[Polywantanomial (OP)]

If an object's velocity effects it's perceived time, did Cassini move into the future by traveling upwards of 44/km for 13 years? Does time dilation work that way under the speed of light? Was there a clock on Cassini's computer? If so did they have to recalibrate as it traveled?

[Janus]

If an object's velocity effects it's perceived time, did Cassini move into the future by traveling upwards of 44/km for 13 years? Does time dilation work that way under the speed of light? Was there a clock on Cassini's computer? If so did they have to recalibrate as it traveled?

At that speed, over 13 years, time dilation would only amount to a difference of roughly 4.4 seconds.
That just means that over the trip, Cassini's clock would have measured that much less time than the Earth clock.*

And there really wasn't any reason for Cassini to keep track of its own time over the trip.  It would collect data, and send it back to Earth.  It made no difference that by  Cassini's clock it collected that data at 12:00:04, and according to Earth it was collected at 12:00:00
This is different than, for example, the GPS system, which does require a tight synchronization between satellites and ground in order to maintain accurate results.


*In realitiy it is much more complicated than that. The Earth itself orbits the Sun at some 30 km/sec. Cassini didn't have a constant speed relative to the Sun over its whole trajectory. You also have to account for gravitational time dilation due to differing distance from the Sun...  But even after all this is taken into account, the total time difference accumulation would be too small to matter.