The Financial Times- Asia had a story on a new anti-ship ballistic missile system. The system would presumably be big, and fast.
Chinese missile shifts power in Pacific by Kathrin Hille in Beijing which ended with the following:
China also needs to deploy more satellites to ensure seamless tracking of a moving target at sea. But defence experts warn that the weapon would immediately be a threat to US carriers because China could make up for a lack in accuracy by launching larger numbers of missiles [emphasis added].Well no actually, the ocean is large, very large, oversized Mens-Only Outlet XXX-large.
As noted here, in broken English, ballistic missiles are fast, but have limited in-flight targeting. A very fast Mach 10 missile will reach 2,000km straight-line in just 11 minutes. Taking into account the (actual) parabolic trajectory of the missle, would lead to an in-flight time of 25 minutes to reach the 4,000km range. In that time frame the 55 km/hr carrier task force will move 23 kilometers. This is probably not not fast enough to make the missile lose sight of the carrier. As the article (I think) notes in a cluster of ten missiles, eight of them would still be on target.
But that requires you know the exact starting of point, of the carrier. As you become less certain, the distance your missiles need to cover does not double, but squares. So if you only knew where the carrier was (via sonar, rpv scouting, etc) within 30 miles (pretty good actually) your carrier coverage area would go from 5,215 km sq, to 29,825 km sq (23 pi r sq versus 55 pi r sq). So maybe only two of the missiles at the edge of the pattern catch the carrier, and that is number the task force might be able to shoot down.
Aircraft carriers are very vulnerable to both modern underwater threats, and missiles, but there is still no magic bullet to knocking them out. The Chinese can certainly make operations off their coast very dangerous, but it won't be free. They will either have to make these land based missiles mobile and hope they can get them close to where they are needed, or they will need a lot of them to be sure all areas are covered.
If they are not able to improve their ship detection systems to where they can be reliably used, they would be better off only making a light investment in the technology and use it in combination with the other systems they have in place.