1. If H is the rate at which the universe expands in kmsMpc, then the Hubble tim
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Question
1. If H is the rate at which the universe expands in kmsMpc, then the Hubble time is t = 1H. Calculate the number of Hubble times in the age of the universe. Please give your answer to one or two significant figures.
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Is this number an underestimate, an overestimate, or neither?
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2.
Among the globular clusters orbiting a distant galaxy, one is moving at 420 km/s and is located 11 kpc from the center of the galaxy. Assuming the globular cluster is located outside most of the mass of the galaxy, what is the mass of the galaxy? (Hint: Use the formula for circular velocity . Remember to convert units to meters and kilograms.) Express your answer in billions of solar masses.
_________ billion solar masses.
Explanation / Answer
1. If H is the rate at which the universe expands in kmsMpc, then the Hubble time is t = 1H. Calculate the number of Hubble times in the age of the universe. Please give your answer to one or two significant figures.
.
Is this number an underestimate, an overestimate, or neither?
.
The age of the Universe is the time spent after bang in expansion of the Universe. As per the estimates the age of the Universe is 13.8 billion years after Big Bang.
Hobble Law helps caulculating the age of Universe and Hubble Constant is H
If H is the rate at which the universe expands in kmsMpc, then the Hubble time is t = 1H.
The time taken Universe to expand its present state t = D/v
As per Hubble Law v= H x D
We know the t = D/v = D/ (H x) = 1/ H
So 1/ H helps in estimating age of the Universe
Estaimte of H= 73 kms/s/Mpc
Make it into age, follow unit conversion
As 1MPC = 3.08x10¹ km, H=(73kms/s/Mpc) x (1Mpc/3.08 x 1019 km) = 2.37 x 10-18 1/s
Therefore, age of the Universe t = 1/ H = 1/ 2.37 x 10-18 1/s = 4.22 x 1017 s = 13.4 billion years
So the age of Universe is 13.4 billion years
2.
Among the globular clusters orbiting a distant galaxy, one is moving at 420 km/s and is located 11 kpc from the center of the galaxy. Assuming the globular cluster is located outside most of the mass of the galaxy, what is the mass of the galaxy? (Hint: Use the formula for circular velocity . Remember to convert units to meters and kilograms.) Express your answer in billions of solar masses.
_________ billion solar masses.
The following equation is for estimation of mass of galaxy
V²c = G Mr/r
V²c = Velocity of galaxy = 420 km/s = 420,000 m/s
G = Gravity Constant = 9.8m/s²
Mr = Mass of galaxy
r = galacto centre distance = 11kpc = 11,000 pc
420000=9.8 x Mr/11000
Mr=420000 x 11000/9.8 = 471,428, 571
So the mass of the Galaxy =0.471,428.571 billion solar
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