Answered: Distances and Velocities of Galaxies…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The table lists the distances (in megaparsecs; 1 megaparsec = 3.085 × 10^24cm, and 1 megaparsec = 3.26 million light-years) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth. (a) Does there appear to be a relationship or trend for the data? (b) Find a linear equation in the form y =max that models these data using the points (520,40000) and (0,0). (c)The galaxy Hydra has a velocity of 60000 km per second. How far away to the nearest megaparsec, is the galaxy according to the model in part (b)? (d) The value of m is the Hubble Constant. The Hubble Constant can be used to estimate the age of the universe A (in years) using the formula A = 9.5 x 10^11/m. Approximate A using the value of m. Round to the nearest hundredth of a billion years. (e) Astronomers currently place the value of the Hubble Constant between 50 and 100. What is the range for the age of universe A?

Distances and Velocities of Galaxies
Galaxy
Virgo
Ursa Minor
Corona Borealis
Bootes
Distance Velocity
15
1600
200
290
520
15,000
24,000
40,000
Data from Acker, A., and C. Jaschek, Astronomical
Methods and Calculations, John Wiley and Sons.
Karttunen, H. (editor), Fundamental Astronomy,
Springer-Verlag.

Expert Solution

Step 1: Given

The table lists the distances (in megaparsecs; 1 megaparsec = 3.085 × 10²⁴cm, and 1 megaparsec = 3.26 million light-years) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth. We have to answer the following...

Solution (a): Plot the data using distances for the x-values and velocities for the y-values. Then we find