Hubble

1
Hubbles Law

• Astrophysics Lesson 16

2
Learning Objectives

• To know-
• What is Hubbles Law.
• How to measure Hubbles constant from a graph.
• How to estimate the age of the universe from
  Hubbles Law based on one assumption.

3
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?

4
Einsteins 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 Masters
  Mistakes, Discover Magazine, http//discovermagazi
  ne.com/2004/sep/the-masters-mistakes/, retrieved
  15 October 2009

5
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.

6
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.

7
Hubbles Law

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

8
Hubbles 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. 

9
Hubbles 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.

10
Determining Hubbles 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, Hubbles Constant.

11
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?

12
Hubble Time - Answers

• Spreadsheet analysis ? H0 74.7 km s-1 Mpc-1
• (Note that 1 Mpc 3.0861022 m)
• ? so we estimate the age of the universe to be
  about 13 billion years!

13
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.