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Explanation: Peace on earth shall be translated as мир на земле. No capitals and no variants. It is the state opposite to status belli. It is the Kingdom of the peace on earth we hear in the Sermon on the Mount (the Gospel of Jesus, Ch. 25), ... и на земле мир...(Luke 2:14); and many of us remember songs by George Harrison, U2, Keith Heffner, David Bowie, Modern Talking, and the Queen's "The thing we are all waiting for is peace on earth".
Why мир на земле only?
Why not мир на планете or мир на свете? Or миру - мир?
Because the Russian планета in this context is not just a heavenly body, but rather an aggregate of progressive forces; свет is the light, or the world, like the Old (New) World, свет is a part of dozens of Russian idioms with their specific usage. And миру - мир (peace to the world) is a euphemism, a slogan of the arms race epoch.
So, in terra pax hominibus bonae voluntatis - Мир на земле всем людям доброй воли.