Proper Motion of a Star GM

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School

Austin Peay State University *

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Course

1020

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Physics

Date

Jan 9, 2024

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pdf

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Uploaded by DeaconHeatMongoose7

Page 1 of 7 Group Members: Gabrielle Miller Proper Motion of a Star In this exercise you will measure the proper motion of Barnard's Star and use it, with a given parallax and radial velocity, to determine the space motion of the star. Background information In 1718 Edmund Halley had noted that some stars were not fixed, but appeared to move in the sky relative to other stars. Arctures in Bodtes and Sirius in Canis Major were the first stars detected by Halley to have proper motion. Proper motion is the angular change in position of a star across our line of sight, measured in arc seconds per year, and symbolized with the Greek letter “mu” p. Proper motion is generally measured by taking photographs several years apart and measuring the movement of the image of a star with respect to more distant background stars over that time period. Usually decades must elapse between successive photographs before a reliable measurement can be made. The star with the largest proper motion was discovered by E. E. Barnard in 1916 at Yerkes Observatory. This star, now called Barnard’'s Star, is a 9.5 magnitude star located in the constellation Ophiuchus. Its proper motion is so much larger than that of any other star that it is considered to be virtually a “runaway” star. Even so, the angular velocity is small enough that measurements must be made from photographs taken many years apart. The negatives of Barnard's Star provided in this lab were taken in 1924 and 1951 respectively. Since proper motion is an angular velocity, we also need to know the star’'s distance to find its real velocity across our line of sight, called its tangential velocity (v;). Two stars with the same proper motions can have vastly different tangential velocities, as shown in the example in figure below. v, - 988 kin/sec Observer v. =47 4km/sec ~y 3ec of are p gt L] | = 3 5pe | 10 pe This exercise is adapted from one developed by D. Scott Birney at Wellesley College

Page 2 of 7 Since stellar parallaxes are usually tabulated rather than stellar distances, tangential velocity can be calculated from the following equation 4.75 x v, = T,U Equation 1 where v is the tangential velocity in km/sec M is the proper motion in seconds of arc/year p is the parallax in seconds of arc Radial velocity (v;) describes the motion of a star along our line of sight. A negative radial velocity indicates motion toward us, and positive motion away. We still need one more piece of information to know the velocity and direction a star moves in space, called its space motion or space velocity (v). The radial velocity (vr) is added vectorially to the tangential velocity (v (at right angles) to give us the total space velocity (v). The magnitude of special velocity (v) can be calculated using the Pythagorean Theorem. — 2 2 - V =4y, 1Y, Equation 2 NG i v T i Ve Observer i O e ————————— e » r Space motion allows us to study the dynamics and interactions of groups of stars, and to see how the arrangement of our local group of stars is changing over the centuries. This exercise is adapted from one developed by D. Scott Birney at Wellesley College

Page 3 of 7 PROPER MOTION of BARNARD'’S STAR ‘ﬂ SEPT. 18, 1924 .. 4 2 - B o 2 s, SEPT. 4, 1951 pa ol e g B This exercise is adapted from one developed by D. Scott Birney at Wellesley College

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