In the first two stanzas, Donne tells his wife that they should part quietly as virtuous men die (because they're not afraid of where they'll go next or their future)--no crying should cheapen their love and marriage. He tells her their love is strong and gives support throughout the rest of the poem.
Moving of th' earth brings harms and fears,
Men reckon what it did, and meant;
But trepidation of the spheres,
Though greater far, is innocent.
In stanza three, Donne offers the support of superstitions popular during the day. Earthquakes and other natural disasters cause much distress since we can see and hear them. People try to assign a meaning to them--it's an omen for this, or a harbinger to some other great event yet to happen. However, this sort of stuff goes on all the time on other planets and elsewhere in the universe. No one sees or hears or feels these events even though they may be greater and more dangerous than those here on earth, so they go without fear and trembling.
Likewise, let us part without all the attention and noise. Our love is based on emotional, mental, spiritual and physical love. It is not a small thing, and a short absence will not harm it. You are my rock--my "fixed foot" in the center of my world. I will always return to you when my adventure (circle) is completed. This is a reference to the metapor he uses of their love to a compass.
The speaker is referring to metaphysical ideas that were popular in Donne's time. There was a belief that earthquakes, the "moving of the earth" was a herald or sign of worse things to come. It was believed that earthquakes could portend great misfortune to come, but the speaker goes on to say that "trepidation of the spheres" or the movement of the heavenly bodies is not harmful. This is the second idea that Elizabethans had of the universe. They believed that the earth was the center of the universe and all the heavenly bodies--the sun, the moon, the stars--revolved around the earth in a series of concentric "spheres."
The third stanza of the poem, which includes lines 9-12, compares dramatic upheavals on earth and in heaven. Lines 9-10 address these upheavals on earth, specifically as they are manifest in earthquakes ("moving of th' earth" - line 9). The poet is saying that these phenomenon bring fear and wonder to men and cause great destruction and turmoil, but upheavals in the heavens ("trepidation of the spheres" - line 11), although more significant, receive less notice because we cannot physically see nor feel them. By introducing this theme, the poet is setting the stage for a comparison of physical vs. spiritual love later in the poem.