Mass and time

If there was a clock in a massive object say... Jupiter and there was a spacecraft that was very light sent into space and it too had a clock on it. Would the clock on Jupiter go slower than the one on the spacecraft?

If the mc^2 of each were the same, they'd make it on time for lunch at Tiffanie's!

First, there is no such thing as time it is Spacetime. What we call time is only relevent to two individuals having near zero velocity, with respect to one another.
Any object accelerated to a significant fraction of C (Light velocity) experiences what is called time dilation..that is to say for the observer upon the moving object, time slows down...to the point that many many years may pass on earth, but to the individual on the fast moving object, only a few menths will have transpired. This is what will make long distance space travel difficult, until we discover FTL drive: You leave on a three year mission to Alpha Centauri system, spend 2 months exploring, and three years returning
only to find that 600 years has gone by on Earth. Not only are all your friends and family long dead, but it is doubtful that anyone will even remember the mission you went on. At light speed, time virtually stops. As an object accelerates towards
lightspeed, three trhings happen: 1. It's mass increases (reaching infinite at C)
2. it's longitudinal axis decreases (it gets shorter front to back) but so do the occupants, so they do not notice. 3. Time dilates, that is clocks on the vehicle are running much slower than clocks on Earth. Theorists allege that lightspeed is impossible due to the object aquiring infinite mass, but this mass increase is,
like the compression, and time dilation, only measurable to a fixed observer NOT traveling on the vessel. Relative to the vessel the mass appears the same, and the
thrust (that which accelerates the vessel) becomes infinite along with the mass.
At lightspeed, the object loses all longitudinal measurement, becoming like a slice of very thin paper when viewed from the side, although to the occupants, it is normal, and the universe appears stretched out, so that a planet looks not like a ball, but like a very very long rod.