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This image shows the path Pluto will take during the next two years, as viewed from Earth. You can't see it with the naked eye. And, it doesn't actually move in such a cyclic way. It moves in a smooth orbit around the Sun.

So, why does the path in the image look so strange?

There are two reasons. Pluto is moving toward the lower left in that part of the sky. And, Earth also is moving around the Sun. It as if you were recording the movement of a slow moving object while riding on a merry-go-round. This cyclical apparent motion is due to Parallax, the subject of this part of the Kosmic Distance Ladder series. Follow this link to the first in the series.

More below the squiggle  ⤵

PARALLAX - An Overview of the Effect

To get a conceptual feel for parallax, it will help to view two animations of the effect. The image below is linked to a segment of an astronomy course by Terry Harter at Cornell. Click on it to load a Java page that animates the motions. It might take a few moments to load. Several controls are available as noted on the web page. The distance to a nearby stationary star is adjustable by dragging it. The important point here is that the farther an object is, the less pronounced is the parallax motion. Another important point is that the motions are greatly exaggerated. Actual stars are much farther away than in this simulation.

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The next image is linked to a graphic at the European Space Agency. It has a distance control and also allows you to see the smaller parallax effect with greater distances. Again, motions are greatly exaggerated.

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The Distance Argument

As promised in part 1 of this series, I will attempt to keep this very conceptual. For those who want to know more details about the mathematical derivation involving radians, parsecs, degrees of arc, etc, click on the graphic below.

The diagram shows a triangle taken from part of the geometry of the Earth-Sun-Star arrangement. One side is the Earth-Sun distance of 1 Astronomical Unit (AU). Another side is the distance to the star (D). And, there is a small angle theta (θ). This angle theta is a very, very small value. For small angles, the value of theta equals the ratio of the side opposite to the side adjacent to theta. In other words, theta  =  1 AU/D.  Rearranged, the distance to the nearby star is calculated as follows.  D  =  1 AU/theta    That seems quite simple. For detail, click the graphic.

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Today, we know the value of 1 AU to high precision and accuracy. Getting a measure of the angular parallax shift theta is quite a difficult challenge. Looking at the Pluto image at the top shows a lot of angular shift side to side. Pluto is 'close'. Theta is large. For stars, theta is incredibly small. The closest star is Proxima Centauri. It has a parallax angle theta larger than any other star. The value of theta is 0.75 arcseconds. For comparison, the width of the Moon is about 1800 arcseconds. Telescopic measurements of parallax are small and only yield useful values and distance calculations for a few hundred stars in our neighborhood near the Sun.

In 2013, the ESA European Space Agency, plans to launch the Gaia spacecraft. More stars will be measured with unprecedented accuracy.

OBJECTIVES:
To create the largest and most precise three dimensional chart of our Galaxy by providing unprecedented positional and radial velocity measurements for about one billion stars in our Galaxy and throughout the Local Group.

Main Sequence Fitting

The method of parallax does not get us distance values very far into our Milky Way neighborhood. The next range of distance can be found using Main Sequence Fitting. First, a little introduction to the H-R Diagram. H-R is Hertzsprung-Russell.

In the early 20th century, scientists reasoned that if all stars were alike, the most luminous ones would be the hottest. And, those with the same luminosity would have equal temperatures.

In 1911, Ejnar Hertzsprung (Denmark), plotted a graph of star’s magnitudes against their color. Independently in 1913, Henry Russell (USA), constructed a plot of stars’ magnitudes against their spectral class, confirming that indeed, there did seem to be some sort of relationship between a star’s luminosity and its temperature, and the stars fell into distinct groups. Such a plot was thereafter named the Hetzsprung-Russell or H-R diagrams.

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Star Clusters

Clusters of stars in distant parts of the galaxy are assumed to have formed from the same cloud of gas and dust, and are at the same distance from us. Their colors and therefore temperatures can be observed. Their place on the temperature scale of the H-R diagram can be plotted. Now, suppose the Y-axis of the H-R is labeled with magnitude. Magnitude is how bright an object looks to an observer. Apparent magnitude is what you actually see. Absolute magnitude is what you would see if the stars were all placed the same distance from you. More specifically, absolute magnitude equals the apparent magnitude an object would have if it were at a standard distance of 10 parsec (32.6 light-yrs) away from the observer.

Distant clusters of stars would have apparent magnitudes less than their absolute magnitudes. The plotted points lie below the red line plot of absolute magnitudes. Think of it this way in terms of car headlights. The farther away the car, the dimmer the apparent brightness of the headlights. This difference in magnitude is judges by your brain to give you a sense of the distance to the car. In astronomy, the light must be measured carefully. But the principle is the same. The difference in magnitudes is used to calculate a distance to the cluster of stars. More details here.

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Open clusters have been known since prehistoric times. The Pleiades (M45), the Hyades and the Beehive or Praesepe (M44) are the most prominent examples. Ptolemy had also mentioned the Coma Star Cluster as early as 138 AD.  First thought to be nebulae, it was Galileo in 1609 who discovered that they are composed of stars while observing Praesepe (M44).  As open clusters are often bright and easily observable with small telescopes, many of them were discovered with the earliest telescopes.

Main sequence fitting can determine distances for star clusters within our Milky Way. To reach distances farther out, other methods must be used.

What Method is Next?

The next rung on the Kosmic Distance Ladder uses the class of stars known as Cepheid Variables. As their name implies, they are not constant, but vary in luminosity. How can you tell how far away something is if it doesn't shine a constant amount. The secret is in it's variability.

Watch for the next diary post. I hope to see you then.

Originally posted to SciTech on Wed Aug 10, 2011 at 09:00 AM PDT.

Also republished by DKOMA, Spiritual Organization of Unapologetic Liberals at Daily Kos, and Community Spotlight.

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