The use of the parsec as a unit of distance follows naturally from Bessel's method, since distance in parsecs can be computed simply as the reciprocal of the parallax angle in arcseconds ( i.e. A parsec is defined as the length of the adjacent side of this right triangle in space when the parallax angle is 1 arcsecond. Therefore, given a measurement of the parallax angle, along with the rules of trigonometry, the distance from the sun to the star can be found. The length of the opposite side to the parallax angle is the distance from the Earth to the Sun (defined as 1 astronomical unit (AU)), and the length of the adjacent side gives the distance from the sun to the star. The star, the sun and the earth form the corners of an imaginary right triangle in space: the right angle is the corner at the sun, and the corner at the star is the parallax angle. Equivalently, it is the subtended angle, from that star's perspective, of the semi-major axis of Earth's orbit. The parallax of a star is taken to be half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. The first successful direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the distance of 61 Cygni. Then the distance to the star could be calculated using trigonometry. The difference in angle between the two measurements was known to be twice the parallax angle, which is formed by lines from the Sun and Earth to the star at the vertex. The distance between the two positions of the Earth for the measurements was known to be twice the distance between the Earth and the Sun. The first measurement was taken from the Earth on one side of the Sun, and the second was taken half a year later when the Earth was on the opposite side of the Sun. One of the oldest methods for astronomers to calculate the distance to a star was to record the difference in angle between two measurements of the position of the star in the sky. Using these two measurements, along with the rules of trigonometry, the length of the adjacent side (the parsec) can be found. The two dimensions on which this triangle is based are the angle (which is defined as 1 arcsecond), and the opposite side (which is defined as 1 astronomical unit, which is the distance from the Earth to the Sun). The parsec is equal to the length of the adjacent side of an imaginary right triangle in space.
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