Mathematical way of predicting a landing site from an interplanetary approach.

[nhnifong]

So I'm coming into Duna hot at 2000 m/s and I'm on the edge of it's SOI. This is the place I tend to stop and move the periapsis 10 km over the surface at a latitude near my destination. But predicting the longitude of the landing site is difficuly because the planet will make several rotations and there will be 5 to 10 km of aerobraking.

Can someone help me with predicting my landing site's longitude?

[blizzy78]

Perhaps you might want to use MechJeb. You don't need to use its landing autopilot, but it can also display estimated landing site or orbit after aerocapture.

[nhnifong]

Perhaps you might want to use MechJeb. You don't need to use its landing autopilot, but it can also display estimated landing site or orbit after aerocapture.

It's predictions are incorrect, at least for duna, on the edge of it's SOI.

[blizzy78]

I guess it's predicting according to its own landing profile, which most probably you don't follow.

[Radiokopf]

Well iam no expert but ive you leave a small periapsis and you got an ETA you could calculate either the distance the planet travels or the fraction of rotations it does with this values:

Sidereal rotation period

65 517.859 s

18 h 11 m 57.9 s

Equatorial radius 320 000 m

Sidereal rotational velocity 30.688 m/s

Like 9h would be half a turn so you could adjust your longitude 180°.

[shand]

yeah, i agree with radiokopf, calculating entry to atmosphere is relatively trivial - landing site, well that will depend on your landing profile.

[glacierre]

Seems quite difficult problem, mostly for the athmospheric part, you will lose speed differently depending on your trayectory/Pe, not to mention if your craft has some parts generating lift (then you get extra corrections depending on the angle of your craft respect to prograde). And add some rounding errors here and there for extra fun.

Most predictable is probably a head-on slam (but with the thin atmosphere of Duna you may not survive that), there you can pretty much use Radiokopf basic calculation and the aerobraking part is well defined (and minimized, too, ahem), the more shallow you enter, the more difficult it gets to predict.

Keep in mind, too, that predicting is not controlling. Depending on your ETA and the rotation period of the planet there are some points (on the back hemisphere) that will simply not be reachable by any direct aerobraking maneuver because you would need a Pe too high to even be captured (with enough dV anything is possible, of course).

Safest (but by far not fastest) way of predicting and controlling is to split it in aerobraking-capture into an orbit and then land from it (at least you can work out an approximate rule of thumb if you keep your orbit radius and deorbit burns similar).