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Parallax is the change of angular position of two stationary points relative to each other as seen by an observer, due to the motion of said observer. By observing parallax, measuring angles, and using geometry; one can determine the distance to various objects. When this is in reference to stars, the effect is known as stellar parallax. The first measurements of star parallax were made by Bessel, in 1838.
The two points in question will be different distances from the observer and the illusion of parallax is caused by the fact that light follows straight lines. When the observer views the nearer point, the line of his vision toward that point is at a given angle within the full arc of his vision. For example, let us say that the view straight ahead is zero degrees, and one point, nearer the observer, is at minus five degrees while a point which is farther away is at minus two degrees. The apparent angular distance between the points is a subjective three degrees to the viewer. If the viewer moves ten meters to his right, the angular direction to the nearer object, as it is on a shorter radius, will change more than the angular direction to the farther object. So, for instance, when the angular direction to the nearer object is at minus ten degrees, the father object may only have moved to minus three degrees. Now the subjective angular difference in position is seven degrees. The objects appear to have moved relative to each other.
On a macro scale, this effect is responsible for the fact that, in a moving car, one can look at distant mountains and see them seem to move (retard) in position beneath a seemingly motionless moon. The moon is at such a distance that the subjective angular change in position relative to an earth-bound observer is extremely slight, even as many miles are covered. The mountains, much closer, exhibit a much greater apparent change in angular position.
Put differently and somewhat more generally, distant objects seem to move with the car. This can be explained as follows: all objects move backward relative to the car, and for nearby objects the speed of change in direction is what the observer considers the normal consequence of his own movement; however, for distant objects the backward change in direction is slow and much less obvious than the forward change in direction relative to nearby objects. It seems as if distant objects move parallel to the car with the same speed or a little slower.
After Johannes Kepler discovered his Third Law, it was possible to build a scale model of the whole solar system, but without the scale. To fix the scale, it suffices to measure one distance within the solar system, e.g., the mean distance from the Earth to the Sun or astronomical unit (AU). When done by triangulation, this is referred to as the solar parallax, the difference in position of the Sun as seen from the Earth's centre and a point one Earth radius away, i.e., the angle subtended at the Sun by the Earth mean radius. Knowing the solar parallax and the mean Earth radius allows one to calculate the AU, the first, small step on the long road of establishing the size -- and thus the minimum age -- of the Universe.
It was proposed by Edmund Halley in 1716, that the transit of Venus over the solar disc be used to derive the solar parallax. And so it was done in 1761 and 1769. There is the famous story of the French astronomer Guillaume le Gentil, who travelled to India to observe the 1761 event, but didn't reach his destination in time due to war. He stayed on for the 1769 event, but then there was cloud before the Sun...
The use of Venus transits was less successful than had been hoped. Much later, the solar system was 'scaled' using radar reflections from asteroids passing close to Earth (Eros, Icarus). Today, use of spacecraft telemetry links has solved this old problem completely.
On an interstellar scale, parallax created by the different orbital positions of the Earth causes the stars to seem to move.
The annual parallax is defined as the difference in position of a star as seen from the Earth and Sun, i.e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. Given two points on opposite ends of the orbit, the parallax is half the maximum parallactic shift evident from the star viewed from the two points. The parsec is the distance for which the annual parallax is 1 arcsecond and hence the maximum parallactic shift is 2 arcsecond. A parsec equals 3.26 light years. The nearest star, α Centauri, is at 4.3 light years or 1.33 parsecs, or 25 200 000 000 000 miles.
Measurements in parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest stars. This method was first used by Friedrich Wilhelm Bessel in 1838 when he measured the distance to 61 Cygni, and it remains the standard for calibrating other measurement methods (after the size of the orbit of the earth is measured by radar reflection on other planets). In 1989, a satellite called "Hipparcos" was launched with the main
purpose of obtaining parallaxes and proper motions of nearby stars, increasing the reach of the method ten-fold.
The open stellar cluster 'Hyades' (Rain Stars) in Taurus extends over such a large part of the sky, 20 degrees, that the proper motions as derived from astrometry appear to converge with some precision to a perspective point north of Orion. Combining the observed apparent (angular) proper motion in seconds of arc with the also observed true (absolute) receding motion as witnessed by the Doppler redshift of the stellar spectral lines, allows us to estimate the distance of the cluster and its member stars in much the same way as using annual parallax.
Dynamic parallax has sometimes also been used to determine the distance to a supernova, when the optical wave front of the outburst was seen to propagate through the surrounding dust clouds at an apparent angular velocity, when we know its true propagation velocity to be that of light.
All these various astronomical parallax methods allow us to establish the first rungs on the cosmic scale ladder, out to a few hundred light years. Beyond that, other methods must be taken into use: "spectroscopic parallaxes" -- not really parallaxes at all --, Cepheids, supernova brightnesses, spherical cluster sizes and brightnesses, complete galaxy brightnesses etc. These are all much more uncertain as they are not based on simple geometry. Yet, parallaxes are the basis of everything, as they allow the calibration of these more uncertain methods in the Solar neighbourhood.
On a micro scale, the thickness of a ruler can create parallax in fine measurements. One is always cautioned in science classes to "avoid parallax." By this it is meant that one should always take measurements with one's eye on a line directly perpendicular to the ruler, so that the thickness of the ruler does not create error in positioning for fine measurements. A similar error can occur when reading the position of a pointer against a scale in an instrument such as a galvanometer. To help the user to avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user positions his eye so that the pointer obscures its own reflection. This guarantees that the user's line of sight is perpendicular to the mirror and therefore to the scale.Solar parallax
Stellar parallax
Dynamic or moving-cluster parallax
The scale of the Universe
Micro scale
