Answer by TheDemonLord for Using a planetary flyby to reduce speed

I am getting serious flashbacks to playing Kerbal Space Program...

So Starfish Prime has a very good answer - but...

AeroBraking

This is something that we used to do in KSP. In short - if you were running low on fuel and needed to slow down, you would buzz a planet with an Atmosphere - not enough for full re-entry, but enough for the drag of the Atmosphere to slow you down - not doing a gravity assisted slingshot.

Depending on Vessel design, heat resistance, dissapation etc. you can get some very drastic changes in delta V by using this technique.

Here is a video about how to do it in KSP - you can borrow the equations/maths if needed or if you want a higher level 'this is what they did' you can do that too.