> The strength plays no part at all when it impacts. At the energy involved it might as well be a noodle. It just needs to handle the heat and resistance of reentry.

So why tungsten, rather than a tungsten skin on a lead bar?

when it impacts. You want your missile to reach the ground in one part, and you want it to have low air resistance, so that most potential energy goes into the kinetic energy at impact, rather than say, heating or melting your projectile or the air.

Also, the density of tungsten is about 75% larger than that of lead. Iridium and osmium are about 15% heavier still, at about twice the density of lead (osmium is heavier, but by only 0.12%)

The shape matters because you want to maximize the impact speed which means minimizing resistance of reentry. A simple rod will not keep its orientation while falling down, it needs either fins or a different shape.

You actually have to decelerate rapidly, so you warheads fall at a steep angle. Gliding reentry is inaccurate

At which point there’s no reason putting this thing in orbit instead of launching it as a regular ballistic missile.

To hit one target on the ground you are going to need thousands of rods in orbit to ensure that one is available to use on the target. This is necessary because things in orbit will only be able to de-orbit on top of things that are close to their orbital plane.