Subject: Relative to time and gravity--are your feet younger than your head?

Is it true that the closer you are to mass then time slows down 
relative to objects farther away from that body of mass? For 
example if I were to stretch my feet all the way to the center 
of the Earth (which is heavier than the mantle or crust) with my 
head sticking out the surface, which would go through time 
faster? My feet or my head?  Also if I were to go into the 
center of the sun (which has more mass and stronger gravity) 
would time go slower for me than for people on the earth?

Re: Relative to time and gravity--are your feet younger than your head?