Astrophil is speaking to Stella (his love).
Astrophil finds himself lovesick. He cannot understand why Stella doesn't love him and scorns his own declarations of love.
Sidney's connection to the moon is an example of a "pathetic fallacy" in which elements of nature appear to experience human emotions. At first Sidney describes the moon in accordance with classical mythology, as an individual being. Yet, his insistence that the moon is lovesick does not make sense in this context because the goddess of the moon is Diana, a perpetual virgin who is not affected by love. Then, Sidney switches his perception of the moon to adhere to Copernican belief, and he describes the moon as a planet. The series of questions he asks expresses his desire for a logical explanation of Stella's behavior. He wants to know if the scorn his love receives at her hands is limited to the earth.