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I was recently looking at the specs of the Antares launch vehicle and I was surprised to find out that they were using a solid fueled motor as their upper stage.
I've always learned that in the upper stage of an LV the ISP is the most important parameter to design for, but solid fueled motors aren't know for their high ISP numbers.
So my question is, why did they do it in the case of the Antares vehicle?
Solid fuel does make sense for a top stage, a so-called kick stage, the most notable example being the Star family. A kick stage has only smaller or similar gross mass as the payload it propels, which means that the weight savings from a high-ISP fuel are limited – you're in either case only getting a small bit of extra Δv. In other words, you're within in the nearly-linear range of the Tsiolkovsky equation. By “nearly linear” I'm referring to $e^x \approx 1+x$ for sufficiently small $x$. The infamous “tyranny of the rocket equation” only strikes when $x$ approaches 1 or larger, in this case meaning $\Delta v\gtrsim v_0$.
Thus for a kick stage, the ISP is not quite as important anymore. You might still theoretically get a better payload/fuel ratio with a good liquid stage, but only linearly better, so the simplicity of a solid design can make up for its ISP disadvantage.
This logic does however not really apply to the Antares, with (if I read the numbers correctly) the Castor 30 having a gross mass 26 t to get 6 t to LEO. So the real reason is likely corporate politics rather than engineering: as CBHacking pointed out in the comments, Orbital ATK is a company focused on solids, so they can leverage a lot of expertise there that made it more economic for them to have a solid second stage.
Sure enough, the Antares often uses also a Star kick stage. Curiously enough they also have a liquid kick stage (BTS) available – that's really a strange combination then, solid only in the second stage where it makes least sense in principle.
