General relativity time dilation

[TrickyDicky]

Accordingto GR, as an object gets farther from a massive body , its proper clock runs faster than the clock of an object nearer to the massive body. So would the planet Pluto for instance measure time significantly faster than we on earth, being further from the sun than us?
If so how could I measure the difference? With the time dilation Schwartzschild formula?

 

[bcrowell]

So would the planet Pluto for instance measure time significantly faster than we on earth, being further from the sun than us?

Faster, but not significantly faster by most people's standards. The atomic clocks aboard GPS satellites, for example, run at a slightly different rate than ones on the ground, and this is partly due to gravitational time dilation: http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html

If so how could I measure the difference? With the time dilation Schwartzschild formula?

You could measure it with an atomic clock. You could calculate it using the Schwartzschild formula if the sun's field was the only relevant field, but that's not the case for the earth/Pluto example. In general, you can calculate it using the gravitational potential: http://www.lightandmatter.com/html_books/genrel/ch01/ch01.html#Section1.5 (subsections 1.5.7-1.5.8).