My own personal favorite solution to these constraints is in Michael Molnar’s 2000 book, The Star of Bethlehem. He argues that there was a conjunction of all the planets and the new Moon, similar to that used by Augustus to support his own royal birth, occurring in the constellation Aries (which he argues is connected with Judea), in late March of 4 BC. Most appealing, this conjunction occurred when the planets rose with the Sun in the east – hence fitting the Matthew description, while explaining why only astrologers were aware of this event. They could calculate its occurrence, but no one, not even them, would actually see these planets: they’d be hidden in the glare of the rising Sun.
It’s all quite neat. And indeed it’s rather startling to realise that such an event really did occur in the sky about the time when Jesus may well have been born. If you have a planetarium program, you can look it up for yourself.
But was this really what Matthew was talking about?