What three heavenly bodies does Romeo compare Juliet to in Romeo and Juliet, Act 2, Scene 2?

The three heavenly bodies that Romeo compares Juliet to in Act 2, scene 2 of Romeo and Juliet are the sun, the moon, and the stars. 

This scene occurs after the Capulets' party where Romeo and Juliet meet. Romeo breaks away from his friends and climbs the outer wall of the Capulets' dwelling. He uses a metaphor to compare Juliet to the sun. He says the moon is jealous of Juliet's beauty, personifying the moon as a woman (or the goddess Diana) whose "vestal livery" (which is a uniform worn by virgins) is pale, sick, and green. 

"But soft! What light through yonder window breaks?

It is the east, and Juliet is the sun.

Arise, fair sun, and kill the envious moon,

Who is already sick and pale with grief,

That thou, her maid, art far more fair than she.

Be not her maid since she is envious.

Her vestal livery is but sick and green,

And none but fools do wear it. Cast it off!"

Tis not to me she speaks. Two of the fairest stars in all the heaven, Having some business, do entreat her eyes To twinkle in their spheres till they return.

How does Romeo compare Juliet to the sun, moon, and stars in Romeo and Juliet?

In act 2, scene 2, Romeo provides some of the most quoted lines in English literature, his words full of figurative language:

But soft, what light through yonder window breaks?
It is the east, and Juliet is the sun.
Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief
That thou, her maid, art far more fair than she. (II.ii.1-6)

And a few lines later, he continues,

The brightness of her cheek would shame those stars
As daylight doth a lamp; her eye in heaven
Would through the airy region stream so bright
That birds would sing and think it were not night. (II.ii.19-22)

In these lines, Romeo establishes the competing symbolism of light and darkness, which is a powerful theme running through the play. The sun is often symbolic of life and power. It provides its own light, not relying on the reflections of other sources to illuminate the world. By contrast, the moon is only useful at night, a time of darkness. It has no power in itself but only reflects the light of the sun.

In these lines, Romeo notes that Juliet is more like the sun than the moon. She radiates her own beauty and represents life for Romeo. Thus, Romeo believes that the moon itself is envious of Juliet, because her own beauty is more powerful than the moon's.

Romeo goes on to compare her to the stars, noting that Juliet's eyes are more beautiful than the stars in the heavens. Romeo considers that if Juliet's eyes were placed in the sky, the beautiful light they would generate would outshine every other star in the sky, making the birds think that night was day. Juliet thus has the ability to transform darkness (often representing evil) into light (or goodness), and Romeo stands in awe of her glorious beauty.

Romeo uses the sun, moon, and stars to convey his sense of awe and wonder for the beautiful Juliet. The passions she awakens within him are warm, like the sun, and outshine other, more pale loves by comparison.