calcuating an intercept

[jedidia]

Ok, I'll have to face this soon I'm afraid if I want my Navtool for constant low thrust...

problem: I want to go to mars. During the time I'm getting there Mars will move. Since its distance will change with that, I will not be able to know which distance I have to cross exactly, without which I won't know how long it will take me, which I would have to know to know where to aim, and that's where the Cat bites it's tail and starts running around in circles...

I know I can solve the problem by iterating... Getting current distance, calculating necessary time to cross it, calculate new position, and start over. The failure will get less with every iteration and will eventually get close to an acceptable value. However, this iterating is terribly clumsy and eats a bit of power.

I know that TransX, IMFD and TransferMFD solve the problem, and I don't think they do it by iterating. It's got something to do with integration too I figured. Maybe someone has an interesting read for me on the problem, so I could eventually figure out how it works...

 

[Enjo]

Have you tried AGMFD ?

[ame="http://www.orbithangar.com/searchid.php?ID=3111"]AGMFD V1.5[/ame]

 

[Face]

Ok, I'll have to face this soon I'm afraid if I want my Navtool for constant low thrust...

problem: I want to go to mars. During the time I'm getting there Mars will move. Since its distance will change with that, I will not be able to know which distance I have to cross exactly, without which I won't know how long it will take me, which I would have to know to know where to aim, and that's where the Cat bites it's tail and starts running around in circles...

I know I can solve the problem by iterating... Getting current distance, calculating necessary time to cross it, calculate new position, and start over. The failure will get less with every iteration and will eventually get close to an acceptable value. However, this iterating is terribly clumsy and eats a bit of power.

I know that TransX, IMFD and TransferMFD solve the problem, and I don't think they do it by iterating. It's got something to do with integration too I figured. Maybe someone has an interesting read for me on the problem, so I could eventually figure out how it works...

Hm... it depends on your trajectory, I'd guess. If you can solve the integration of your trajectory analytically, I'm sure you'll find a analytical solution for the whole problem. If not, you'll have to use numerical integrator-methods like RK4, which are almost always iteration solutions. IMFD is using RK4 (or even higher) in a separate thread, IIRC.

That said, constant low-thrust would mean some kind of spiral-trajectory, wouldn't it? So IMHO a numerical solution would be necessary, anyway.

regards,
Face

 

[Urwumpe]

You can make a rough numerical estimate for spiral trajectories, if you know the thrust of the engine. The problem is just, that gravity of other bodies has much more influence on low thrust trajectories to ignore them - one kind of iterative solution will always be needed - either you have a iteration over each orbit, or you work with osculating elements and for example calculate each orbit in 5° steps.

Also, that is why many low thrust missions aim for a WSB to get somewhere - regions of weakened gravity are great as you can change your course a lot with only minimal thrust.

 

[jedidia]

That said, constant low-thrust would mean some kind of spiral-trajectory, wouldn't it?

in a way yes...
in another way not necesarily.

The trick is to get away from a major body. This can be done by slowly extending the apoapsis, while periapsis remains the same (less thrusting and using the oberth effect). It takes a while, but works reliably... if you know in which direction you have to extend your orbit.

after the final stage of this manouver (after a few days normaly), you have a trajectory leading away from the parent body towards the target. That's where the fun starts: since you're thrusting constantly, after a few days, travelling speeds start to exceed speeds during normal Homan transfers, which means that gravity of bodies you'll encounter on your trajectory actually matters less (of course there is still the fact that you got less thrust for correcting your trajectory, but never forgett that you got days and days of time). It's far from a straight line, but straighter tha a homan anyways. I still have to figure out exact behaviour at encounter, but basically you just have to get to the right place at the right speed. Which means that planing must be more acurate than for homan transfer, or you'll overshoot the target for several weeks, since fast manouvers aren't possible.

which are almost always iteration solutions.

oh... so the big guys iterate too... no shame in it then :lol:

thanks for the link!

Have you tried AGMFD ?

Yes, I did... the results were not very encouraging, since it was made for constant HIGH thrust. It's not acurate enough to give you a clean Jupiter insert at accelerations of normaly less than 0.02 m/s square, because this means you got to start braking within a window of a few hours. With higher thrust, you have more tolerance for course correction and braking. I'm not completely through with AGMFD yet, but it doesn't look promising so far.