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How US Patriot defences are reducing ‘unstoppable’ Russian missiles to shrapnel
(www.thetimes.co.uk)
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As I see it, there are 2 flaws with your thinking: First, even a wildly manoeuvring missile eventually has to point the nose at the target and dive in. It is vulnerable then at the very least. Second, manoeuvring alone does not render something immune to interception. For example, fighter aircraft manoeuvre like crazy and they get shot down handily.