Distances_Motions - Distances and Motions Determining the...

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Unformatted text preview: Distances and Motions Determining the AU Today, the Earth-Sun distance (= 1 AU) is known to high precision from radar measurements of the distances to the planets. (The relative scale of the planet distances is known from Copernicus and Kepler.) Radar observations of Venus began in 1958. Since we know the distance to each planet in AUs, measurement of the time required by radar signals to travel from the Earth to a planet and return establishes the size of the AU in km. c = 299,792.458 km/s AU = 149,597,870.7 km (3.0 x 105 km/s) (1.5 x 108 km) Triangulation and Parallax To reach the nearest stars, we use the orbit of the Earth as a baseline and the technique of triangulation. The greater the angular change (i.e., parallax), the nearer the star. http://highered.mcgraw-hill.com/sites/007299181x/student_view0/interactives.html# Parsec Definition Baseline = 1 AU = 1 arcsec d = 206,265 AU = 1 parsec = 1 pc Distance d = 1 / p" (pc) = 1 / " (pc) d = 206,265 / p" (AU) where p" or "is in arcseconds Example: if then or p" = 0.11 arcseconds d = 9.1 pc = 9.1 x 206,265 = 1.9 x 106 AU Early Measurements of Distances Stars are so distant that the parallaxes of even the nearest ones are too small to be measured with the techniques available to Aristotle. William Herschel tried to measured parallaxes, but instead got orbits of binary stars. Parallaxes were eventually detected, but even the nearest star shows a total annual displacement of only about 1.5 arcsec. The first observation of parallax of a star is usually credited to the German astronomer Friedrich Bessel (in 1838). Light Year Light travels at a speed of about 186,000 miles per second (300,000 km/s). So in one second, light has traveled 186,000 miles; in two seconds it has gone 372,000 miles. Let the clock run for one entire year, and the light will have traveled 5.9 x 1012 miles (9.5 x 1012 km) or 63,240 AU. The distance that light travels in one year is defined as 1 Light Year. The nearest star is about four light years away (distance), or you can say that the light emitted by this star takes four years (time) to travel the expanse of space between it and us. Units of Distance Astronomical Unit (AU) Distance from the Earth to the Sun Parsec (pc) Parallax of 1 arcsecond Light Year (LY) Distance light travels in one year d = 1 / p" (pc) d = 206,265 / p" (AU) pc = 3.26 LY The Nearest Stars Alpha Centauri or Sirius d = 1.3 pc p" = 0.76 arcsec d = 2.6 pc Good parallaxes can only be measured for stars within 100 pc of the Sun. There are about 5000 stars in this region of space, but most are invisible to the naked eye. PRS Question 1. If a star has a parallax of 0.04 arcsec, its distance is a. 4 pc d. 25 pc b. 4 ly e. 25 ly c. 4 AU Radial Velocity The radial velocity is the speed that a star has as it approaches or recedes from the Sun. It is counted as positive if it is moving away from the Sun. = v / c = (obs – ) / v = c Since the motion of either the star or the observer (or both) produces a Doppler shift in the spectral lines, a knowledge of the radial velocity alone does not enable one to decide which one “is doing the moving”. What is really measured is the speed with which the distance between the star and Sun is increasing or decreasing. Proper Motion The proper motion is the rate at which a star’s apparent position on the sky changes. With respect to “background” stars, the motions of a few nearby stars can be observed. is in arcseconds / year Barnard’s Star changes its position by 10.25 arcsec per year. Tangential Velocity Radial velocity is the motion of a star along the line of sight, while proper motion is the angular motion produced by the star’s motion across the sky. Whereas the radial velocity is known in km/s and is independent of distance, the proper motion of a star does not give the star’s actual speed. The latter is called the tangential velocity. To calculate it, one must know the proper motion and distance (or parallax). T = 4.74 d = 4.74 / p" (km/s) where is in arcsec/year, d is in parsecs, and p" is in arcsec. PRS Question 2. If a star has a proper motion of 10 arcsec per year and is at a distance of 2 pc, what is its tangential velocity? a. ~100 km/s d. ~20 km/s b. ~25 km/s e. ~5 km/s c. ~1 km/s Space Velocity The total space velocity is V2 = VR2 + VT2 ...
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This note was uploaded on 03/04/2012 for the course PHYS 2022 taught by Professor Jarrio during the Spring '12 term at Central GA Tech.

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