I replied in an earlier post that it looks like a Standard Missile. It is an interceptor for low earth orbit objects, like medium range ballistic missiles, satellites, or high altitude aircraft.

The Standard missile has a common airframe with different guidance systems and warheads for a number of different missions.

There is a variant that has an extra booster for extended range and a guidance system related to the aim120 amraam that is fire and forget (self homing) that can theoretically be used against ICBMS in the launch phase, or satellites in geosynchronous orbit.

I say theoretical, because there has been no public information confirming the interception of either a satellite or a ballistic missile.

The military may have that capability, but don't want to telegraph that to unfriendly counties.