Maybe they could have their own talk show. And it could broadcast coast to coast

If they’re unaffected by gravity, chances are they don’t have mass. If they don’t have mass, they’re not constrained by the Higgs field, which in turn means that they can never move at any velocity below light speed.

Their unfortunate fate is to roam across all of space at the maximum possible velocity in perpetuity.

I misread ghosts as “goats”

This sounds like it should be the premise of a Doctor Who episode.

Or they’re flung in a straight-line tangent out from Earth’s orbit, like water drops flying off a spinning sponge