A report on Proper motionDouble star and Ursa Major

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 constellation Ursa Major as it can be seen by the unaided eye.
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.
Ursa Major and Ursa Minor in relation to Polaris
Barnard's Star, showing position every 5 years 1985–2005.
Ursa Major shown on a carved stone, c.1700, Crail, Fife
Proper motion of 61 Cygni in one year intervals.
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

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

Ursa Major or Crux, for example, look nearly the same now as they did hundreds of years ago.

- Proper motion

Mizar, in Ursa Major, was observed to be double by Benedetto Castelli and Galileo.

- 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

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

- Ursa Major

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.

- Ursa Major
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.

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