![]() The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, where the other leg is 1 AU long. Stellar parallax measures are given in the tiny units of arcseconds, or even in thousandths of arcseconds (milliarcseconds). The more distant an object is, the smaller its parallax. So that d = E-Sun / tan(½θ), where E-Sun is 1 AU. The distance d from the Sun to S now follows from simple trigonometry: Since line E'-v' is a transversal in the same (approximately Euclidean) plane as parallel lines E-v and E'-v, it follows that the corresponding angles of intersection of these parallel lines with this transversal are congruent: the angle θ between lines of sight E-v and E'-v' is equal to the angle θ between E'-v and E'-v', which is the angle θ between observed positions of S in relation to its apparently unmoving stellar surroundings. Thus a line of sight from Earth's first position E to vertex v will be essentially the same as a line of sight from the Earth's second position E' to the same vertex v, and will therefore run parallel to it - impossible to depict convincingly in an image of limited size: ![]() This means that the distance of the movement of the Earth compared to the distance to these infinitely far away stars is, within the accuracy of the measurement, 0. The vertices v and v' of the elliptical projection of the path of S are projections of positions of Earth E and E’ such that a line E-E’ intersects the line Sun-S at a right angle the triangle created by points E, E’ and S is an isosceles triangle with the line Sun-S as its symmetry axis.Īny stars that did not move between observations are, for the purpose of the accuracy of the measurement, infinitely far away. The plane of Earth’s orbit is at an angle to a line from the Sun through S. The center of the ellipse corresponds to the point where S would be seen from the Sun: The farther S is removed from Earth’s orbital axis, the greater the eccentricity of the path of S. The observed path is an ellipse: the projection of Earth’s orbit around the Sun through S onto the distant background of non-moving stars. Stars that did not seem to move in relation to each other are used as reference points to determine the path of S. Throughout the year the position of a star S is noted in relation to other stars in its apparent neighborhood:
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