Distances: mostly Unit 54

We can use triangulation to calculate how far away objects are!

Finding the distance to the Moon by Triangulation The Moon is a relatively close object, and measuring the necessary angles is not too difficult. Other astronomical objects of interest are much farther away, and measuring the necessary angles in degrees is impractical Degrees have been sub-divided into arc-minutes and arc-seconds 1 degree = 60 arc-minutes 1 arc-minute = 60 arc seconds

A more modern way of finding the distance to the Moon Apollo astronauts left faceted mirrors behind when they returned to Earth Scientists can bounce laser beams off these mirrors, and measure the time it takes the laser pulse to travel to the Moon and back. We know the speed of light, c, so calculating the distance is easy!

Parallax As a person’s viewing location changes, foreground objects seem to shift relative to background objects This effect is called parallax, and can be used to measure the distance to closer astronomical objects

Measuring the Distance to Astronomical Objects using parallax

Just a little Trigonometry…

Moving Stars The positions of stars are not fixed relative to Earth They move around the center of the galaxy, just as Earth does. This motion of stars through the sky (independent of the Earth’s rotation or orbit) is called proper motion Over time, the constellations will change shape! The speed of a star’s motion toward or away from the Sun is called its radial velocity

Cepheid and RR Lyrae Variables as another way of measuring distances The Period-Luminosity Relation

Supernovae Type 1a presents another way to measure distances If mass is added to a white dwarf, its gravity increases If the white dwarf mass exceeds 1.4 solar masses (the Chandrasekhar Limit), the end of the white dwarf is near. The additional gravity squeezes the degenerate material in the white dwarf, causing it to compress by a small amount This compression causes the temperature to soar, and this allows carbon and oxygen to begin to fuse into silicon The energy released by this fusion blows the star apart in a Type 1a supernova

Type 1a Supernova – Another standard candle! The light output from a Type 1a supernova follows a very predictable curve Initial brightness increase followed by a slowly decaying “tail” All Type 1a supernova have similar peak luminosities, and so can be used to measure the distance to the clusters or galaxies that contain them!

Explosions of massive stars is yet another, but not yet working Iron cannot be fused into any heavier element, so it collects at the center of the star Gravity pulls the core of the star to a size smaller than the Earth’s diameter! The core compresses so much that protons and electrons merge into neutrons, taking energy away from the core The core collapses, and the layers above fall rapidly toward the center, where they collide with the core material and “bounce” The “bounced material collides with the remaining infalling gas, raising temperatures high enough to set off a massive fusion reaction. The star then explodes. This is a supernova!

Before and After – a Supernova

Light Curve for a Supernova Other types of supernova can play a role of standard candle when we learn more of them.

Distances to other galaxies We can use Cepheid variable stars to measure the distance to other galaxies A Cepheid’s luminosity is proportional to its period, so if we know how rapidly it brightens and dims, we know much energy it emits If we see a Cepheid in another galaxy, we measure its period, determine its luminosity, and calculate its distance! Distance between galaxies is huge! M100 is 17 million parsecs away.

Knowing distances we learn about our neighbours The Universe is “clumpy” – galaxies tend to pull together by gravity Our immediate neighborhood is called the Local Group, a cluster of around 3 dozen galaxies (3 million light years across The Local Group is part of the Virgo Cluster, a large (collection of smaller clusters and groups of galaxies Superclusters: collection of larger clusters The Universe – simply everything! Central region of the Virgo Cluster

A Sense of Scale I

A Sense of Scale II

Outward to the Universe!

The Redshift and Expansion of the Universe Early 20th century astronomers noted that the spectra from most galaxies was shifted towards red wavelengths Edwin Hubble (and others) discovered that galaxies that were farther away (dimmer) had even more pronounced redshifts! This redshift was interpreted as a measure of radial velocity, and it became clear that the more distant a galaxy is, the faster it is receding!

Distances + redshifts give the Hubble Law In 1920, Edwin Hubble developed a simple expression relating the distance of a galaxy to its recessional speed. V = H  d V is the recessional velocity D is the distance to the galaxy H is the Hubble Constant (70 km/sec per Mpc) This was our first clue that the universe is expanding!