A report on Proper motion and Double star

Relation between proper motion and velocity components of an object. A year ago the object was d units of distance from the Sun, and its light moved in a year by angle μ radian/s. If there has been no distortion by gravitational lensing or otherwise then μ = is the distance (usually expressed as annual velocity) transverse (tangential or perpendicular) to line of sight from the Sun. The angle is shaded light blue from the sun to the object's start point and its year later position as if it had no radial velocity. In this diagram the radial velocity happens to be one of the sun and object parting, so is positive.
Astronomers have mistakenly reported observations of a double star in place of J 900 and a faint star in the constellation of Gemini.
The celestial north and south poles are above/below CNP, CSP; the origin of all 24 hours of Right Ascension (the measure of absolute celestial east–west position), the March equinox (center of the sun's position then) at the J2000 epoch, is vector V. In red the diagram adds the components of proper motion across the celestial sphere. An ideal time to measure exactly such a small annual shift is at culmination. The culmination of the star is daily reached when the observer (and earth) passes as shown by the blue arrows "beneath" the star. The positive axes of the two components of its usually annually measured or published shift in proper motion are the exaggerated red arrows, note: the right arrows point to the east horizon. One red annotation is subtly shorter as the cosine of a star resting at 0° declination is 1, so such a star's east or west shift would not need to be multiplied by the cosine of its declination. The proper motion vector is μ, α = right ascension, δ = declination, θ = position angle (simply the 90° compliment of declination).
Artist's impression of the discs around the young stars HK Tauri A and B.
Barnard's Star, showing position every 5 years 1985–2005.
Proper motion of 61 Cygni in one year intervals.

If the relative motion of a pair determines a curved arc of an orbit, or if the relative motion is small compared to the common proper motion of both stars, it may be concluded that the pair is in mutual orbit as a binary star.

- Double star

Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so-called shared or common proper motion (or cpm.), suggesting they may be gravitationally attached or share similar motion in space.

- Proper motion
Relation between proper motion and velocity components of an object. A year ago the object was d units of distance from the Sun, and its light moved in a year by angle μ radian/s. If there has been no distortion by gravitational lensing or otherwise then μ = is the distance (usually expressed as annual velocity) transverse (tangential or perpendicular) to line of sight from the Sun. The angle is shaded light blue from the sun to the object's start point and its year later position as if it had no radial velocity. In this diagram the radial velocity happens to be one of the sun and object parting, so is positive.

3 related topics with Alpha

Overall

The constellation Ursa Major as it can be seen by the unaided eye.

Ursa Major

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Constellation in the northern sky, whose associated mythology likely dates back into prehistory.

Constellation in the northern sky, whose associated mythology likely dates back into prehistory.

The constellation Ursa Major as it can be seen by the unaided eye.
Ursa Major and Ursa Minor in relation to Polaris
Ursa Major shown on a carved stone, c.1700, Crail, Fife
H. A. Rey's alternative asterism for Ursa Major can be said to give it the longer head and neck of a polar bear, as seen in this photo, from the left side.
Ursa Major as depicted in Urania's Mirror, a set of constellation cards published in London c.1825.
Johannes Hevelius drew Ursa Major as if being viewed from outside the celestial sphere.
Starry Night Over the Rhone by Vincent van Gogh (1888)
Polaris and the Big Dipper on the flag of Alaska.
The Pinwheel Galaxy

Except for Dubhe and Alkaid, the stars of the Big Dipper all have proper motions heading toward a common point in Sagittarius.

ζ Ursae Majoris, Mizar, the second star in from the end of the handle of the Big Dipper, and the constellation's fourth-brightest star. Mizar, which means "girdle," forms a famous double star, with its optical companion Alcor (80 Ursae Majoris), the two of which were termed the "horse and rider" by the Arabs.

Alpha Centauri is the brightest object in the constellation of Centaurus (top left).

Alpha Centauri

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Gravitationally bound system of the closest stars and planets to the Solar System at 4.37 light-years from the Sun.

Gravitationally bound system of the closest stars and planets to the Solar System at 4.37 light-years from the Sun.

Alpha Centauri is the brightest object in the constellation of Centaurus (top left).
Apparent and true orbits of Alpha Centauri. The A component is held stationary, and the relative orbital motion of the B component is shown. The apparent orbit (thin ellipse) is the shape of the orbit as seen by an observer on Earth. The true orbit is the shape of the orbit viewed perpendicular to the plane of the orbital motion. According to the radial velocity versus time, the radial separation of A and B along the line of sight had reached a maximum in 2007, with B being further from Earth than A. The orbit is divided here into 80 points: each step refers to a timestep of approx. 0.99888 years or 364.84 days.
The relative sizes and colours of stars in the Alpha Centauri system, compared to the Sun
Relative positions of Sun, Alpha Centauri AB and Proxima Centauri. Grey dot is projection of Proxima Centauri, located at the same distance as Alpha Centauri AB.
The two bright stars at the lower right are Alpha (right) and Beta Centauri (left, above antenna). A line drawn through them points to the four bright stars of the Southern Cross, just to the right of the dome of the Danish 1.54 m telescope at La Silla Observatory in Chile.
Alpha Centauri AB taken in daylight by holding a Canon Powershot S100 in line with the eyepiece of a 110-mm refractor. The photo is one of the best frames of a video. The double star is clearly visible.
View of Alpha Centauri from the Digitized Sky Survey-2
Alpha Centauri A is of the same stellar type G2 as the Sun, while Alpha Centauri B is a K1-type star.
Closest stars to the Sun
Distances of the nearest stars from 20,000 years ago until 80,000 years in the future
Animation showing motion of Alpha Centauri through the sky. (The other stars are held fixed for didactic reasons) "Oggi" means today. "Anni" means years.
The discovery image of Alpha Centauri's candidate Neptunian planet, marked here as "C1".
Looking towards the sky around Orion from Alpha Centauri with Sirius near Betelgeuse, Procyon in Gemini, and the Sun in Cassiopeia generated by Celestia.
Simulated night-sky image with a "W" of stars from Cassiopeia connected by lines, and the Sun, labeled "Sol", as it would appear to the left of the "W"
The Very Large Telescope and Alpha Centauri

(Presently the ecliptic latitude is 43.5° South, but it has decreased by a fraction of a degree since Ptolemy's time due to proper motion.) In Ptolemy's time, Alpha Centauri was visible from Alexandria, Egypt, at 31° N, but, due to precession, its declination is now –60° 51′ South, and it can no longer be seen at that latitude.

For example, in about 6,200 AD, α Centauri's true motion will cause an extremely rare first-magnitude stellar conjunction with Beta Centauri, forming a brilliant optical double star in the southern sky.

Detail of Bayer's chart for Orion showing the belt stars and Orion Nebula region, with both Greek and Latin letter labels visible

Bayer designation

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Stellar designation in which a specific star is identified by a Greek or Latin letter followed by the genitive form of its parent constellation's Latin name.

Stellar designation in which a specific star is identified by a Greek or Latin letter followed by the genitive form of its parent constellation's Latin name.

Detail of Bayer's chart for Orion showing the belt stars and Orion Nebula region, with both Greek and Latin letter labels visible
Orion constellation map

The proper motion of Rho Aquilae, for example, carried it across the boundary into Delphinus in 1992.

Usually these are double stars (mostly optical doubles rather than true binary stars), but there are some exceptions such as the chain of stars π1, π2, π3, π4, π5 and π6 Orionis.