Relatively speaking, what time is it in the center of the Earth?

I was delighted to see your post and learn that you were not a complete ignoramus!

(Maybe just a partial ignoramus, like me.)

The post was clear; it was only the title that was a bit misleading, but fun anyway.

Molten O’clock

You can get a rough estimate of the time dilation factor via this expression:

T[sub]A[/sub] = (1 + GM/2Rc[sup]2[/sup])T[sub]B[/sub]

where A is at the surface and B is at the center. This expression assumes a Newtonian potential so it won’t work so well for things like neutron stars or black holes, but it does well enough for planets and stars.