Matthew 2:9 Moreover having heard the King, they went away; and behold, the star which they saw [*while] in the East went before them until having come, it stood over where was the Child.

[*The Magi are not saying that they saw this significant star in an astrological "eastern" position, nor that they saw the star in the "East" relative to where they were when observing it, but that they saw the star accompanying the birth of Jesus while they themselves were located in the "East" relative to Jerusalem.]

I think it is reasonable to assume that in the context of the nativity the general form of the "star" is some form of a floating or flying object that is composed of or radiates light.  This star is not described as making any sound.   It is reasonable to assume that there is not a known modern-day meteorological equivalent to this "star".  It is not "swamp gas", as it were.

In fact, it is not described as having a gaseous field around it - as new stars do - or this quandry would be more easily explained.  It could be readily assumed and accepted that while stationary near Jerusalem it gave off a gas cloud that made it appear larger - and more easily seen from afar - and while moving the gas cloud was dispersed.

If a star without a gas field were to indicate by proximity the location of a birthplace, it must by some reasonable means create association with an area that is approximately "personal".  

The star must by one of at least two means do this.  Either the star itself moved close enough to the proper hut, cave, or barn; or it radiated light at the location indicated.

The star is not described as radiating beams of light in particular directions.  

It is described as moving relative to the Magi and the points of interest.

Bethlehem is a relatively small place - especially compared to a celestial "star". A star similar to the Sun could not indicate by means of proximity any particular continent to the perception of observers, much less a particular place of birth. The "star" is comparatively small, and is itself the expression of direction. 

The parameters of the size of the star are seemingly presumable. It must be small enough to indicate relative proximity of the birthplace, and either large enough or close enough to be observable by the Magi.  For greater distances, a larger span between the Magi and the star is reasonable - and possibly necessary. If the star were not at sufficient elevation, the curvature of the Earth could block it from the Magi's view. 

At an international scale, a star could indicate sufficient directions by being in a general area between the Magi and Judah. For lesser distances, such as a metropolitan scale, that direction would still remain reasonably general, but could account for the best means of travel (accounting for terrain and other physical realities) between cities, villages, and other municipalities. Within the constraints of an actual village, such as Bethlehem in the year 4BCE, a star as a guidance tool would need to be personably small. This star as described indicates the appropriate entrance - whether it be of a house, barn, or cave - to the place of birth, and moves with recognizable relativity to the Magi. The Magi travel from "the East" and are anticipating and observing stars to signal the birth of a king of the Jews. To my sense of appropriate cultural relativity, this must include at least all of Mesopotamia, if not all of what was then considered the "Orient". All of the major Mesopotamian cultures celebrated royalty and deification through the symbolism of "stars" (and also what we would now consider "planets"). 

It seems necessary that the star of the Christ must be visible from at least the birthplace of the cultures it was intimately associated with. Jesus was considered to be a High Priest in the Order Of King Zedek. King Zedek was the first king of Jerusalem (Jeru-/YHWH's- -Salem/-Peace), and a contemporary of Abraham.This must include at least what is now NorthEastern Turkey (which contains the "Garden Of Eden" - the place of creation of and for YHWH's people), if not also what is now Southern Iraq (which contains Ur, the birthplace of Abraham, who purchased the Foundation Stone as a threshing floor, and was personally covenanted with Elohim). 

The question then becomes - assuming that the star does not change its size or brightness as required - how big and bright must a star near Jerusalem be to be observable from those relatively similar distances? The light that is described may be assumed to be "starlight". It is not a laser-beam, and it is not described as having any particular focus of radiation. 

The Bat Signal is a spotlight (being focussed) of a reasonable size (perhaps as much as ~10' diameter) to give relative indication of an entranceway - but could not be seen in Ur from Jerusalem. The light would diffuse in the atmosphere long before reaching the Chaldees, and the spotlight would be indecipherable.

Could an orb the size of the Epcot Center indicate a very particular "room" from the perspective of human observers? Spaceship Earth is 165 feet in diameter, and has a very particular "bottom" from a human perspective.

The Epcot Center (Spaceship Earth) is observable to the eye at a distance of only approximately 18kms.

The distance between Ur and Jerusalem is ~1000km, and the distance between Göbelbakan, Türkiye and Jerusalem is ~1200km.

I don't math real good... but it seems that the star would have to be about 61 times the size of Spaceship Earth.  That is approximately 1000 feet (or ~300 meters).

The Eiffel Tower is slightly more than 300 meters high.

It may be of interest to some, that the parameters wherein a star could fulfill the descriptions given of it in the Gospel Of Matthew are very slim but only just possible.   Those of faith are more likely to assume these conditions to be proof of a miraculous nature, and those without faith more likely to reject the assertion wholecloth.

Here is the approximate scale of a star that is observable across Mesopotamia, but small enough to indicate by its presence the location of a particular dwelling:

https://i.imgur.com/pCJyK5h.jpg

Matthew 2:10 Having seen moreover the star, they rejoiced with joy great exceedingly.