Yes - it's fine
No - it's crazy
Some ships have that, most have the older SM-2 which was designed for shooting down aircraft. They both work fine with Aegis. The SM-2 is just a plain old surface to air missile like any other. It is 30 years old now. It comes from way before Aegis was invented. Russia most definitely has surface to air missiles more sophisticated than that now. Probably a dozen countries in the world sell surface to air missiles that sophisticated or better and virtually every country owns surface to air missiles that sophisticated or better.
What Russia is after here isn't the missile, it's the Aegis system that pinpoints the incoming missile and whatnot. The missiles are nothing special or secret. A bunch of countries have Aegis too: the Netherlands, South Korea, Japan, the UK, etc. But that is the more unique technology and Russia doesn't have it or any equivalent currently. But that tech is purely defensive, so it's safe to use it as a bargaining chip.
But, yeah, you raise a good point. One of the reasons Obama wants to share anti-missile tech with Russia is to defuse concerns that the US might be deploying anti-missile tech because once it has a missile shield up it can start threatening the world with it's nukes without worrying about retaliation. That's a silly fear. The anti-missile systems are nowhere near reliable enough to do anything like that and ICBMs aren't the only way to deliver a nuke. But, whatever, if it makes Russia less jittery about it, that's a big plus.
After the two bombs were dropped over japan, president truman informed Stalin of their research into nuclear technology (up to that point only the US and Britain were involved in its development). Stalin was already aware of their progress because he had spies who kept him informed throughout the entire process... as a show of cooperation truman gave stalin the tech publicly since he already had it. Kind of a PR campaign but still. Thats all available on wikipedia.Er what? Where did you hear that? I've never heard anything like that. Do you have a source?
A normal surface to air missile does not have the capability to intercept an ICBMNo, no, no... The clever innovation of Aegis is the ability to pinpoint the incoming missiles. Surface to air missiles have existed for decades. That's nothing new. We just use our normal surface to air missiles with it, not any specialized missile.
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What a normal surface to air missile does not have the capability to do by itself is pinpoint the incoming ICBM and calculate exactly where it will be in X seconds precisely enough. Any surface to air missile can be told "go to these exact coordinates and blow up", it's getting those coordinates right that is the tough part. That's what Aegis does.
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And check out the link in OP again. Obama is NOT planning to give up Aegis, he's planning on sharing specs (not the specific technology) of the SM-3. The Russians may want Aegis tech, but that's not part of the deal.The second generation of Standard missile, the Standard Missile 2, was developed for the Aegis combat system,