[Tutorial] Interplanetary Travel without Angles: The Launch Calendar

[martscht]

To me it seems like one of the biggest problems in interplanetary travel seems to be determining whether the angle between the departure planet (mostly Kerbin) and the target is correct. Now since the cooperation of Kosmo-not and Olex gave us this beautiful brain-child (http://ksp.olex.biz/) the only thing we actually need to determine is whether the picture shown in the browser is the same as the one seen onscreen in KSP. I know there are some nice tools out there that allow us to measure angles in KSP, but in my opinion this isn't necessary, because all-stock KSP provides everything we need: an exact measure of time.

Working under the assumption that all new games of KSP start with the same constellation it is extremely easy to determine when you reach the exact phase angle required for smooth interplanetary sailing. I've written an R-function that can determine the next occurence of a launch window, but basically this is all you need to know:

The Eve launch window opens every 170 days, for the first time on day 138. For Jool it opens every 117 days and does so for the first time on day 45. For Duna I've also only come up with a rough approximation so far (because of the slightly elliptical orbit): here the launch window opens every 228 days and is open for the first time on day 56.

Now when I say "launch window" here, I actually mean "injection burn window", meaning that it's probably better to already be in your parking orbit, when the moment comes. If rough approximations is all you need, this should do. For a bit more precision:

EVE

Period: 170 days, 7 hours, 56 minutes, 21 seconds

Initial Wait: 137 days, 15 hours, 17 minutes, 54 seconds

DUNA

Period: 227 days, 19 hours, 24 minutes, 58 seconds

Initial Wait: 55 days, 21 hours, 55 minutes, 37 seconds

JOOL

Period: 117 days, 0 hours, 45 minutes, 4 seconds

Initial Wait: 45 days, 20 hours, 44 minutes, 36 seconds

I haven't come around to doing Moho yet, because I've been busy visiting the outher planets ;-). Anyway my tactic was to launch a spacestation as my clock (i.e. launch it at the very beginning of the game). Then I was able to see the total time that had passed in the space centre and simply time my launches and injection burns accordingly.

Edited October 12, 2012 by sal_vager

[maltesh]

Convert those numbers to seconds, and you'll have values you can set the UT= parameter in the Flightstate section of persistent.sfs file to, instead of waiting.

[Grizzlol]

But you would still need to know the (almost) exact ejection angle, or did I miss something? You replaced the phase angle with a measurement of time, which is useful, but what about the ejection angle? Are you using the same ejection angle for all transfers (I wonder if that is even possible) ?

[martscht]

But you would still need to know the (almost) exact ejection angle, or did I miss something? You replaced the phase angle with a measurement of time, which is useful, but what about the ejection angle? Are you using the same ejection angle for all transfers (I wonder if that is even possible) ?

You are correct. I didn't post fix numbers, because the time you need to wait for injection is dependent upon your parking altitude, but is fairly easy to compute.

My standard parking altitude is 125 km. For this orbit around Kerbin the period (i.e. the time it requires to go around a full orbit) is 2064.292 seconds. From Olex's site we know that if we were to go to Jool the ejection angle is 113.86°. Using this info we can compute our wait time from Kerbin prograde as

(360-113.86)/360 * period = 1411.402 seconds.

Thus we'd have to wait 23 minutes and 31 seconds for the correct ejection angle.

Edit: The period is computed by 2 * pi * sqrt( (altitude + 600)^3 / mu ) with mu being 3530.461 for Kerbin

Edited September 23, 2012 by martscht

[Banarath]

Thanks, I made a spreadsheet calender for KSP launches

Can you post your maths and your formula?

I would like to calculate the other planets

[martscht]

Thanks, I made a spreadsheet calender for KSP launches

Can you post your maths and your formula?

I would like to calculate the other planets

Sure, you can can calculate the wait time as

(phi2 - phi1) / (omega2 - omega1)

phi represents angles (with phi1 being the initial angle and phi2 being the final angle, i.e. the phase angle Olex's calculator gives you) in radians. Omega is calculated by

sqrt(mu / a^3)

where mu is the gravitational parameter and a is the semimajor axis. Again Omega1 is computed for your origin (i.e. Kerbin) and Omega2 is for your goal.

The Period is computed as 2*pi/(omega2-omega1) (and is returned in seconds).

Though there seem to be some problems in my calculation (perhaps my initial angles were off), because the angles aren't quite aligned at the time I predicted (I checked with the Kerbal Engineer Mod)...

[Diche Bach]

I've been looking for this thread