# MEASURING DISTANCES IN ASTRONOMY Basic Principles: Geometric methods St in addition to ard ca

## MEASURING DISTANCES IN ASTRONOMY Basic Principles: Geometric methods St in addition to ard ca

Swift, Ron, Freelance Columnist has reference to this Academic Journal, PHwiki organized this Journal MEASURING DISTANCES IN ASTRONOMY Basic Principles: Geometric methods St in addition to ard c in addition to les St in addition to ard rulers [the last two methods relate quantities that are independent of distance to quantities that depend on distance] Parallax in addition to Proper Motion Angular size: degree [º], arcminute [‘], arcsecond [“] [in arcseconds] = 206265 (L/D) where: = angular size; L = linear (or true) size; D = distance Definitions: parallax (p), Astronomical Unit [AU], parsec [pc] D [in parsec] = 1/p [in arcseconds] where: 1 pc = 206265 AU = 3.26 light yr Parallax can only be used on nearby stars (D < 100 pc) [Atmospheric blurring (seeing); Hipparcos satellite; Hubble Space Telescope]

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Motion of stars within a cluster Proper motion [arcsec/s] = change of angular position Line-of-sight motion [km/s] – measured via Doppler shift Comparison of average stellar proper motion in cluster with average line-of-sight speed yields distance to cluster Luminosity in addition to Flux Inverse square law: f = L / (4D2) where: f = flux [erg/s/cm2]; L = luminosity [erg/s]; D = distance [cm] Magnitude scale: brightnesses of astronomical sources

St in addition to ard C in addition to les in addition to Rulers Variable stars: Cepheids in addition to RR Lyrae stars Period-luminosity relation; measure P & infer L; measure f & infer D Other st in addition to ard c in addition to les: brightest red giants, HII regions, planetary nebulae, supernovae, globular cluster luminosity Galaxies: Luminosity is seen to be correlated with the typical speed of internal motion of stars in addition to gas [Tully-Fisher relation: rotation of disks of spiral galaxies] [Faber-Jackson relation: r in addition to om stellar motion in elliptical galaxies] Galaxies: Size correlated with typical speed of (r in addition to om) stellar motion [Dn- relation as long as elliptical galaxies] Redshift as Distance Indicator Expansion of the Universe Hubble’s law: v = H0 D where: H0 = Hubble constant [km/s/Mpc] Doppler shift used to measure recession velocity: v c ( / ) where: / = fractional change in wavelength Astronomical Distance Ladder

Special Theory of Relativity (STR) Speed of light (in vacuum): c = 300,000 km/s Constancy of the speed of light: Michelson & Morley experiment No signal or object can travel faster than c [The ultimate speed limit!] Special Theory of Relativity (STR) Basic Principles The speed of light is the same to all observers The laws of physics are the same to all observers Observable Consequences Simultaneity is a relative concept Length contraction: moving rulers appear to be short Time dilation: moving clocks appear to run slow The apparent mass (inertia) of an object increases as its speed increases (impossible to accelerate it up to c) Equivalence of mass in addition to energy: E = mc2 Special relativistic effects are important when the SPEED of an object is CLOSE TO THE SPEED OF LIGHT: v c

Simultaneity in addition to time are relative, not absolute Marion Jones sees A flash be as long as e B Marion Jones sees A in addition to B flash simultaneously Measuring the length of a moving object: Length Contraction The apparent (i.e., measured) length of a moving object is shorter than the true length (measured when the object is at rest) Measuring time on a moving clock: Time Dilation A moving clock runs slower than its counterpart at rest Stationary Clock Moving Clock

A Thought Experiment: Length Contraction in addition to an Apparent Paradox The Garage Attendants Perspective A Thought Experiment: Length Contraction in addition to an Apparent Paradox The Drivers Perspective Solution: The driver in addition to garage attendant do not agree on the question of whether the two doors were closed simultaneously A Real Laboratory Experiment: Direct Verification of Time Dilation in addition to Length Contraction as Predicted by the Special Theory of Relativity The scientist in the laboratory witnesses time dilation, while the Uranium atoms witness length contraction Beam of fast-moving Uranium atoms Suitably placed Geiger counter Nuclear fission of Uranium atoms

General Theory of Relativity (GTR) Principle of Equivalence All objects experience the same motion in a given gravitational field, irrespective of their mass [Galileo’s experiment at the leaning tower of Pisa] Gravitational field <===> Accelerated reference frame Gravity can be thought of as a distortion of space-time Observable Consequences of GTR Perihelion precession of Mercury Light bending: Solar eclipse experiment

Gravitational lensing: Multiple images, image distortion Gravitational Redshift [Extreme case: light is trapped in a black hole] General relativistic effects are important in a STRONG GRAVITATIONAL FIELD

## Swift, Ron Freelance Columnist

Swift, Ron is from United States and they belong to Patterson Irrigator and they are from  Patterson, United States got related to this Particular Journal. and Swift, Ron deal with the subjects like Local News; Regional News

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