Can I hold a Hammock up with Star Pickets?
The thing about hammocks is that they create tremendous sideways forces. With the following configuration, you balance them well, but still create large tensions in the cables and a very large compressive load on the upright:



Plugging in 150 pounds for mg, 4 ft for the post height h, 3 ft for d and w, and 20° for theta, you end up with a hammock tension (T1) of 263 lbs, a guy line tension (T2) of 240 lbs, and a pole compressive load (Fa) of 420 lbs.

Changing the mg, h, w, d, and theta variables will result in new values for each of these forces. For example, increasing w in relation to h will result in a lower compressive load on the pole, and a lower tension in the guy lines. For all other variables constant, changing w to 6 ft results in T2 = 161 lbs, and Fa = 255 lbs.

For best results, you want to minimize the bending moment of the posts, since that's what tends to pull them out of the ground. So attach your guy lines at the same spot as the hammock on the upright posts, and then attach the other end as close to the ground as possible. You'll probably just need some very beefy stakes, rather than T-posts for the end of the guy lines attached to the ground.

@Ratchet Freak's suggestion of angling the base of the poles in toward the center will increase compressive load on the poles an minimize tension in the guy lines, since Fa will be pointing up and away instead of just up. However, you run the risk of adding buckling and twisting as a problem with that solution.

Might I suggest using a hammock stand instead? They're not too much more expensive, and they'll do a much better job remaining stable.