Ohio University - Lancaster Campus slide 1 of 17 Spring 2009 PSC 100 Hubble’s Law: The Age, Size, and Expansion of Our Universe

Ohio University - Lancaster Campus slide 2 of 17 Spring 2009 PSC 100 In the early 20 th century, Vesto Slipher and Edwin Hubble discovered that all galaxies outside of our Local Group are moving away from us. Lunarmark.blogspot.com

The motion of every galaxy has 2 components: proper motion (perpendicular to our line of sight) and radial motion (along our line of sight.) The radial motion component of nearly every galaxy we can see is away from us. How can we tell this? proper motion radial motion actual motion Earth

Ohio University - Lancaster Campus slide 4 of 17 Spring 2009 PSC 100 The Doppler Effect If the source of light is moving away from an observer, the wavelength of the light is stretched. This is a redshift. Image Credit: Wikipedia (Redshift)

Ohio University - Lancaster Campus slide 5 of 17 Spring 2009 PSC 100 Hubble determined the distances to many of these galaxies using cepheid variable stars as ‘standard candles.’ What he discovered was astounding: The radial velocity of a galaxy is directly proportional to its distance. A galaxy 100 MLY away from us is receding away from us twice as fast as a galaxy 50 MLY away.

Ohio University - Lancaster Campus slide 6 of 17 Spring 2009 PSC 100 This relationship, which has come to be known as Hubble’s Law, can be used to establish both the size and the age of the universe. Credit: imagine.gsfc.nasa.gov

Ohio University - Lancaster Campus slide 7 of 17 Spring 2009 PSC 100 Doppler Shift Equation: change in wavelength = speed of recession unshifted wavelength speed of light Δλ = v r λ 0 c

Ohio University - Lancaster Campus slide 8 of 17 Spring 2009 PSC 100 Example: The normal wavelength of H-α light is nm. This light is observed to be shifted to 670 nm when coming from a galaxy. What is the recessional velocity of the galaxy? (670 nm – nm) = v r nm 3.00 x 10 5 km/s 13.7 nm x 3.00 x 10 5 km/s = 6300 km/s nm

Ohio University - Lancaster Campus slide 9 of 17 Spring 2009 PSC 100 Hubble determined the distance to many such galaxies, finding that their velocities and distances were directly proportional. Today, Hubble’s Law is written: Velocity = H 0 · distance velocity is in km/secdistance is in MLY or MPc H 0 is the Hubble Constant. H 0 has units of 1/time.

Ohio University - Lancaster Campus slide 10 of 17 Spring 2009 PSC 100 Different experiments have attempted to define H 0 accurately: 70.1 ± 1.3 km/sec/MPc (WMAP) 72 ± 8 km/sec/MPc (HST) 70.8 ± 4 km/sec/MPc (NASA average) What is NASA’s average value for H 0 in units of km/sec/MLY?

Ohio University - Lancaster Campus slide 11 of 17 Spring 2009 PSC 100 How does this determine the age and size of the visible universe? Re-arrange the equation: Velocity ÷ H 0 = distance Since light moves at a finite speed (3 x 10 5 km/s) it takes time to cover distance.

Ohio University - Lancaster Campus slide 12 of 17 Spring 2009 PSC x 10 5 km/s ÷ 21.7 km/s/MLY = 13,825 MLY Our universe has been expanding for 13.8 billion years, and our “horizon” i.e. the edge of our visible universe is 13.8 billion light years away. This value includes a number of assumptions, which we’ll look at when we study cosmology.

Ohio University - Lancaster Campus slide 13 of 17 Spring 2009 PSC 100 Credit: - ESA/ESO’s Astronomy Exercise Series

Ohio University - Lancaster Campus slide 14 of 17 Spring 2009 PSC 100 Some Examples: 1)How fast should a galaxy be receding from us, if the galaxy is 200 MLY away? H 0 · distance = velocity 21.7 km/s/MLY · 200 MLY = 4340 km/sec

Ohio University - Lancaster Campus slide 15 of 17 Spring 2009 PSC 100 2)How far away is a galaxy that has a recessional speed of 35,000 km/sec? Give your answer in both MLY & MPc. velocity ÷ H 0 = distance 35,000 km/sec ÷ 21.7 km/s/MLY = 1613 MLY or 1.61 billion LY or 495 MPc

Ohio University - Lancaster Campus slide 17 of 17 Spring 2009 PSC 100 What happens when you do too much math! Credit: snoedel.punt.nl