Aim a proper gravity assist/powered slingshot?

[Uberick]

Hi all!

I've been experimenting with gravity assists for the past couple of days, and was wondering if there's a way to calculate or predict how a gravity assist will affect your trajectory. I know this IS possible, because real life spacecraft seem to do it all the time. However, I don't know if it's simple enough where it can be done by hand for this game, or if its complexity restricts its use to real rocket science. Ideally, I'd like to be able to use gravity assists and powered slingshots to lessen the fuel costs of interplanetary travel, and be able to use the moon to help accelerate out to the outer and inner reaches of the solar system.

I'm only proficient in pre-calc level math, so if it takes anything more than that I'll have to study up a bit first(calc is next semester), but I'd love an explanation that'd take me a semester to understand if that's what it takes

Thank you in advance for everyone's time and consideration:)