Death Star-esque space ship in Earth's orbit - how to destroy it without destroying earth?

I'm writing my first sci-fi novella and I'm looking for a bit of guidance from some scientifically literate people. My main premise is that an alien space ship similar to the death star enters Earth's orbit at a low orbit point. Its gravity causes earthquakes, tsunamis, meteor showers and all that fun stuff. My only problem is that I'm not sure how my characters are going to destroy the ship in a way that is scientifically plausible. I have a few ideas so far;

They somehow launch it into the moon, destroying it.

They somehow use gravitational slingshot method to launch it around the moon, Venus and Mercury and into the sun, destroying it.

They somehow pull the ship towards earth into the Roche limit, causing Earth's gravity to tear the ship apart, destroying it.

The problem is that, from my understanding, these methods would either complete destroy earth as well, or they're just scientifically implausible. I'm a bit of a science nerd, but I won't pretend to understand enough astrophysics to finish this story without some help and further research. Obviously, it doesn't need to be completely scientifically accurate, but I'd like to avoid any embarrassingly obvious errors. Any help would be GREATLY appreciated! (go easy on me, it's my first attempt at writing a book!) Thank you in advance!

posted about 8 years ago

Jon James‭

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