How would one do a brachistochrone curve/straight-line trajectory in-game?

[UbuntuLinuxKing]

Hi,

What I'm trying to find out if it's possible to do a brachistochrone curve/"straight" line trajectory. Essentially, you would burn towards, say, Duna until you were halfway there, and then flip around and burn to decelerate. I've already made an engine that can burn for that long, I would mainly like to know how I could do this in-game and how I could determine the halfway point of the path (roughly speaking).

Thanks!

[qzgy]

Math, probably. I personally don't know how to do that, but I'm sure there are mathemagicians on the forums  who do.

[HebaruSan]

Scott Manley has shown how to do it in detail in this video:

 

[purpleivan]

Not quite the same thing, as I didn't burn halfway there or decelerate with anything other than atmospheric friction, but I've entered a couple of "get to planet X in the shortest time" challenges.

My chosen technique involved some very broken, back of an envelope calculations involving working out how many degrees of arc the target planet would travel through in the time that the expected delta-v would get me there directly, then add a bit for my inevitable errors, then do a bunch of high speed course correction burns after the big one.

This was not an accurate method... at all, but worked well enough for my purposes.

The good old days of getting to Duna in 16 days courtesy of the lack of damage from atmospheric friction

[UbuntuLinuxKing]

13 hours ago, HebaruSan said:

Scott Manley has shown how to do it in detail in this video:

 

YES!

SCOTT MANLEY TO THE RESCUE FOR THE 23,457th TIME!