Hubble’s Law

Astrophysics Lesson 16

Learning Objectives

To know:- What is Hubble’s Law.

How to measure Hubble’s constant from a graph.

How to estimate the age of the universe from Hubble’s Law based on one assumption.

Fate of the Universe

What do you think?

Is it static, contracting or expanding?

Will it remain constant or will it contract in a “big crunch” or expand forever?

Einstein’s Greatest Blunder

• THE COSMOLOGICAL CONSTANT: LAMBDA   

“In 1917 Einstein published an equation that described an expanding universe. But he inserted a fudge factor called lambda to allow the equation to describe a static universe.”

• Wright, Karen (30 September 2004), The Master’s Mistakes, Discover Magazine, http://discovermagazine.com/2004/sep/the-masters-mistakes/, retrieved 15 October

2009

T)g– (T - g– G v21

vv

Vesto Slipher• In 1912, he was the

first to observe the shift of spectral lines of galaxies, making him the first to discover galactic redshifts.

• Slipher first reports on the making the first Doppler measurement on September 17, 1912 in The radial velocity of the Andromeda Nebula in the inaugural volume of the Lowell Observatory Bulletin, pp.2.56-2.57.

Edwin Hubble• In 1929, along with

Milton Humason discovered a rough proportionality of the objects' distances with their redshifts.

• the universe is, in fact, expanding.

Hubble’s Law

• A relationship between the velocity of recession of a galaxy and its distance from the Earth. 

Hubble’s Law

• The equation from this graph is:

• v is the recession velocity (km s-1), • d is the distance to the galaxy (Mpc).

• H0 is called Hubble's Constant (km s-1

Mpc-1)• Currently accepted value = 65 km s-1 Mpc-1. 

d 0Hv

Hubble’s Law

The recession velocity can be worked out using the red shift.

The distance is worked out by other means which is not needed here.

you can read about this on the sheet I will give you.

Determining Hubble’s Constant

Look at the data for members of clusters of galaxies given on the worksheet

Plot the recession speed, v, versus the distance, d.

Draw a line of best fit through the origin.

Determine the gradient of the line to determine a value for H0, Hubble’s Constant.

Hubble Time - Exercise

Note that H0 has units of km s-1 Mpc-1

Convert this into units of s-1.

Then take the reciprocal, 1/H0 to estimate the age of the universe in seconds.

Convert your answer into years this estimate for the age of the universe is known as the Hubble Time, tH

What assumption does this rely on?

Hubble Time - Answers

Spreadsheet analysis H0 = 74.7 km s-1

Mpc-1

(Note that 1 Mpc = 3.086×1022 m)

so we estimate the age of the universe to be about 13 billion years!

118-1-22

113

0 s102.420Mpc m 103.086

Mpc s m1074.7

H

s104.132s102.420

11 17118-

0

HtH

yr101.309yr s10156.3

s104.132 1017

17

Ht

Some points to note…

There is significant scatter in the data mostly from the poor accuracy in measuring distances.

The data suggests the universe is expanding:-

all the galaxies appear to be moving away from each other which suggests a common starting point.

This estimate assumes a constant expansion rate since the universe was formed look at this next lesson.