Delta V Calculations for a lagrange 4- type orbit

[Rakaydos]

I am looking at putting a refueling depot 2,250 km ahead of the leading side of Minmus. (Minmus's SoI is only 2,247 km) with a circular orbit at exactly the same radius as Minmus's, so the relative velocity remains zero.

How much deltav is needed to reach such an orbit from Low Kerbin?

How much deltav does it take to lift kethane from minmus, given a ballistic escape launch?

What would be the longitude (laditude would presumably be 0) of the best minmus launch site to reach the station? (presumably the point directly under the station, but minmus's rotation may throw this off)

How much deltaV would it take to slingshot a cargo past minmus such that it drops to low kerbin orbit to the east? and how much to the west?

EDIT: and how long should I allow for to drop to LKO, before any major transfer windows?

Edited March 1, 2014 by Rakaydos

[Silverchain]

I make it 1134ms-1 for a Hohmann from 100km x 100km LKO, but that seems to be on the high side so I'm confused... I'll try again.

[Claw]

Perhaps this is a good place to start. You can use the wiki page for calculating delta V and combine with the delta V map below (or this one if you prefer it a little simpler).

where:

mu = GM is the standard gravitational parameter of the primary body (Kerbin)

Therefore the delta-v required for the Hohmann transfer can be computed as follows, under the assumption of instantaneous impulses:

(from your "inner" orbit)

to enter the elliptical orbit at r=r_1 from the r_1 circular orbit

(to circularize your "outer" orbit)

to leave the elliptical orbit at r=r_2 to the r_2 circular orbit where r_1 and r_2 are, respectively, the radii of the departure and arrival circular orbits; the smaller (greater) of r_1 and r_2 corresponds to the periapsis distance (apoapsis distance) of the Hohmann elliptical transfer orbit. The total \Delta v is then:

You can do this math backwards to figure out how much it costs to lower your orbit.

Here's the delta V map. It might save you some math getting to/from Minmus or into Minmus orbit.

BTW: I haven't done much with Lagrange points myself, but I hear they don't work very well yet. Good luck.

Edited March 1, 2014 by Claw

[Rakaydos]

The thing about Lagrage points, is they break the DeltaV Roadmap by having easy access to slingshots.

The hoffman transfer to the station is the easy one. The drop into minmus SoI can be done with RCS, but you probably need a burn (with oberth) to reach low kerbin from Suborbital Escape Minmus.

[Claw]

(Edit: Some of this info is updated in the next post.)

The thing about Lagrage points, is they break the DeltaV Roadmap by having easy access to slingshots.

The hoffman transfer to the station is the easy one. The drop into minmus SoI can be done with RCS, but you probably need a burn (with oberth) to reach low kerbin from Suborbital Escape Minmus.

Yep, sorry. I've been trying not to dump too much info at once into my postings. I was aiming at your first two questions.

I am looking at putting a refueling depot 2,250 km ahead of the leading side of Minmus. (Minmus's SoI is only 2,247 km) with a circular orbit at exactly the same radius as Minmus's, so the relative velocity remains zero.

How much deltav is needed to reach such an orbit from Low Kerbin?

How much deltav does it take to lift kethane from minmus, given a ballistic escape launch?

Sounds like you already know to get the answer to your first question then. And for your second question, I didn't know exactly what your goal was, Since achieving escape from Minmus is a slightly different question than getting "from Minmus to specific place." Ballistic escape launch to where? If you're just looking to break SOI, then I would guess the delta V chart can get you some rough idea (and escape velocity is ~243 m/s).

What would be the longitude (laditude would presumably be 0) of the best minmus launch site to reach the station? (presumably the point directly under the station, but minmus's rotation may throw this off)

How much deltaV would it take to slingshot a cargo past minmus such that it drops to low kerbin orbit to the east? and how much to the west?

Minmus' rotation isn't synchronous with it's orbital period. So there's no best launch location to constantly point at an L4/5.

Delta V to slingshot past Minmus back to Kerbin will depend on a variety of things how low you want to slingshot. If your goal is to hit Kerbin's atmosphere, you can calculate all that out (as there would be an optimal Mun altitude) but this one is probably easier to just try out and see. My guess is that it would be in the neighborhood of 150 m/s. But the reality is that it will probably take a lot more than that because KSP doesn't really support Lagrange points. You can sort of simulate L4/5 by being there, but you're not actually in a Lagrange point from a physics standpoint.

So since Minmus has an orbital velocity of about 274 m/s, you would need twice that to reverse your orbit for a retrograde slingshot back to Kerbin. Then whatever dV to correct the slingshot velocity. (So I suppose my guess without math is around 650 to 700m/s.)

EDIT: and how long should I allow for to drop to LKO, before any major transfer windows?

Depends on how fast you want to get there. Returning from Minmus with minimum dV is around 56 hours. You can knock it down quite a bit, but I don't know how that lines up with coming back from L4. I haven't calculated where the Kerbin-Minmus L5 is, but if you're 60 deg ahead in the arc, you would need a little over a day to get from L4 to Minmus, then roughly two days to get from Minmus back to Kerbin for a burn. I think the bigger problem is waiting for Minmus' orbit to line up so that it's on the right trajectory for an interplanetary transfer. Plus Minmus' inclination is going to play havoc.

Edited March 2, 2014 by Claw

[Claw]

Okay, so I went ahead and tried this out on the Mun. I had been wanting to try having a station or something like this, but I had (in my head) already settled on leaving whatever it was in Munar orbit. Instead of Munar orbit, I aimed for L4. (I chose the Mun because I didn't feel like dealing with Minmus' inclination and it's easier to deal with transfer timing.)

I set myself up in front of the Mun, just outside of it's SOI (2.4Mkm). I ended up about 2.6Mkm.

I started playing with the maneuver node, thinking as if I was trying to slide out of L4 (which KSP doesn't really simulate). I figured this was probably inefficient and I verified my thought above. If I really wanted to slide out of L4 it was going to be too much dV. It was cheaper to just burn and drop straight back onto Kerbin. You might be able to just slide out the back if you can get the station just in front of the SOI, but that's tough in addition to getting a perfect orbit. So I sought a better way.

Instead of thinking like Lagrange points, I thought about it like I was trying to rendezvous with the Mun. Instead of sliding out the back of L4, I misaligned the orbit slightly so that my craft swung outside the Mun's orbit. (It actually took about a 45deg burn to slow and go wide.) I spent about 30 dV and ended up in what would have been an elliptical orbit, except the Mun was there to catch me. This caused the craft to enter the Mun's SOI slightly outside the Mun's orbit and pass in front. This actually set up for a bit of a retro slingshot inbound with a prograde slingshot outbound to ~30Mkm (think like an elliptical horseshoe). So this ended up behaving as if I had simply slid out the back of L4. It took a little while though, something like 1/3 to 1/2 of a Mun orbital period, which could be sped up with more dV.

From there, it was a burn much like leaving Munar orbit for Kerbin. Roughly 150ish dV for a 13 hr return flight in prep for a slingshot, which could be reduced by spending more dV. (So inline with my Lagrange guess in the above post.)

So while the physics isn't perfect, it is reasonably possible to simulate. There are still some hurdles to overcome, such as getting the craft orbit perfect so it doesn't decay into or away from the Mun/Minmus (especially when time warping). I think the Mun is a bit easier to manage, but is probably less economical for Kethane. If you mine it from Minmus, you could potentially tug it to the Mun station when the orbits align.

I'm not saying don't do Minmus. I think it would be a bit more challenging if you're looking for that.

That being said, while the above dV numbers aren't for Minmus, you could probably get a rough guess. I suppose after having flown it, I think I understand what you're after a little bit better. Given KSP's physics, you might be better off in L5 where you can drop inside the Mun/Minmus' orbit to catch up. This would cause you to "horseshoe" retro-slingshot around the Mun/Minmus back toward Kerbin and potentially reduce the dV requirement further. (Just a thought.)

(Edit: I'm using the term L4 pretty loosely here, so don't beat me up to hard.)

Edited March 2, 2014 by Claw