Tatjana has revealed why our NBS was so secret in those days. The RAF was at pains not to let the Russians know that we were using equipment salvaged from WW2 Lancasters, mated with a few dustbins full of cog-wheels (mechanical computers) to navigate to the targets and drop a big bomb. Meanwhile the Russians were at great pains not to let us know that they were using equipment they had built from copies of our own drawings, but manufactured to lower tolerances by conscripted farmers wives. Such was the mad, mad world of mutually assured destruction.
At Nagasaki, Fat Boy detonated over two miles away from the intended ground zero, so getting within a mile with a Yellow Sun would probably have been good enough.