How does Sidney critique the "courtly love" relationship using his Sonnet Sequence Astrophil and Stella?

Sir Philip Sidney's Astrophil and Stella is a sonnet sequence that was inspired by Sidney's relationship with Penelope Devereux. Sidney was in love with Penelope, but she married another man. This caused Sidney to write a long sonnet sequence that includes many poems expressing the pain caused by his love for this woman.
The courtly love tradition is basically a set of behaviors in the medieval period that governed the way upper class men wooed upper class women. In many cases, the woman would have already been married and nothing was actually expected to happen romantically between the man courting the woman. Sidney's sonnet sequence is a bit different because he isn't wooing her so much as mourning the loss of her and expressing how much he wishes he could forget her. Take for example Sonnet 39, in which Sidney (Astrophil) addresses sleep through an apostrophe (poetic address to someone/something that can't answer back). He asks sleep to provide a space for him where he can escape the memory of Stella (Penelope). The poem indicates the pain he is in because of his love for her; the only escape he has is in the oblivion of sleep. In another poem, Sonnet 31, Sidney asks the moon if lovers are rejected and lonely on the moon, as they are (he is) on Earth.
Based on these poems, we can see that Sidney's Astrophil and Stella has more in common with the Petrarchan sonnet tradition than it does with courtly love tradition. Petrarch, "the father of the sonnet," also wrote his poems about a woman he could not be in a relationship with. The central theme is unrequited love and the unique combination of pleasure and pain that come from that experience.