Cosmic Distance Ladder | Part 2

In this second part of the Cosmic Distance Ladder series, we see how parallax and main sequence fitting help us to know the distance to objects in space. Follow this link to the first in the series if you missed it.

This image shows the path Pluto will take during the next two years, as viewed from Earth. You can’t see Pluto with the naked eye. And, it doesn’t actually move in such a cyclic way. It moves in a smooth elliptical orbit around the Sun. So, why does the path we see in the image look so strange?

There are two reasons. Pluto is actually 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. The merry-go-round motion imparts a back and forth cyclical pattern. This cyclical apparent motion is due to Parallax, the subject of this part of the Cosmic Distance Ladder series.

PARALLAX – An Overview of the Effect

To get a conceptual feel for parallax, it will help to view an animation of the effect. The image below is linked to an animation of parallax. Several controls are available on the right once you click and are at the web page. The important point here is that the farther an object is, the less pronounced is the parallax motion. Another important point is that these motions are greatly exaggerated by the animation. Actual stars are much farther away and move much less than this.

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, you can get those by clicking on the graphic below.

The graphic shows a triangle taken from part of the geometry of the Earth-Sun-Star arrangement. One side of the triangle 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 details of that derivation, click the graphic.

Today, we know the value of 1 AU to high precision and accuracy. Getting a measure of the angular parallax shift of nearby stars for 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 late 2013, the ESA European Space Agency, plans to launch the Gaia spacecraft. More stars will be measured by it with unprecedented accuracy as it moves around the Sun.

GAIA MISSION 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 stands for 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 magnitudes against their color. Independently in 1913, Henry Russell (USA), constructed a plot of star 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. The stars fell into distinct groups. Such a plot was thereafter named the Hetzsprung-Russell or H-R diagrams.

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. For example, car headlights come in a variety of magnitudes of brightness. Their apparent magnitudes depend on how far down the road they are viewed and what kind of headlights are shining from the cars. If you parked all the cars the same distance down the road from you for comparison, you would be able to assign them absolute magnitude values.

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 again. The farther away the car, the dimmer the apparent brightness of the headlights. This difference in magnitude is judged 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.

Open star 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. Bear in mind, as distances to farther objects are determined, they are reliant upon the accuracy of the methods used for the closer object distances. Inherent in this is an increasing uncertainty of the farther distances.

What Method is Next?

The next rung on the Cosmic 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 the variability pattern.

Watch for the next post of part 3. I hope you will join me.

Part 1 – Cosmic Distance Ladder

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6 thoughts on “Cosmic Distance Ladder | Part 2

  1. Amazing how the the universe can be measured. Great graph of star magnitudes.

    BTW – I didn’t give you the link in my last comment. You’ll enjoy the toy in this post.

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