   Chapter 11, Problem 77AP ### University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185

#### Solutions ### University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
Textbook Problem

# (a) What Hubble constant corresponds to an approximate age of the universe of 1010 y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of 1010 y. (b) Similarly, what Hubble constant corresponds to a universe approximately 2 × 10 10 years old?

To determine

(a)

The Hubble constant corresponding to an approximate age of the universe of 1010 years.

Explanation

Given:

Age of the universe (t) = 1010 years

Distance between the two galaxies in the universe (d) = 1 Mly

Formula used:

The Hubble's constant tells us the speed in km/s, with which two galaxies move apart when they are 1Mly away from each other. So it can be expressed as,

Hubble constant = velocity with which the two galaxies move apart (in km/s)distance between the two galaxies (in Mly)

Or, H=v (in km/s)d (in Mly) and the unit of H will be km/s/Mly

Calculation:

First, we calculate the velocity with which the galaxies move apart a distance of 1Mly in 1010 years. This is given by

v=dt

Converting d = 1 Mly into km, we get, d=106 ly=9.46×1018 km

Similarly, t = 1010 years = 1010×365×24×3600 = 3

To determine

(b)

The Hubble constant corresponding to a universe 2×1010 years old.

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