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Chapter 24: Problem 39

A certain galaxy is observed to be receding from the Sun at a rate of \(7500 \mathrm{~km} / \mathrm{s}\). The distance to this galaxy is measured independently and found to be \(1.4 \times 10^{8} \mathrm{pc}\). From these data, what is the value of the Hubble constant?

Short Answer

Expert verified
The Hubble constant is approximately 54 Km/s/Mpc.

Step by step solution

01

Convert the distance unit

Firstly, the distance need to be converted from parsecs to megaparsecs. Note that \(1 \mathrm{Mpc} = 10^{6} \mathrm{pc}\). Hence, the provided distance in megaparsecs becomes \(1.4 \times 10^{8} \mathrm{pc} \times \frac{1 \mathrm{Mpc}}{10^{6} \mathrm{pc}} = 140 \mathrm{Mpc}\)
02

Use Hubble's Law

The Hubble constant is given by Hubble’s law, which states that velocity = Hubble constant * distance. To solve for the Hubble constant, rearrange this formula to find Hubble constant = velocity / distance. Substitute the given values into this formula: Hubble constant = \( \frac{7500 \mathrm{Km/s}}{140 \mathrm{Mpc}} \)
03

Compute the result

By carrying out the division, the value of the Hubble constant is approximately \( \frac{7500 \mathrm{Km/s}}{140 \mathrm{Mpc}} = 54 \mathrm{Km/s/Mpc}\)

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Most popular questions from this chapter

Explain why the apparent shape of an elliptical galaxy may be quite different from its real shape.

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In the early twentieth century, there was considerable debate about the nature of spiral nebulae and their distance from us, but the debate was resolved by improvements in technology. As a group, list three issues that we, as a culture, did not un-derstand in the past but understand today, and explain why we now have that understanding.

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