Donne contrasts earthly natural disasters with the bigger, grander motions of the heavenly bodies (planets, stars, moons). He lived in an age of discovery, an age in which people were thinking and theorizing beyond their technology. In other words, it was a time of great curiosity. So even though John Donne is cloistered away in the heart of England, he is fixated on geology and astronomy and uses these ideas to show the colossal, even cosmic, power of his love.
Line 4: It starts slow, with just the simple metaphor of the couple "melting" away from one another. It works literally—as solids melt into liquids, they spread out and cover a larger area.
Line 5: "Tear-floods" and "sigh-tempests" give us another quick introduction to the natural world. Obviously, he's using floods and winds to exaggerate the over-the-top emotions of shallow couples who are forced to be apart.
Line 9-10: The strong contrast is introduced here with the "moving of th' earth," which is a polite way of talking about earthquakes. Donne brings up earthquakes as obvious, loud events that send everyone into a panic, even though most of the time, they are only a quick rumble and then done.
Line 11-12: It's the "trepidation of the spheres," or motions of the planets and stars, though, that Donne is really interested in. Even though we humans are "innocent" of these motions, everything in our universe (according to popular belief) was determined by the alignments and shifting of these objects. That's like the deep love he has—it doesn't have to make a show to matter.