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Are the stars in constellation located in a plane or they are in different distances from each other and when we observe them from the Earth we think they are all in a plane?

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Constellations and asterisms are generally not proximate in space, but rather happen to be nearby only when viewed from Earth. From Wikipedia's article on asterisms:

Like constellations, asterisms are in most cases composed of stars which, while they are visible in the same general direction, are not physically related, often being at significantly different distances from Earth.

A recognizable example of this would be the brightest star in Taurus, Aldebaran. Aldebaran appears in the V-shaped bull's head, mostly formed by stars in the Hyades star cluster. However, while those stars are actually close to one another, Aldebaran is less than half as far away.

Since the star is located (by chance) in the line of sight between the Earth and the Hyades, it has the appearance of being the brightest member of the more scattered Hyades open star cluster that makes up the bull's-head-shaped asterism; however, the star cluster is actually more than twice as far away, at about 150 light years.

Similarly, the stars of Orion's belt are actually hugely separated in space.

In addition, it's worth noting that the stars have different velocities across the sky, so the constellations will look increasingly different over long periods of time. Here is one prediction for 50,000 years time, and the effect will get proportionately larger as time goes on.

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Only very rare instances would get close to such stars being on a plane, if any can be found.

A nice graphic image showing how the Big Dipper stars appear on an imaginary plane as viewed from Earth combined with a side-view showing approximate distances can be seen at this earthsky.org page.

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Like the above: they can be significantly separated by space.

One way to visualize this is to turn on constellations in Celestia then travel to a different star. The constellation outlines can shift significantly.

Celestia is an open source visualization thing, it is available at: http://www.shatters.net/celestia/

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The stars are not in the same plane and move in different directions. See this youtube video.

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Star are far away from each other : many light years separate them but they appear to be in the same plane because from Earth, many light years away, we see them as if they are besides each other.

For example, take a person standing at 80m in front of you and another man 100m. You see that both are standing besides each other and the one which is the farthest from you appears to be smaller than one nearby. This same logic applies for the stars.

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