Calculating launch windows for transfers to other planets from Mun or Minmus

[Colonel_Panic]

Hi, has anyone made a tool or mod that helps calculate optimal launch windows for using Mun or Minmus as a departure point and Kerbin as a gravity assist? Because of the long orbital periods of Mun and Minmus, it can interfere with planning a launch if you're in the wrong point of its orbit during the ideal window.

In addition to the above, I'd like to know whether Mun or Minmus would be more optimal for a staging area for interplanetary flight, and whether there are cases where a direct ejection instead of slingshot may be almost as efficient.

[Red Iron Crown]

I don't think you can use Kerbin to gravity assist out of Kerbin's SOI, though you get more benefit from the Oberth effect if you drop to LKO on your way out system.

A better profile would be to start from LKO and use the Mun for a slingshot. Though the Mun's gravity is low enough that it's hardly worthwhile, I just do the transfer burn from LKO.

[Colonel_Panic]

I don't think you can use Kerbin to gravity assist out of Kerbin's SOI, though you get more benefit from the Oberth effect if you drop to LKO on your way out system.

A better profile would be to start from LKO and use the Mun for a slingshot. Though the Mun's gravity is low enough that it's hardly worthwhile, I just do the transfer burn from LKO.

Maybe gravity assist isn't the right term. The thing is that launching from Kerbin takes a lot of fuel, as does burning to Kerbin escape. So the idea is to circumvent both of those by establishing a colony on either Minmus or Mun (using Kethane etc), with re-usable landers and a fuel depot as a staging point for interplanetary travel. Escape from Minmus (and to a lesser extent, Mun) is virtually free due to low gravity, no atmosphere, and extremely low orbits, and if you escape to retrograde, that puts you on a close pass to Kerbin, where you can do a prograde burn at the periapse which will get you (due to the already elongated orbit), a virtually free kerbin escape as well... from there it's just a matter of burning your ejection to intercept. This saves (in the example of Minmus) up to 5100 delta v over a launch from Kerbin from liftoff to escape.

Here's the problem though. The direction you eject from Kerbin depends almost entirely on the position of minmus when you make your retroburn. If Minmus is in the wrong position in its orbit, you could lose several months waiting for it to orbit around to the right position to put your ejection on the right path, but by then you may miss the transfer window to your destination planet.

[Yasmy]

I haven't made a tool or mod, but I did do the dV calculations from every moon to every other planet. I posted the results for Minmus and the Mun.

The interesting thing to note is that from the Mun (ignoring plane change maneuvers), it is cheaper to go directly to Eve or Duna than to swing around Kerbin. For other destinations from the Mun, and for all destinations from Minmus, you save dV by swinging by Kerbin.

[FREEFALL1984]

The best bet is to have a refueling tug depart from minmus, and enter an LKO then dock with your interplanetary vessel, then you can burn right on the transfer window.

Alternatively just depart from the mun or minmus for all transfers, then you take up the relative velocity of the orbiting body, although you'll only be able to launch when the mun or minmus is traveling more or less prograde or retrograde.

[Kasuha]

To calculate optimal launch windows, use any calculator and enter Kerbin as your starting point. It will tell you when is the optimum time to launch from LKO and what is the ejection angle.

With some reserve before the launch window let your station travel to the point exactly opposite to where you need to eject. Then launch from the base and lower your Kerbin periapsis to LKO height. Then add your ejection burn at appropriate place - it should be reasonably close to periapsis of your orbit.

[Red Iron Crown]

Maybe gravity assist isn't the right term. The thing is that launching from Kerbin takes a lot of fuel, as does burning to Kerbin escape. So the idea is to circumvent both of those by establishing a colony on either Minmus or Mun (using Kethane etc), with re-usable landers and a fuel depot as a staging point for interplanetary travel. Escape from Minmus (and to a lesser extent, Mun) is virtually free due to low gravity, no atmosphere, and extremely low orbits, and if you escape to retrograde, that puts you on a close pass to Kerbin, where you can do a prograde burn at the periapse which will get you (due to the already elongated orbit), a virtually free kerbin escape as well... from there it's just a matter of burning your ejection to intercept. This saves (in the example of Minmus) up to 5100 delta v over a launch from Kerbin from liftoff to escape.

http://i.imgur.com/SY44bQg.jpg

Here's the problem though. The direction you eject from Kerbin depends almost entirely on the position of minmus when you make your retroburn. If Minmus is in the wrong position in its orbit, you could lose several months waiting for it to orbit around to the right position to put your ejection on the right path, but by then you may miss the transfer window to your destination planet.

Ah, I didn't realize you were refueling at your staging point, that does change things a bit. In that case, Kasuha's method mentioned above is best though if you use Minmus you may miss your transfer window by a few days waiting for it to align; the Mun is better in this regard as its orbital period is much shorter.

FREEFALL1984's method means you don't have to wait as long for things to align, but if you're refueling in LKO it's simpler to just launch a tanker from KSC. Though if Kethane mining is fun for you, by all means have at it.

[LethalDose]

As Yamsy pointed out above, Minmus is the better choice because Minmus saves you fuel. Also, I think calling it a "gravity assist" is totally fine, because, even though you're burning at periapsis. You're using gravity to maximize your velocity relative to Kerbin (burning at periapsis around Kerbin). After watching this video (Sorry, can't insert link. address is here:

) by Scott Manley, I started launching my interplanetary (IP) missions from Minmus, and never looked back.

Anyway, If you want to use Minmus as a staging area for IP travel, then you have to let go of "optimal" windows, because they ain't gonna happen. THis is because to Minmus is really never going to be in the perfect location when the launch window is at it's peak.

But do not lose hope, for all is not lost! Minmus will probably still be in a really good position at some point during the launch window. Minmus makes a full rotation around Kerbin once about every 300 hours (rounded, for quick dirty math). This means that it's never more than 150 hrs away from the perfect position. This leads to a choice. YOu can either:

1. Wait until Minmus is in the right position to start your escape burn, understanding you might be departing for your window early or late.
   
2. OR Start your ejection burn from Minmus when the window is optimal, understand that your ejection angle may not be ideal
   

I personally prefer the first option, understanding I'll be a little early or late to the window, because overall, I'm doing this to save fuel and I think that saves the most fuel. Its been my experience (really, with Duna and Eve, but I can't imagine its very different for other bodies) that the windows are actually pretty wide, and very, very small (and therefore cheap) midcourse corrections can get you where you're going.

Just my two cents. Hope it helped.

[Red Iron Crown]

Also, I think calling it a "gravity assist" is totally fine, because, even though you're burning at periapsis. You're using gravity to maximize your velocity relative to Kerbin (burning at periapsis around Kerbin).

A gravity assist is entering and exiting a body's SOI to use its gravity to change your velocity in a desirable direction, no burn is required. What is being described here is taking advantage of the Oberth effect, which is a very different thing. Though the two are often combined.

[Kasuha]

1. Wait until Minmus is in the right position to start your escape burn, understanding you might be departing for your window early or late.
   
2. OR Start your ejection burn from Minmus when the window is optimal, understand that your ejection angle may not be ideal
   

Third option is to lower your periapsis when Minmus is in ideal position and spend the wait in this elliptical orbit which is about 100 hours long rather than 300. And you can perform some orbital period tuning at periapsis for almost no dv.

The only catch is that you need to match right ejection angle - since a lot of time may pass between your ejection from Minmus and your ejection from Kerbin SOI, what's 100 degrees to prograde at the time of Kerbin ejection is not 100 degrees prograde at the time when you leave Minmus. The angle changes by approximately 1 degree every 7 hours. It's not important if you just travel to periapsis but if you intend to spend several orbits in the waiting zone, you have to account for that.

[LethalDose]

A gravity assist is entering and exiting a body's SOI to use its gravity to change your velocity in a desirable direction, no burn is required. What is being described here is taking advantage of the Oberth effect, which is a very different thing. Though the two are often combined.

Fine, in a very narrow interpretation of "Gravity assist", it's wrong. It's also not the point of the discussion, so I'm not going to be involved in hijacking an otherwise legitimate thread engage in an argument about semantics. Whatever you call it, it works.

Third option is to lower your periapsis when Minmus is in ideal position and spend the wait in this elliptical orbit which is about 100 hours long rather than 300. And you can perform some orbital period tuning at periapsis for almost no dv.

The only catch is that you need to match right ejection angle - since a lot of time may pass between your ejection from Minmus and your ejection from Kerbin SOI, what's 100 degrees to prograde at the time of Kerbin ejection is not 100 degrees prograde at the time when you leave Minmus. The angle changes by approximately 1 degree every 7 hours. It's not important if you just travel to periapsis but if you intend to spend several orbits in the waiting zone, you have to account for that.

This is a good point I hadn't considered. It's more complex, but moves you closer to the "optimum" solution. You're also more more likely to have a Mun encounter during these orbits simply because there are more orbits. And if you have an Mun encounter during your wait, you're gonna have a bad time.

[Kasuha]

This is a good point I hadn't considered. It's more complex, but moves you closer to the "optimum" solution. You're also more more likely to have a Mun encounter during these orbits simply because there are more orbits. And if you have an Mun encounter during your wait, you're gonna have a bad time.

You got a lot of degrees of freedom to avoid such things, but it may be also a good argument to put the station near Mun.

Transfer from Minmus LO to 70 km Kerbin periapsis: 160 m/s (227 without Minmus Oberth effect)

Transfer from Mun LO to 70 km Kerbin periapsis: 265 m/s (375 without Mun Oberth effect)

Difference between apoapsis at Mun level and Minmus level from 70 km periapsis: 66 m/s

So you spend 265 - 160 + 66 = 171 m/s more if you make your station near Mun.

I would almost say it's worth the added comfort.

Edited April 29, 2014 by Kasuha

[LethalDose]

I haven't made a tool or mod, but I did do the dV calculations from every moon to every other planet. I posted the results for Minmus and the Mun.

The interesting thing to note is that from the Mun (ignoring plane change maneuvers), it is cheaper to go directly to Eve or Duna than to swing around Kerbin. For other destinations from the Mun, and for all destinations from Minmus, you save dV by swinging by Kerbin.

You got a lot of degrees of freedom to avoid such things, but it may be also a good argument to put the station near Mun.

Transfer from Minmus LO to 70 km Kerbin periapsis: 160 m/s (227 without Minmus Oberth effect)

Transfer from Mun LO to 70 km Kerbin periapsis: 265 m/s (375 without Mun Oberth effect)

Difference between apoapsis at Mun level and Minmus level from 70 km periapsis: 66 m/s

So you spend 265 - 160 + 66 = 171 m/s more if you make your station near Mun.

I would almost say it's worth the added comfort.

You could, but I've included Yamsy's quote from earlier in this thread because he pointed out that there's some conditionality to where you're going. Not sure that I really understand that but he's done the math and I haven't, so I'm no position to argue the issue.

Really, I think it comes down to what you're most comfortable with and what works best in your hands. There's a lot of different ways perform these maneuvers that work very well. I think there's way too much effort and bickering in these forums about what's "optimal" instead of discussing what works how it can be improved. Basically, since everyone flies differently, everyone is going to have different preferences.

In my hands I can make the Minmus refueling/escape station work really well. It took me a while to really understand it (the Scott Manley Oberth effect video really helped crystallize my thoughts on it), but after I had it figured out, yeah, I think it's cool and effective. I like it's advantages (Good savings on dV) and it's disadvantages (having to "fudge" windows, Mun encounters on trip down, midcourse corrections) just don't bug me that much.

Other people are going to prefer other systems (Mun stations, Kethane, Direct launches) and that's cool. I just have a problem when state that X way is wrong based on inaccurate or exaggerated facts.

</soapbox>

[Northstar1989]

You got a lot of degrees of freedom to avoid such things, but it may be also a good argument to put the station near Mun.

Transfer from Minmus LO to 70 km Kerbin periapsis: 160 m/s (227 without Minmus Oberth effect)

Transfer from Mun LO to 70 km Kerbin periapsis: 265 m/s (375 without Mun Oberth effect)

Difference between apoapsis at Mun level and Minmus level from 70 km periapsis: 66 m/s

So you spend 265 - 160 + 66 = 171 m/s more if you make your station near Mun.

I would almost say it's worth the added comfort.

Good point- but your ejection burns around Minmus are shorter than your ejections burns around the Mun- and thus more precise, further saving fuel and adding to comfort...

An added benefit from a Minmus station is that it gives you the back-up option of making a direct transfer from Minmus to your intended destination if you can't get away with the method of dropping your periapsis and waiting. Since Minmus' orbital velocity around Kerbin is so low, it can *almost* be ignored with some of the more distant transfers (or if, like me, you spend extra Delta-V on Duna transfers so your poor Kerbals don't have to wait in space as long... Good for roleplaying. Also good if you're running a life-support mod, as it reduces the total mass in provisions you need to pack...) It's also sometimes possible to make most of the burn near Minmus, but a small part of it closer to Kerbin (say a bit beyond the Mun's orbit), which is still better than making the entire burn near Minmus...

Regards,

Northstar

[Yasmy]

... Since Minmus' orbital velocity around Kerbin is so low, it can *almost* be ignored with some of the more distant transfers ...

You have that backwards. Look at the table I posted earlier.

If you are at Minmus and want to go to distant planets, you can double the cost by going direct. It's not quite that bad for Eve or Duna.

[LethalDose]

You have that backwards. Look at the table I posted earlier.

Did you ever post the equation and derivation you used? Some of those numbers look a little... Hinkey.

[Yasmy]

I'll write up the derivation in a tutorial in a day or two. Like I said in the other post, all you need is the vis-viva equation.

The numbers should make sense though, if you think about it. At Minmus, you are nearly at Kerbin escape velocity.

Thus you don't need much of a boost to get to Eve or Duna, compared to the extra dV it takes to get back to low Kerbin periapsis.

But here is the clearest example of the Oberth effect I can offer: For an interplanetary transfer from Minmus,

your starting velocity is about 150 m/s, iirc. Direct interplanetary transfers need like 10-20 m/s to escape Kerbin.

After that you are using the escape Kerbin and then burn method, more or less. Much more expensive than direct from Kerbin.

On the other hand, it costs about 100 m/s to get back to a 100 km Kerbin periapsis, and when you get there,

you'll be going, (I don't remember off-hand) 3 km/s?

So compare the Oberth effect at 150 m/s vs 3 km/s. Now these are large maneuvers, so you can't use the small dV approximation: de = v dV.

(For a small dV, the change in specific orbital energy is approximately equal to your velocity times the small dV spent: de = 1/2 (v+dV)^2 - 1/2 v^2 ~= v dV.)

For a small burn, you get 20 times (3000/150) the specific orbital energy on a slingshot past Kerbin from Minmus that you do from a burn at Minmus.

Edited April 30, 2014 by Yasmy
fixed my stupid units: 3k m/s. really? really?

[Colonel_Panic]

Good info in here folks, thanks.

One thing I'm not really clear on, is someone mentioned the best time to launch is when the starting body is opposite the desired ejection angle, but shouldn't it really be somewhere between 70 and 120 degrees from it? Since you want to burn at the periapse... Is there any "rule of thumb" someone can provide for where you want your moon of choice and kerbin's prograde/retrograde to be with relationship to each other when using this sort of maneuver?

You got a lot of degrees of freedom to avoid such things, but it may be also a good argument to put the station near Mun.

Transfer from Minmus LO to 70 km Kerbin periapsis: 160 m/s (227 without Minmus Oberth effect)

Transfer from Mun LO to 70 km Kerbin periapsis: 265 m/s (375 without Mun Oberth effect)

Difference between apoapsis at Mun level and Minmus level from 70 km periapsis: 66 m/s

So you spend 265 - 160 + 66 = 171 m/s more if you make your station near Mun.

I would almost say it's worth the added comfort.

There is one other thing which makes Minmus easier--getting to the surface of minmus and back is far easier and cheaper than on Mun, so less fuel is wasted in getting to orbit. Even if you're refueling your vessel in orbit, you still need to bring fuel from wherever you're mining it to get it to the station to top off your tanks, so if you're using the moon as a fuel source, minmus is going to be the obvious choice.

Perhaps it would be wise to have bases on both Mun and Minmus so if one of them isn't going to be in the right spot during a shorter launch window, we can use the other....