because 100km x 105km is not very elliptic really.

Before you are in orbital altitude but not at orbital speed, you must hurry with the burn (with low-thrust, high-ISp engine) before you begin descending back in the atmosphere - you must raise the periapsis to the 70km, and the apoapsis does different things in the process depending how you aim your nose - the burn is far too long to perform strictly -at- the periapsis, and often ends way past you crossing it - plus often below the 70km limit already. At that point, getting the periapsis above 70km (when you ARE at near the periapsis) without doing weird things to the apoapsis is difficult to say the least.

Why "at that point"? Obviously waiting until apoapsis and circularizing would be preferable. Except my launch stage is *just* falling into the atmosphere and I need to switch to it quickly to save it from vanishing and guide it to a gentle recoverable landing, and to be able to switch to it, I need to be above 70km - right now!

Afterwards, my orbit is all kinds of wonky with periapsis just above 70km and apoapsis... somewhere out there, where it happened as I struggled to get above the 70km limit. Probably some 130, maybe 300km.

And at that point circularizing is a pure waste. Whatever transfer I'm planning, its dV will vary a lot with what orbital altitude I start it at, but it will be always lower than if I were first to circularize and then perform the transfer burn from a proper circular orbit. Yes, circularizing at that point is trivial - and entirely useless! Burning fuel just to make adjusting the node easier? Yeah, there's a lot of sliding prograde/retrograde markers as I move the node, because the same dV at apoapsis won't let me reach the Mun, while at periapsis it sends me into escape trajectory. Plus I wasted some of the transfer stage fuel getting the apoapsis so high while raising the periapsis.

But that's an acceptable price for: 1) not burning extra fuel to circularize, 2) having a lighter launch stage that doesn't need to reach orbital speeds on the wasteful atmospheric engines, 3) saving said launch stage.