I assume the Russian missile is a nuclear powered jet engine, assuming it exists, while for space you need a nuclear powered rocket engine. Different tech. The US tested a nuclear rocket engine on the ground in 1967 and it looked well cool. I'd vote for giving it's development a go. https://en.wikipedia.org/wiki/Nuclear_thermal_rocket#/media/...

The US also built nuclear powered jet engines in the 60s but found for piloted aircraft you'd either need tons of lead shielding or kill the pilots. It's rumoured the Russians actually flew one and killed said pilots.