# Acceleration needed to go from a point to another

## Main Question or Discussion Point

Hello !

I'm working on an informatic project where there is spaceship and other bodies in space.

I'm searching for a way to my spaceship to calculate an itinary between two points in space. I know how much my spaceship can accelerate (my reactors has an acceleration of Rx, Ry and Rz) and i need to calculate when and where i need to accelerate or decelerate it to go from one point A in space to another point B.

My spaceship have already a velocity preset and a constant force toward the nearest star !

I didn't find the answer by myself so i thought maybe some of you would know how to do it or maybe you can give me some hints on the web !

Thanks !

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mfb
Mentor
There are many way to reach a specific point. A constant force? This is a strange star.
In real systems, you usually do not need a minimal acceleration - not even a minimal integrated acceleration (velocity change). But if the velocity change should be small, the required time to reach the destination can become really long.

The movement of the spaceship just follows Newton's laws of motion, you can find a lot of material about this in the internet. If you have more specific questions, ask them.

The question is vague, you might want to draw a diagram or something, is point B the star you're going to? Or are you moving through space from A to B with the star nearby? You can draw a crude diagram in paint or something so we can conceptualize the problem.

Ok so here is a diagram !

My spaceship is at point A. It needs to go and stay at point B but it has a velocity of V and an overral force of F applied to it (by the nearest star)

Its reactor only provide a maximum acceleration of R (in Newton).

How can i go to point B in minimum time using the reactor ?

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Ok so here is a diagram !

My spaceship is at point A. It needs to go and stay at point B but it has a velocity of V and an overral force of F applied to it (by the nearest star)

Its reactor only provide a maximum acceleration of R (in Newton).

How can i go to point B in minimum time using the reactor ?
This is a very hard problem that lacks any analytical solution. googling for "minimum time orbit transfer" will get you some articles, such as

http://www.dept.aoe.vt.edu/~cdhall/papers/AIAA-4125-357.pdf

and also some matlab packages

Thank you Willem ! I will look into it and try to make my way out of this !