The speaker personifies the sun throughout nearly the entire poem as a self-important old man in order to rob the sun of its authority. This personification begins in the very first line, when the speaker addresses his words to a "Busy old fool, unruly sun." The poem thus opens with the introduction of the sun as a character with human traits. These traits are not to be looked upon favorably. In the speaker's ageist portrayal of the sun, it is getting "unruly," meaning that it is getting worse as it ages at serving those it is supposed to serve, but it is too "foolish" to realize its own decline.
The negative characterization of the sun remains consistent throughout the poem, so that the speaker's proposition at the end, for the sun to confine itself to the bedroom, is founded on the assumption that, "Thine age asks ease." Essentially, the speaker is telling the sun, "You're too old to be working so much these days." This is a veiled insult that, on the surface, might be read as a show of care and respect for the sun. However, the use of the familiar "thine" rather than the respectful "your" (again, in Donne's day "you" was actually a more formal form of address than "thou") demonstrates that the speaker is talking down to the sun rather than up to it: the uppity speaker turns himself into the sun's boss and offers it semi-retirement if it will only consent to do his bidding. The speaker's personification of the sun as an aging man thus allows him to invert the power dynamic between himself and the sun over the course of the poem.
Although the speaker only explicitly describes the characteristics of the sun in lines 1 and 5, the speaker orders the sun to take many actions, such as "go chide," "look," and "ask for." The speaker also implies that the sun has eyes to be blinded and that it leaves colonies lying around like collectibles. By the time the speaker tells the sun in line 25 that "Thou, sun, art half as happy as we," it seems natural that the sun would experience a human emotion like happiness. After all, it seems to have plenty of human agency and other human features. By turning the sun into a sentient being that thinks, acts, and feels, the speaker sets the stage to assign the sun "duties" in line 27. If the sun wants to be a person, the speaker seems to say, it will have to get a job like everyone else.