The word "moon" occurs in the poem's first and ninth lines, and much of the rest of the poem is made up of the speaker's descriptions of the moon's very strange behavior. He seems sad, his face is "wan," and he climbs the sky really slowly. In reality, the speaker is projecting his own feelings of sadness onto the moon. The moon doesn't really move that differently from night to night, and the color of its "face" has to do with various environmental factors (the position of the sun, for example). Really, it's not sad at all. The speaker is so sad, in other words, that he starts to think everything around him is sad as well, including the moon, which becomes his partner in crime (or tears), so to speak.
Lines 1-2: The personification fiesta begins as the speaker imagines the moon climbing slowly, silently, and with a "wan" appearance. As we soon will find out, the speaker is beginning to think the moon is love-sick.
Lines 3-4: The speaker makes his point very clearly. He asks the moon if Cupid (that "busy archer") also shoots arrows at heavenly bodies and makes them feel the pains of love as well. What a great, little guy.
Lines 5-6: Astrophel reminds us that he is qualified to judge in matters of love, and makes the identification between his own feelings and the moon's complete. He personifies the moon as a fellow sufferer of the "lover's case."
Lines 7-8: Astrophel reiterates his claim that he and the moon are experiencing the same thing. The moon's "languisht grace" (i.e., his drooping stature) is a clear sign that it "feels the like." Note that the personification just keeps going and going. Can the moon really languish, after all?
Lines 9-10: If the moon can languish, and feel sad, and climb slowly, it can also speak—well, kind of. The speaker asks the moon a question, and seems to imply that, true to the personification that is everywhere in this poem, he can answer. We get the sense that Astrophel is having a hard time explaining his own feelings, and wants the moon to tell him that love does indeed cause pain, even up in the heavens. Now, would that really cheer you up?