Go in friendly. Make an effort to assume and embody good will and rationality. The premise of most conspiratorial thinking is very dichotomous. They see themselves as the open minded against dismissive, closed minded opposition. Don't play into this by being dismissive. Be generous instead and assume that they are truth seeking just like you.
Don't be too defensive. If you don't know the "proof" for Gm1m2/r^2, don't pretend you do. Spend time. Be proactive instead. What's the proposed alternative to Gm1m2/r^2 and why do they think that one is true. Instead of seeking out logical holes and dunking, seek out points you can concede. This creates a common ground and gives them permission to concede points too. Intellectual honest is a reciprocal game.
Make it an interesting conversation, not a game you're trying to win. Almost all of their exposure to the topic(s) is either monologue (probably youtube), or ridiculing/dismissive debate. Good faith dialogue will be a rarity. Be that. It often gets epistemological, and that actually is interesting.
Last, remember that almost no conversation ends with a change of mind. That happens later, if at all. What you can "prove" within the conversation is that not all spherists are closed minded, dismissive arseholes.
I'd also recommend doing it. There's a lot to learn here that transposes onto less fringy stuff... especially politics. You likely can't convince Democrat to be a Republican, but you can convince them that some Republicans have reached their conclusions with an open mind, good faith and good intentions. That's the myth which needs to be busted. Other myths are secondary.
Conspiracy theories are about people and their perceptions of other people, primarily. The object of the conspiracy is secondary.