what assumptions do we make when we use the hubble constant to estimate the distance to a galaxy?
Hubble's Distance - Redshift Relation
Edwin Hubble, redshifted spectra, and distances to galaxies
During the 1920's, Edwin Powell Hubble demonstrated that the small hazy patches of low-cal which were then known as "spiral nebulae" are actually unabridged galaxies containing hundreds of billions of stars.
Utilizing the 100-inch telescope at California's Mount Wilson Observatory (at the time the globe'south largest telescope) Hubble obtained spectra and measurements of the distance to a few dozen galaxies, leading to the discovery that the Universe is expanding. Hubble compared recession velocities of galaxies measured from their spectra to their apparent brightness estimated from photographic plates. In 1929 Hubble published his findings, detailing revealed that the fainter and smaller a milky way appeared, the higher was its redshift.
Redshift is a term used to describe situations when an astronomical object is observed to being moving away from the observer, such that emission or assimilation features in the object's spectum are observed to take shifted toward longer (ruby) wavelengths. The change in wavelength of the spectral features is due to the Doppler upshot, the change in wavelength that results when a given object and an observer are in motion either toward or away from each other. The radiation coming from a moving object is shifted in wavelength:
where "lambda_0" is the rest wavelength of the radiation, and is "lambda_v" is the observed wavelength which has been shifted due to the radial motion between the object and the observer. Information technology is mutual to employ "delta_lambda" to represent the observed wavelength minus the residuum wavelength. Wavelengths of optical light are normally measured in either Angstroms (1 � = 10-10 m) or nanometers (i nm = x -nine m).
In the data collected by Hubble, the characteristic assimilation and emission line features in the spectrum due to hydrogen, calcium and other elements which announced at longer (redder) wavelengths than in a terrestrial laboratory. I tin apply the measured wavelengths of known spectral lines to determine the velocity of a galaxy. For example:
Assimilation lines of hydrogen, normally measured to exist at 4861� and 6563�, are measured in the spectrum of a detail milky way to be at 4923� and 6647�.
The speed of low-cal, c, has a constant value of 300,000 km/sec.
Therefore this galaxy has a redshift of
z = [(4923 - 4861) / 4861] and z = [(6647 - 6563) / 6563]
z = [62 / 4861] and z = [84 / 6563]
z = 0.01275
and the is moving away from us with a velocity, v = c * z = 300,000 km/sec * 0.01275 = 3826 km/sec
The Hubble Distance - Redshift Human relationship
When Hubble plotted the redshift vs. the distance of the galaxies, he found a surprising relation: more distant galaxies are moving faster away from united states. Hubble concluded that the fainter and smaller the galaxy, the more than distant it is, and the faster it is moving away from us, or that the recessional velocity of a galaxy is proportional to its distance from us:
v = Ho d,
where v is the galaxy'southward velocity (in km/sec), d is the distance to the milky way (in megaparsecs; ane Mpc = 1 meg parsecs), and Ho proportionality abiding, called "The Hubble constant".
Hubble'south Law states that the milky way'southward recession speed = Ho * distance, where Ho is known as the Hubble constant and is a measure of the slope of the line through the altitude versus recession velocity data. The line goes through the origin (0,0) because that represents our home position (nada altitude) and we are non moving away from ourselves (nix speed).
To determine a galaxy's altitude, we must rely on indirect methods. For instance, 1 assumption used by Hubble, and other early 20th century astronomers, is to assume all galaxies of the same type are the same concrete size, no matter where they are. This is known every bit "the standard ruler" supposition. To determine the distance to a galaxy one would only need to measure out its apparent (athwart) size, and utilize the pocket-size angle equation: a = due south / d, where a is the measured angular size (in radians!), due south is the galaxy's true size (diameter), and d is the distance to the galaxy.
In social club to precisely make up one's mind the value of Ho , we must decide the velocities and distances to many galaxies. Hubble's police force has been confirmed past subsequent research and provides the cornerstone of modernistic relativistic cosmological theories of our expanding universe. In 1963 astronomers discovered cosmic objects known equally quasars that exhibit larger redshifts than any of the remotest galaxies previously observed. The extremely big redshifts of various quasars suggest that they are moving away from the Earth at tremendous velocities (i.due east., approximately ninety percentage the speed of light) and thereby constitute some of the most distant objects in the universe.
Historical Note: It is not common for any other astronomers to be mentioned along with Edwin Hubble as beingness responsible for figuring out how the distance to a galaxy is related to its recession velocity. Nevertheless, Hubble did not work alone and many other astronomers deserve credit for establishing the distance--redshift human relationship.
Click below to begin the exercise:
Measuring the Altitude to Nearby Galaxies
Source: http://astro.wku.edu/astr106/Hubble_intro.html
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