## key Concepts

distances in the world are vital to know, butdifficult to measure. The distance to a nearby star deserve to be uncovered from that PARALLAX. Top top average, a nearby star will have a larger ideal MOTIONthan a remote star. (1a) ranges in the world are crucial to know. Distances are compelled to compute: The luminosity of an object (a 25-watt pear 50 meter awayappears just as bright together a 100-watt pear 100 meters away). The size of an item (a big distant object**parallax**.After measuring p, and also knowing the dimension of the Earth"s orbit,we can compute the distance to the star using trigonometry.Note the the distance to also the nearest stars (otherthan the Sun) is much bigger than 1 AU;therefore, the angle ns is small. Measuring little angles: 360 levels = full circle 60 arcminutes = 1 degree 60 arcseconds = 1 arcminuteFull one = 360 X 60 X 60 = 1,296,000 arcseconds1 arcsecond = angular size of dime 2 kilometers away

### crucial Equation: computing a street from a Parallax

## d = 1/p

d = distance to star, measure in parsecs ns = parallax, measure in arcsecondsThe**parsec**is characterized as the distance atwhich a star has a parallax that 1 arcsecond. In other units,1 parsec = 3.26 irradiate years = 206,000 AU.Parsecs are the systems most often used by professionalastronomers in measuring interstellar distances. Example: The star Proxima Centauri has a parallax ns = 0.77 arcsecond.d = 1/0.77 = 1.30 parsec = 4.23 light yearsBecause mainly parallaxes room so small, they canonly be measured correctly for fairly nearby stars.From the ground, the smallest measurable parallax is p = 0.01 arcsec(corresponding come a street d = 100 parsecs = 326 irradiate years).From a satellite, the the smallest measurable parallax isp = 0.002 arcsec (corresponding to a street d = 500 parsecs = 1600 irradiate years).For comparison, the distance from the sunlight to the center ofour galaxy is around 8000 parsecs. Thus, we have the right to only use the techniqueof mainly parallax come measure distances in our immediateneighborhood, no for the whole galaxy. (3) ~ above average, a nearby star will have a large proper motion.

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**Proper motion**is the steady adjust in a star"sapparent position on the sky, resulting from its motion through space.Proper movement is measure in arcseconds every year.On average, near stars have faster proper motions than far-off stars.(This is just an median statement: a star which wake up to bemoving straight toward or far from the Sun, for instance, willhave no proper motion.)Examples:Proxima Centauri:proper activity = 3.85 arcseconds/year, distance = 1.3 parsecsBetelgeuse:proper movement = 0.03 arcseconds/year, street = 150 parsecsSearching for stars likely to be nearby? Look because that stars v largeproper motion.Prof. Barbara Ryden (ryden