be glad that they're invading when they should simply destroy the entire solar system instead
If these aliens were intent on destroying us, they'd simply drop something large, fast and nasty into the sun and cause some sort of X-Ray eruption. Since there is a massive nuclear reactor so close, it would be silly not to leverage that to your goals. No need for ships or an invading force.
So we can assume that if aliens did arrive here, our destruction would not be their goal. They might, for example, just be neighbours popping over to ask politely if we'd mind turning down our electromagnetic emissions: TV, radar, etc.
If domination / subjugation / removal of humans to make way for their own settlers was their intent, then there's no reason to expect it would have to be done quickly. It could be a centuries long process. And, again, climate control or sunlight restriction would be a straightforward approach that would cause little permanent damage and wouldn't involve their actual presence in our system.