With a noninteracting pair, astronomers can precisely measure the change in the orbital period of the stars as they spiral toward each other.
Due to the near-circular orbits of Earth and Jupiter, as Earth has a faster orbital period than Jupiter, from our point of view we will appear to "overtake" the gas giant.
Whether you have a very light object or a very heavy satellite, they have the same velocity in orbit if they are at the same distance, and they have the same orbital period.
