when we look at the night sky , we can see thousands of stars twinkling , but we cant actually say how far away those stars really are.It is one of the amazing as well as limiting factor that all the stars look like they are at same distance from earth as all other stars. In order to know observable physical properties of any star it is necessary to know the distance of that star from Earth. For example say I see a star moving through space , Am i seeing a star that is very close by moving slowly or a star that is far away and moving fast . Also I cannot determine the Luminosity , mass, orbit etc if I don’t know the distance of the star.
So the first question that comes to our mind is How do we measure this distance. It is quite difficult and challenging to measure the distance of stars, moon or galaxies because we cannot walk the distance to the star and measure it. So what do we do? Astronomers use the indirect method that is geometrical methods to measure stellar distances. All it takes to measure the distance to a star is knowledge of basic trigonometry and geometry.
Hold out your thumb at arms length so that it covers your view of the more distant object. Now close each eye in turn. The thumb seems to move relative to the distant object when a different eye is closed. This effect is called Parallax and can be used to measure the distance to nearby stars, that is your eye makes the base of the triangle and thumb plays role of foreground star and the distant object plays role of background distant stars, So it forms a triangle . Once we have the triangle if we know the inside angle and the length of opposite side , we can get length of other two sides.
We can measure this angle by observing the apparent change in stars position with respect to background stars by looking at it from one side of Earth’s orbit to another and this angle is known as parallax angle. It is found that distance to a star increases as the parallax angle decreases and found that distance in parsec= 1/(parallax angle). Thus if the parallax angle of the star is 0.001 sec then the star is 100 parsec away from Earth.
There are limitations of distance measurement using stellar parallax because of the effect of Earths atmosphere, It is similar to going inside swimming pool and trying to look out from the surface of water, all we can see is the distorted blur image. In similar way ground based telescopes limits our ability to measure small angles from the ground because we are looking at the stars through our atmosphere. So what we do instead is send our telescopes into space. These telescopes work pretty good but there are also certain limitations.So they use special purpose telescopes for this and the process is known as astrometry. Hipparcos was the first space experiment devoted to precision measurement of position of celestial objects on the sky. Currently there are lot of space telescopes which are used for astrometry.