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Speed of Recession of a Galaxy

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Estimate the speed of a galaxy that is 10 billion light-years away.
The correct answer is .5c. Can someone show me how it was calculated?

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https://brainmass.com/physics/galaxies/speed-recession-galaxy-180783

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To calculate the speed of recession of a galaxy that is 10 billion light years away, we need to plug in the value of the Hubble Constant (H0) in the formula v = d * H0, where d = Distance of the galaxy from the Milky way.

The Hubble Constant is not really a constant because it is a function of time. ...

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See Also This Related BrainMass Solution

Astronomy - Parsec and Hubble's Constant

Question:

(1) If a galaxy has a luminosity of 6.6x10^39 W and a brightness measured as 1.25x10^-11 W m^-2, How far away is the galaxy in mega parsecs?

(2) An absorption line of the element beryllium is observed in the spectrum of the galaxy above as lying 509.4 nm. What is the speed of the recession of the galaxy in km s^1 assuming that the speed of light is c = 3.00 x 10^5 km s^-1

(3) Using the answers above calculate the value of the hubble constant

Answers:

(1) L = 6.6 * 10^39 W, b = 1.25 * 10^-11 W/m^2

b = L / (4 * pi * d^2)

4 pi d^2 = L / b

d^2 = L / (4 pi b)

d = sqrt [L / (4 pi b)]

d = sqrt [6.6 * 10^39 / (4 * pi * 1.25 * 10^-11)] = 4.20 * 10^49 m

Since 1 Mparsec = 3.262 * 10^22 m, d = 4.20 * 10^49 / 3.262 * 10^22 = 1.29 * 10^27 Mparsec

(2) The speed of recession of a galaxy is given by v = c z,

where c = speed of light = 3 * 10^5 km/s and z = fractional change in the wavelength of light

Here, z = (509.4 - 488.2) / 488.2 = 0.043

So, v = 3 * 10^5 * 0.043 = 0.13 * 10^5 km/s

(3) The Hubble Constant is not really a constant because it is a function of time. Therefore, it is preferrably called

the "Hubble Parameter" (referred to present time)

The value of the Hubble Parameter has been a subject of debate since long. The best estimates of H0 lie in the range of 50

km/s per Mparsec to 100 km/s per Mparsec. The current value of Hubble parameter is about 75 km/s per Mparsec.

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