Proper intercept angles for moons

[Tuupertunut]

There are many exact calculations for interplanetary phase- and ejection angles. Some of them have average values like ksp.olex.biz which don't take account of eccentricity, and some have exact time-dependent values like eiden.fi/ksp. There are more than enough tutorials on how to do interplanetary transfers and it is possible to do a very efficient one by following those values.

But, apparently there are no advanced moon transfer tutorials which contain exact calculated intercept angles (lead or lag angles) for going from a planet parking orbit to a moon of the planet (like from a Kerbin parking orbit to Mun or Minmus. Everyone knows the rule of starting the burn when the moon comes above the horizon. There are few other rules too like this and the 45° shown on the training scenario of the game.

I tried to google that for many hours but found no answer. Then I found this old tool called KSP Orbit Mechanic and by putting there a low Kerbin parking orbit (80km) and the altitude of Mun (11400km) I found out the intercept angle to be 111°. (Image) The same value for Minmus is 115°. Now the problem is that the orbit mechanic is old and therefore doesn't include other planets and their moons. Also if it did, it would still not take account of orbit eccentricity like in the case of Gilly.

Have you people found/made any documents of those intercept angles? Someone more comfortable with orbital math could do one or even a calculator for the angles. Or ksp.olex.biz could include this to their calculator.

Edited October 25, 2013 by Tuupertunut

[Tuupertunut]

I found

which shows how to calculate these angles. It is meant for rendezvous of two ships but works also with a ship and a moon. I made a simple calculator for it: http://instacalc.com/16221

Now someone could make a real calculator (ksp.olex.biz style) of it including graphics, presets for different planets and maybe even support for eccentricity if possible.

[Nibb31]

To travel from a planet to one of its moons, the easiest way is to burn prograde when the moon rises on the horizon. That's all there is to know.

[Tuupertunut]

It seems to vary between 93° (laythe) and 115° (minmus). The difference is a lot smaller than I expected but is still important if trying to be as efficient as possible.

The importance of these angles grow significantly if your current orbit is higher.

Edited October 25, 2013 by Tuupertunut

[KerbMav]

Simply set a maneuver node, raise AP to orbit of moon, grab node an move it along your orbit, maybe adjust AP again, move it around along your orbit until you get an encounter. Make sure to align your orbits inclination if needed.

[SRV Ron]

Simply set a maneuver node, raise AP to orbit of moon, grab node an move it along your orbit, maybe adjust AP again, move it around along your orbit until you get an encounter. Make sure to align your orbits inclination if needed.

Look for the ideal intercept while adjusting the handles and moving the node along your existing orbit. Such an intercept should slingshot you back to Kerban reentry if you miss the orbital insertion burn.

[Tuupertunut]

There is now a new version of my lead angle calculator. This version is pretty robust, and can be used for ship-to-ship, ship-to-moon and planet-to-planet Hohmann transfers.

https://instacalc.com/51180

[Kryxal]

A Free Return Trajectory in the prograde direction is really more time and delta-v than you need to spend ... but it's a neat trick!

[Daniel Prates]

8 hours ago, Kryxal said:

A Free Return Trajectory in the prograde direction is really more time and delta-v than you need to spend ... but it's a neat trick!

Aiming at coming in front or in the rear of the moving moon also affects the direction of your final moon orbit,  depending on the speed you are coming in. Its a thing to keep in mind:  if you are looking to dock with a clockwise-orbiting moon station,  you cant end up in a counter-clockwise orbit! The speed and angle you inject may alter your plan of entering the target orbit in the right direction.

[Kryxal]

7 hours ago, Daniel Prates said:

Aiming at coming in front or in the rear of the moving moon also affects the direction of your final moon orbit,  depending on the speed you are coming in. Its a thing to keep in mind:  if you are looking to dock with a clockwise-orbiting moon station,  you cant end up in a counter-clockwise orbit! The speed and angle you inject may alter your plan of entering the target orbit in the right direction.

Granted, but it's probably better to go directly to your target altitude than to go to the trouble of a free-return trajectory in a usual game ... unless you place those sorts of restrictions on yourself.