Astronomy - Parsec and Hubble's Constant
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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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Solution Summary
Detailed and step-by-step explanation for both the questions.
Solution Preview
(1) To convert 1 Megaparsec into meters, we do the following:
1 Mparsec = 10^6 parsec [Because Mega is 10^6, that is a million]
10^6 parsec = 10^6 * 3.262 light years [Because 1 parsec is equal to 3.262 lightyears]
So 1 Mparsec = 10^6 * 3.262 light years
But 1 light year = Distance traveled by light in one year at a speed of 3 * 10^8 m/s
Thus, 1 lightyear = time * speed ...
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