Parallax in astronomy

The most important fundamental <a href="/facts/Distance_measurement/rGJdrNrl">distance measurements</a> in <a href="/facts/Astronomy/0ArJVM1p">astronomy</a> come from trigonometric <a href="/facts/Parallax/Gu8W21LP">parallax</a>, as applied in the <a href="/facts/Stellar_parallax_method/ywI9UWEJ">stellar parallax method</a>. As the Earth orbits the Sun, the position of a nearby star will appear to shift slightly against the more distant background. This shift is the apex angle in an <a href="/facts/Isosceles_triangle/rvLe3yqK">isosceles triangle</a>, with 2 <a href="/facts/Astronomical_unit/gjsbu5xU">AU</a> (the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal-length legs (because of a very long distance from the Earth orbit to the observed star). The amount of shift is quite small, even for the nearest stars, measuring 1 <a href="/facts/Minute_and_second_of_arc/tybs6YGC">arcsecond</a> for an object at 1 parsec's distance (3.26 <a href="/facts/Light-year/IGc5NdQb">light-years</a>), and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of <a href="/facts/Parsecs/SwSsk57J">parsecs</a> (parallax arcseconds); light-years are used in popular media.
Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars which are near enough to have a parallax larger than a few times the <a href="/facts/Accuracy_and_precision/JQ47xXDq">precision</a> of the measurement. In the 1990s, for example, the <a href="/facts/Hipparcos/Th2HW7VN">Hipparcos</a> mission obtained parallaxes for over a hundred thousand stars with a precision of about a <a href="/facts/Minute_of_arc/tybs6YGC">milliarcsecond</a>, providing useful distances for stars out to a few hundred parsecs. The <a href="/facts/Hubble_Space_Telescope/NQeIf0vw">Hubble Space Telescope</a>'s <a href="/facts/Wide_Field_Camera_3/XPTKFGBx">Wide Field Camera 3</a> 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. The <a href="/facts/Gaia_(spacecraft)/dlvcdkoN">Gaia</a> space mission provided similarly accurate distances to most stars brighter than 15th <a href="/facts/Magnitude_(astronomy)/f4FbscJu">magnitude</a>. 
Distances can be measured within 10% as far as the <a href="/facts/Galactic_Center/TI4MwWwM">Galactic Center</a>, about 30,000 light years away. Stars have a velocity relative to the Sun that causes <a href="/facts/Proper_motion/ECByRQ8c">proper motion</a> (transverse across the sky) and <a href="/facts/Radial_velocity/B3NmbVLP">radial velocity</a> (motion toward or away from the Sun). The former is determined by plotting the changing position of the stars over many years, while the latter comes from measuring the <a href="/facts/Doppler_shift/bzrK1BKf">Doppler shift</a> of the star's spectrum caused by motion along the line of sight. For a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from <a href="/facts/Statistical_analysis/DNPsKGYU">statistical analysis</a> of the proper motions relative to their radial velocities. This <a href="/facts/Statistical_parallax/ywI9UWEJ">statistical parallax</a> method is useful for measuring the distances of bright stars beyond 50 parsecs and giant <a href="/facts/Variable_star/Ac8mp2gy">variable stars</a>, including <a href="/facts/Cepheid_variable/WQXaAFmW">Cepheids</a> and the <a href="/facts/RR_Lyrae_variable/vjoHuKUe">RR Lyrae variables</a>.

The motion of the Sun through space provides a longer baseline of the parallax triangle that will increase the accuracy of parallax measurements, known as <a href="/facts/Stellar_parallax/ywI9UWEJ">secular parallax</a>. For stars in the <a href="/facts/Milky_Way/ulF6lccN">Milky Way</a> disk, this corresponds to a mean baseline of 4 <a href="/facts/Astronomical_unit/gjsbu5xU">AU</a> per year, while for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of observed stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the uncertainty is inversely proportional to the <a href="/facts/Square_root/AfrzfBdQ">square root</a> of the sample size.
<a href="/facts/Moving_cluster_parallax/ogK75dbS">Moving cluster parallax</a> is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster. Only <a href="/facts/Open_cluster/UodlJqcx">open clusters</a> are near enough for this technique to be useful. In particular the distance obtained for the <a href="/facts/Hyades_(star_cluster)/XmNqJhqA">Hyades</a> has historically been an important step in the distance ladder.
Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a <a href="/facts/Supernova_remnant/tYboe2n4">supernova remnant</a> or <a href="/facts/Planetary_nebula/5Vy84cPq">planetary nebula</a>, can be observed over time, then an expansion parallax distance to that cloud can be estimated. Those measurements however suffer from uncertainties in the deviation of the object from sphericity. <a href="/facts/Binary_star/TYlDe1bD">Binary stars</a> which are both <a href="/facts/Binary_star/TYlDe1bD">visual</a> and <a href="/facts/Binary_star/TYlDe1bD">spectroscopic</a> binaries also can have their distance estimated by similar means, and do not suffer from the above geometric uncertainty. The common characteristic to these methods is that a measurement of angular motion is combined with a measurement of the absolute <a href="/facts/Velocity/Q3o1LVDe">velocity</a> (usually obtained via the <a href="/facts/Doppler_effect/bzrK1BKf">Doppler effect</a>). The distance estimate comes from computing how far the object must be to make its observed absolute velocity appear with the observed angular motion.
Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio <a href="/facts/Interferometry/X3E1SsQT">interferometers</a> which can measure very small angular motions. These combine to provide fundamental distance estimates to supernovae in other galaxies. Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.

Parallax in astronomy open-in-new

Parallax in astronomy