In Astrophel and Stella, the speaker/poet is Astrophel whose name means love of a star. "Phel" or "phil" as it is sometimes spelled is a suffix meaning "love." "Astro" comes from the Greek word "astron" which means "star." "Astra" is the Latin translation of "star." "Stella" means "star" so Astrophel is the "star lover" who is in love with Stella. This set of poems is loosely based on Sidney's own love for Penelope Devereux.
Like Penelope Devereux, Stella is married. Astrophel can only pine for her. Therefore, this is a story of unrequited love. The speaker is conflicted with thoughts of love and frustration that he can never fulfill his desires. Astrophel is never satisfied or certain that Stella loves him completely. There is the idea that he can only love her from afar, just as a person/lover can never grasp a star.
We see this conflict in Sonnet 62. Keep in mind that Love is personified as a Cupid figure or just as the emotional force of love personified. He calls his love "unkind" because Love compels him to love Stella but she does not feel the same:
She in whose eyes Love, though unfelt, doth shine,
Sweet said that I in her true love should find.
Love said to Astrophel that he would find true love in Stella; he sees this in her eyes. But she, Stella, does not feel (unfelt) this connection. Astrophel can never become fully accepted and thus fully intoxicated with Stella because she is married. He considers the possibility that she might convince him to abandon his feelings for her, "these tempests of vain love to flee." Thus, he could at least be virtuous in not pursuing a married woman, respecting her honor. In a way, this would start to put an end to his suffering. By absolutely refusing his love, Stella would shun Astrophel and allow him to be virtuous. In Astrophel's rationalizing logic, she would be showing her love for him (allowing him to claim virtue in the absence of love) but not loving him.