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tomf

Analytical solution for constant thrust trajectories

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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?

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Posted (edited)

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 by mikegarrison
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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.

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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.

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Posted (edited)

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 by kerbiloid

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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.

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