Parallax method....?

Parallax is the displacement or the change in the apparent position of the object when viewed from two different points of view. The two points of view have their own line of sights and parallax is measured as half of the angle between the two lines of sights. When you are traveling in a vehicle and you look around as you are moving, you will see that objects in the distances appear to move more slowly than the objects closer to you. This is the effect of parallax. Nearby objects have a larger parallax than the distant objects, so the parallax can be used to determine distances. The phenomenon of parallax, when combined with triangulation, will yield the location of the object with considerable accuracy. Astronomers regularly use the parallax method to measure the distances of the closer stars. Distance Measurement by Parallax Distance measurement by parallax is a special application of the principle of triangulation. From triangulation, we knew that a triangle can be described completely if two angles and sides are known.  In the image shown above, the distance of a distant star is being calculated. The star being closer to earth than the far away starts exhibits a finite parallax value. This way, we can obtain the value of the parallax angle by viewing the star from two known points on Earth forming the baseline of the triangle. Let’s define the parallax half-angle from two distinct points on Earth as ‘p’. Here the maximum value of‘ ‘d’ is the radius of Earth and the distance of the star can be assumed to be only slightly farther than the sun. Here the value of the distance from the sun is many magnitudes smaller than the radius of the earth due to which the value of the parallax angle we get is extremely small. Too small to be even detected. This is the fact behind, why the great Astronomer Cassini and his colleagues were unsuccessful in finding the parallax for even a single star. This was considered by his detractors to be proof that heliocentricity was wrong. Cassini’s theory was correct but the least count of the equipment used then wasn’t small enough. Application Assuming the angle ‘p’ is small, the distance to the object measured in parsecs (in terms of speed of light) is equal to the reciprocal of the parallax angle measured in arcseconds. D(parsec)=1p(arcsec) In order to overcome the problem of the small ratios, star parallax is most often measured using annual parallax which is defined as the difference in the position of a star as seen from the earth and sun. Instead of taking the fixed baseline as the Earth’s radius, the fixed baseline is taken as the radius of Earth’s revolution around Earth which increases the size of the baseline therefore the top angle making it easier to measure.  Measurement of stellar distances and the parallax angle in terms of distancesUnfortunately, the ground-based telescopes can only measure parallax reliably for stars that are within a few hundred light-years from us. Telescopes above the atmosphere such as the Hubble Telescope can measure smaller parallax shifts and thus larger distance, but even in that case the most distant objects for which distance can be determined by parallax of a few thousand light-years away. To measure further distances, we use other methods which you will learn in the coming classes.