Brigo Explorer

Let me also add: If the issue is truly "getting the probe to the proper orbit" meaning you can get it into orbit around Brigo just not at the right inclination without conducting a large inclination change burn once in orbit....
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there are some relatively simple techniques you can use to set up your flyby so that the flybys inclination and close approach is very close to the final orbital parameters you need in the contract (and then only require one big orbit insertion burn to essentially complete the contract). I'd be more then happy to give you instructions on how to do that if the issue is as simple as this

Can you not pair it with one of those ridiculously lucrative "Brigo Flyby" contracts?
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I didn't make these contracts of course, so I can't speak to the intent behind them with certainty, but there are few of the "probe" "impactor" & "lander" contracts that don't pay out very much that I suspect is due to the fact the "Flyby" & "orbit" contracts payout ridiculously high sums so they figured players would just pair these lower payout contracts with those higher paying ones.