system
Given the following post, respond as if you're commenting on Reddit:
human
Orbital mechanics question: can you burn for a direct capture of mars orbit as you leave earth orbit?

A friend and I got into a discussion about this.  He says its impossible to do without a significant retro burn.  I say it’s just requires a lot of precision and is impractical but possible.  What say you?
gpt
The only way to be captured into the orbit of a massive body when you are starting from outside the sphere of influence is either:  
A: you do a retroburn after getting there to stabilize the orbit.  

B: you slow down with an aerocapture, and the do a prograde burn at apoapsis to circularize (otherwise you would eventually crash into the planet)  

C: You use a gravitational interaction with a second massive object orbiting the planet to alter your trajectory. This is how rogue planets get captured by stars. The problem is it is exceptionally rare if the orbiting massive object is exceptionally small (like for instance, Mars' only moon.)  

Without one of these things happening, then if you are starting from outside a planet's gravitational influence, then your velocity will by definition always be enough to escape its gravitational influence on the other side (discounting relativity, which would only really come into play with black holes) because of the concept of conservation of energy.