Analytical solution for constant thrust trajectories

[tomf]

In the suggestions forum I see yet another thread about wanting a buff/debuff to ion drives

It it possible to find analytical solutions to constant thrust trajectories?

E.g. If I am in a solar orbit and I propose to spend 6 months thrusting with a very low thrust at a fixed offset to my prograde vector is it possible t draw the path my craft will take without running a numerical simulation.

I'm assuming that a fixed prograde angle will be the most effective plan to match inclination and rendezvous with a target. Is it any easier if the thrust is simply prograde?

[mikegarrison]

It depends. Are you trying to minimize time? Usually you wouldn't be constantly thrusting unless you were. These are called brachistochrone trajectories, and yes there are analytical solutions. But it's pretty close to just pointing at the target and thrusting.

Edited March 27, 2017 by mikegarrison

[Steel]

1 hour ago, tomf said:

In the suggestions forum I see yet another thread about wanting a buff/debuff to ion drives

It it possible to find analytical solutions to constant thrust trajectories?

E.g. If I am in a solar orbit and I propose to spend 6 months thrusting with a very low thrust at a fixed offset to my prograde vector is it possible t draw the path my craft will take without running a numerical simulation.

I'm assuming that a fixed prograde angle will be the most effective plan to match inclination and rendezvous with a target. Is it any easier if the thrust is simply prograde?

Short answer I'm afraid: no.

As @mikegarrison mentioned, unless you're doing brachistochrone trajectories (you're definitely not with an ion drive), any orbital trajectory where the impulse cannot be assumed to be instantaneous needs to be computed numerically.

[YNM]

Believe it or not, Andy Weir (writer of The Martian) actually made a software for that. You can set the thrust and direction wrt Sun's surface prograde. Not sure whether it's on the .net or not.

[kerbiloid]

On 28.03.2017 at 9:37 AM, YNM said:

 

Believe it or not, Andy Weir (writer of The Martian) actually made a software for that.

 

Unlikely it's analytical.

P.S.
Also not analytical but may be enough solace:

P.P.S.
This is Science&Spaceflight rather than Gameplay/Mod questions. This man indeed sticks on the solar orbit!..

Edited March 29, 2017 by kerbiloid

[YNM]

6 hours ago, kerbiloid said:

Unlikely it's analytical.

I thought it is or something... It entails solving some accelerated circular motions. He explained it during a visit to some university or something - videos are on YouTube.

[Phelan]

On 29.3.2017 at 4:45 PM, YNM said:

I thought it is or something... It entails solving some accelerated circular motions. He explained it during a visit to some university or something - videos are on YouTube.

Do you by any chance remember the title or ideally can provide a link? I'd rather not go through the dozen or more hour-long vids on YT alone where he gives a talk

[YNM]

10 hours ago, Phelan said:

Do you by any chance remember the title or ideally can provide a link? I'd rather not go through the dozen or more hour-long vids on YT alone where he gives a talk

Sorry, completely forgot it by now. Unlikely either to reappear on the feeds on mine (it was back at a time when logging in to YouTube feels like logging in to e-mails).

[Phelan]

1 minute ago, YNM said:

Sorry, completely forgot it by now. Unlikely either to reappear on the feeds on mine (it was back at a time when logging in to YouTube feels like logging in to e-mails).

Dammit... Ah well, maybe I'll just occasionally watch a likely talk and hope I'll stumble over it sooner rather than later, I'll try to remember posting the link if I should find it

Thanks anyways!

[YNM]

It was sometime in between the book being a hit and going to be made into films, and the film being released. If that helps that is !

[wumpus]

Obvious, to do [anything] correctly you will be stuck with a numerical solution.  But I would suspect that a solar orbit would be the most accurate of simply computing the velocity you have and the velocity you need and figuring out just how long that will take.  The big gotchas are you can't use any "subway maps" or other previously generated delta-v tables as they all assume Oberth and other things you won't have.

Oddly enough, an Earth-Mars burn will spend nearly all its time in Earth orbit (unfortunately in the Van Allan belts which is a huge problem, especially for the solar panels).

And what would a KSP forum answer be without a Scott Manley link:https://www.youtube.com/watch?v=000zDI2nmq8&list=PLYu7z3I8tdEknQK8KQqHA5sc0wbvj2q7z&index=20&t=6s  I'm not sure which one has it (there are three parts) but it does show how the delta-v calculation goes.  Not sure if Oberth is included "for free", if so you have to make sure it isn't calculated in your answer.