Best way to come back to an equatorial mun station

[Skalou]

Hi,

I was asking how to find most efficient way(fuel) to going back to an equatorial station when landed with an offset (not 0° of lattitute),

So here is an example with a nearly 45° of lattitude lander, an equatorial orbiter at 50 km around the Mun:

the start situation:

what i want:

docking the orbiter on the top to an orbiter.

what i have tried:

1)

Launch in low orbit, homman transfert for an intercept with an inclinaison correction at the Ap. ( i tried with different launch inclinations,it is worst than the other case and i didn't took pictures even in doing the correction in a hight bi-elliptic transfert when >45°, sorry), i also tried to jump and land on the equator then re-launch in an equatorial orbit.

2)

Launch to reach at the lowest speed the target and then correct the inclination (90° here!)

better than all the 1) cases, but there is a huge inclination to correct.

3)

Launch to reach the targeted orbit with the lowest inclination beffore complete an orbite (to keep a low Ap speed)

better than 2) and 1), but the Ap speed is increased an so the DV to correct the inclation is still a bit high.

4) most interesting,

i tried finally a between 2) and 3) solution

The best i found for now, the better compromise between a low speed at Ap and a low inclination. but it is empiric, i just tried different angle to find some better than other.

Thing to do:

- spread it to the world!

-find a way to determine the inclination to launch into (i'm really unable to calculate this, specialy for different situations: lattitude of the lander, height of the orbiter,...).

however if also found some workaround to avoid this:

-don't RDV with the station and go back directly to kerbin, but it's less efficient in most of cases.

- have an inclined orbiter, and so just wait his orbit cross over the lander head to launch directly in a coplanar orbit.( and so the solution seems to be: launch in the lowest orbit then RDV with a Hohmann transfert)

-move the orbiter the RDV with the lander, and so save a bit of fuel> weight for the lander, i didn't tried it myself to compare. but the idea in my example is to don't move the orbiter(imagine it is a big station).

note:

you can see on some pictures i tried to RDV directly with the orbiter, that's because it was my initial challenge: "dock to the orbiter before complete 1 orbit", but don't care about that, in this discussion it's not needed.

Did you find some other solutions?

or are you able to calculate it?

Edited October 13, 2015 by Skalou

[Skalou]

moved to here:

http://forum.kerbalspaceprogram.com/threads/136614-Best-way-to-come-back-to-an-equatorial-mun-station

Edited October 13, 2015 by Skalou

[Snark]

You always want to launch on a heading of due east, regardless of latitude; that will give your ship the lowest possible inclination relative to your orbiting station. Of course, if you're off the equator, it won't stay eastbound; for example, in the picture, where you're way up north, your trajectory will bend southwards pretty soon. But at the point of takeoff, always head due east.

You also want to take off at the shallowest possible angle, as close to horizontal as you can get away with without scraping your toes on inconvenient mountains or crater walls. This maximizes the Oberth effect.

Therefore, the optimal intercept looks like this:

• Bearing: due east.
  
• Elevation: as close to horizontal as you can get away with
  
• Velocity: raise your apoapsis so that intersects the station's orbit
  

At the point where your orbit intersects the target's (which is also the ascending/descending node), you do a big expensive burn to match velocity.

Incidentally, there is an alternate option for some cases. The above strategy will work best for most cases, but if you are doing this on a world that has a big SoI and your inclination is extreme (i.e. you're way up to the poles when you launch), this other method may be more efficient. It looks like this:

1. Launch due eastbound, and horizontally, same as above. However, don't raise your apoapsis to the target's. Keep your apoapsis as low as possible without hitting the ground.
   
2. Circularize into the lowest possible circular orbit you can manage.
   
3. At the ascending/descending node, do a prograde burn that raises your apoapsis as high as possible (way higher than the target). How high you can go will be limited by the size of the body's SoI.
   
4. Coast up to apoapsis, which will happen to be the opposite node-- e.g. if you did your burn at the descending node in the previous step, your apoapsis will be at the ascending node.
   
5. At apoapsis, do a burn with enough normal (or antinormal) component to match your orbital inclination with the target, and enough prograde component to raise your periapsis to the target's orbit.
   
6. Coast down to periapsis and intercept. You'll be doing a retrograde burn to match velocities with the target.
   

This strategy works because inclination changes are much cheaper to make when your velocity is very low. Whether this strategy is worthwhile enough depends on how big an inclination change you're making, and how big the target's SoI is. This strategy saves dV on inclination, but loses dV on raising/lowering the apoapsis. The former changes with inclination (the more inclination difference there is to start with, the more dV you save), but the amount you lose to apoapsis raising/lowering stays the same regardless of inclination change.

Edited October 13, 2015 by Snark

[Skalou]

I posted here too, i don't know where is the best place to discuss it:

http://forum.kerbalspaceprogram.com/threads/136614-Best-way-to-come-back-to-an-equatorial-mun-station

But i don't agree with you,

with your technique, the inclination will be lower than 45° so it's better to correct it directly without doing it with a bi-elliptic transfert at the SOI edge (or lower altitude after being in orbit),

and i also found i my case it is evencheaper to raise directly the Ap to the target altitude and correct the inclination and finalize the circularisation in the same time: case 3), the lower Ap speed counter-balance the oberth effect lost.

Edited October 13, 2015 by Skalou

[tomf]

The best orbit to launch into is going to be the one with minimum inclination as plane changes are always expensive. I would start of from the surface by burning due east and then follow slightly to the east of the prograde marker.

If I were significantly inclined ~>40degrees of latitude on my landing site I would try to get a large AP and Keep the AP near the ascending or descending node. The plane change will be much more efficient done far from the centre and combined with a burn to raise the PE to the orbit of the target station.

Then a burn at PE to create a rendevous of less than 500m on the next orbit whill hopefully will require an AP similar to the target. Then rendevous as normal.

[katateochi]

without doing any maths;

launch as you've done in pic 3 and circularize at that inclination. At the point the orbits intersect burn to raise Ap by several 100km so you're in an elliptical orbit. Warp round to Ap and change inclination. return to Pe and lower Ap back to target orbit (or one that puts you on course to rendezvous).

edit:

ninja'd by tomf!

[Lukaszenko]

As others have mentioned, try raising your AP (and making sure it's directly above the orbital plane intersection) so that you are moving much slower. I'm not sure how high and at what inclination, but there's a point where it is worth it to raise the AP, change the inclination, and then lower it again.

[Skalou]

with your technique, the inclination will be lower than 45°(38.64° in fact) so it's better to correct it directly without doing it with a bi-elliptic transfert at the SOI edge (or lower altitude after being in orbit),

http://forum.kerbalspaceprogram.com/threads/4374-KSP-Orbit-Mechanic-1-2a-Optimize-Your-Orbits.

And i also found i my case it is even cheaper to raise directly the Ap to the target altitude and correct the inclination and finalize the circularisation in the same time before being in a real orbit: case 3), the lower Ap speed counter-balance the oberth effect lost.

tomf , it is a bit what you said but i do it in a suborbital flight (can be considered as a highly eccentric orbit?): lower Ap speed and lower Pe altitude too> lower Dv to change plane, a bit more Dv to circularise but it's counter-balanced.

And then the solution 4) which is even better: higher inclanation to correct but lower AP speed that give a lower Dv cost for the entire RDV.

Edited October 13, 2015 by Skalou

[Red Iron Crown]

Merged duplicate threads.

[Skalou]

Merged duplicate threads.

Thank you, i've done my Jeb, and was scared to nuke the forum's astronaut complex.

[Champ]

You also want to take off at the shallowest possible angle, as close to horizontal as you can get away with without scraping your toes on inconvenient mountains or crater walls. This maximizes the Oberth effect.

I think the Oberth has nothing to do with it, it is more about minimising gravity losses.

[LostOblivion]

More over, there's a reason all space stations to date were put on a highly inclined orbit. :-)

Because, unless you're on Mercury, you can always wait until the planet rotates into its path.