We have to distinguish “the universe” with local space. The *universe* is, as far as we know, expanding, but it’s not expanding at a rate that makes an appreciable difference to local systems (yet. One theory posits that the speed of expansion will continue to get faster and faster until eventually not even individual atoms will maintain their composition, the theory is sometimes called the Big Rip)
Comets like Halley’s Comet are still gravity bound to our sun and orbit it just like Earth does.
The fact that *space* is expanding doesn’t mean it’s expanding *fast enough* to impact orbits of objects in a local system. It might. Eventually. But not yet.
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