Parallax in astronomy

Astronomers usually express distances in units of parsecs (parallax arcseconds); light-years are used in popular media.

The Hubble Space Telescope's Wide Field Camera 3 has the potential to provide a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to 5,000 parsecs (16,000 ly) for small numbers of stars.

For a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from statistical analysis of the proper motions relative to their radial velocities.

However, secular parallax introduces a higher level of uncertainty because the relative velocity of observed stars is an additional unknown.

[9] Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.

[a] The parsec unit is obtained by the use of parallax and trigonometry, and is defined as the distance at which 1 AU subtends an angle of one arcsecond[10] (⁠1/3600⁠ of a degree).

[12] The word parsec is a shortened form of a distance corresponding to a parallax of one second, coined by the British astronomer Herbert Hall Turner in 1913.

Partly for this reason, it is the unit preferred in astronomy and astrophysics, though in popular science texts and common usage the light-year remains prominent.

Annual parallax is normally measured by observing the position of a star at different times of the year as the Earth moves through its orbit.

The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age.

It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed entirely implausible: it was one of Tycho's principal objections to Copernican heliocentrism that for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn (then the most distant known planet) and the eighth sphere (the fixed stars).

[20] In 1989, the satellite Hipparcos was launched primarily for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold.

The European Space Agency's Gaia mission, launched in December 2013, can measure parallax angles to an accuracy of 10 microarcseconds, thus mapping nearby stars (and potentially planets) up to a distance of tens of thousands of light-years from Earth.

[23][24] The diurnal parallax has been used by John Flamsteed in 1672 to measure the distance to Mars at its opposition and through that to estimate the astronomical unit and the size of the Solar System.

[26] The Astronomical Almanac and similar publications tabulate the lunar horizontal parallax and/or the linear distance of the Moon from the Earth on a periodical e.g. daily basis for the convenience of astronomers (and of celestial navigators), and the study of how this coordinate varies with time forms part of lunar theory.

This yields for the Earth-Moon distance 60.27 Earth radii or 384,399 kilometres (238,854 mi) This procedure was first used by Aristarchus of Samos[29] and Hipparchus, and later found its way into the work of Ptolemy.

If the word parallax appeared to amaze them, they were told that it was the angle subtended by two straight lines running from both ends of the Earth's radius to the Moon.

If they had doubts about the perfection of this method, they were immediately shown that not only did this mean distance amount to a whole two hundred thirty-four thousand three hundred and forty-seven miles (94,330 leagues) but also that the astronomers were not in error by more than seventy miles (≈ 30 leagues).After Copernicus proposed his heliocentric system, with the Earth in revolution around the Sun, it was possible to build a model of the whole Solar System without scale.

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 expansion age[31] of the visible Universe.

Using correct geometry but inaccurate observational data, Aristarchus concluded that the Sun was slightly less than 20 times farther away than the Moon.

[29] Aristarchus pointed out that the Moon and Sun have nearly equal apparent angular sizes, and therefore their diameters must be in proportion to their distances from Earth.

[40] The value of the Astronomical Unit (roughly the Earth-Sun distance) obtained by this program was considered definitive until 1968, when radar and dynamical parallax methods started producing more precise measurements.

[41] The open stellar cluster Hyades 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 estimation of the distance to the cluster (151 light-years) and its member stars in much the same way as using annual parallax.

Then, event fields in spacetime can be deduced directly without intermediate models of light bending by massive bodies such as the one used in the PPN formalism for instance.