The Star of Bethlehem.

^{Matthew 2:9} When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was.

In order for the Nativity story to be true and for the wise men to follow a star hovering over a city, it would have been necessary to believe the earth was flat.

If the earth was flat. The wise men could just look up and move towards the star. When they were directly underneath the star, they would be in the right place. Also the star would need to move then stop and hover over Bethlehem. The star the Magi followed to find Jesus is a physical impossibility, a pious embellishment. This story could only be physically possible if the Earth was flat.

Let me explain... We know the earth is spherical and rotating on it's axis. If a star is visible on the horizon in the East at sunset, The Magi could start walking East towards the star... As the night wore on, the position of the star would rotate about the pole star. In the middle of the night, the star would not be in the east. it would be overhead or on a line north or south of the observer depending on the inclination of the star from the polar axis. Later on, just before dawn, the star would have rotated approximately' 180 around the polar axis and would now be setting on the Western Horizon. 

So, if the Magi were following the star, They would start walking East towards the star on the eastern horizon. They keep following the star as it rises, but as it passes overhead or through the north/south line of longitude, they would have to change direction and start walking West. If they walked at a constant speed through the night, by Dawn, they would be back where they started the previous evening.

Now... come on.... even a believing Christian can see that's a pretty useless way to navigate.

Here's a star field time lapse video to demonstrate the apparent passage of stars overhead. Note the absence of stationary stars. The only stationary star that could possibly exist would need to be above the rotational axis of the Earth at either the North or South rotational pole. 

For an object to remain stationary over a city, it would need to be in a geostationary orbit (not to be confused with a geosynchronous orbit) around the Earth. A geostationary orbit is directly above the equator, not Bethlehem.

Additionally, a "star", even a very small star can not orbit the Earth due to it's mass. OK, I know Christians believed the Sun revolved around the Earth until quite recently but thanks to People like Copernicus, Galileo and Newton we understand why this is not possible.

Could it have been a comet? 

No, Astronomers have tried many times to fit the known orbits of comets to the time period in question. There are no likely candidates. A comet would also be seen to rotate with the star field as the Earth rotated. 

Could it have been a planetary conjunction or a supernova. 

No. Both would rotate with the star field.

Perhaps it was a UFO.
Well surprisingly, this is more plausible than the possibility of an actual Star. However we would simply be substituting an absurd myth with an un-evidenced speculation. 

Besides, the Bible clearly states it was a star (ἀστήρ = astēr). 

Something other than a star would negate the intended divine sign. A UFO (Alien Spaceship) would totally destroy any divine explanation and promote The Bible to a Sci-Fi novel.

There is another small problem. The Magi could see a star in the East and walked towards the star until it hovered over Bethlehem. That means they must have been due west of Bethlehem. So unless they started off very close to Bethlehem (within 32 miles), they would have real problems because there is nothing but Mediterranean Sea for a thousand miles west of that point.

A rather obvious solution
The Magi were probably Persian religious leaders or senior figures representing the Persian religious leaders. The Persians were excellent astronomers and would not make such an obvious error. The Bible writers were ignorant religious zealots and would happily embellish the story of the birth of their prophet with mystical nonsense and pious embellishments to add import to their stories.

The Persians were also keen Astrologers and engaged in fortune telling, horoscopes, prophesy and the reading of signs in the constellations. This is a far more plausible explanation. They were not following a physical star in the sky, but were travelling looking for a king predicted in a horoscope or by the interpretation of a particular constellation configuration.

 This fits very well because at that time, the Astrological age of Aries was coming to an end.(The constellation where the sun passes through at the vernal equinox) . The new astrological age was the age of Pisces, This may even be from where Christianity gets it's fish symbol. The king of this age would be a water sign associated with fish. The Persians were out looking for such a king. Likewise, in a few hundred years we will enter age of Aquarius.... hence the song.

The evidence points to a mistake by the Christian story writers. The Persians were skilled astronomers and would not have made this mistake. The Jews were not a scientifically knowledgeable people, They explained everything in terms of their religion and were ruled by religious zealots who enforced this ignorant mentality. The early Christians didn't understand celestial mechanics, to them, a star hovering over a city would not seem impossible simply because they didn't know what a star was or that the earth was a rotating sphere. Any mention of a geostationary orbit would have just got blank looks.

It seems quite clear that they just made a mistake when they made the story up. The mistake is quite understandable when you consider Judeo/Christian knowledge of the universe at that time. It does however throw big questions onto the authenticity of the divine origins of the Bible. This is not simply a scribal error, it is an integral part of the story that simply is not true.

If this story is to be considered true, that a physical star literally remained static over Bethlehem, the only way this can be reconciled is by supernatural magic.

.... OR...... Perhaps it's just a nice story constructed to ensure the origins of the Christian figurehead complied with known prophesy.