General Astronomy

Distance Units in Astronomy

“You’ve never heard of the Millennium Falcon?…It’s the ship that made the Kessel Run in less than twelve parsecs.”

The quote, as any Star Wars fan would know, is from Han Solo boasting about the speed of his ship to Obi Wan Kenobi in the Mos Eisley Cantina. But you may have wondered what a parsec is. As we’ll see, the most famous smuggler in the galaxy is actually unit confused!

In astronomy, we typically work with objects that are enormous in size compared to things we experience in our everyday life. Meters work well for things we might measure on Earth, but aren’t suited for measuring the distance to a star or the size of a galaxy—the numbers become too large and cumbersome to work with. There are a couple of commonly used measurements of distance in astronomy: the astronomical unit (AU or au), the light year, and the parsec (pc).

The astronomical unit is roughly the distance from the Earth to the Sun. This is about 150 million kilometers (93 million miles). The light-year is the distance that light travels over a period of one year in a vacuum, which is about 9 trillion kilometers (6 trillion miles). It is NOT a measurement of time. Light years are more often used in popular science than in professional research.

The last common unit of length is the parsec, which is frequently used in professional astronomy. It takes a little understanding of parallax to see how it is defined. Parallax is the apparent change in position of an object when viewed from two different lines of sight. This concept can be easily demonstrated by holding out your thumb at arm’s length and looking at it through your right eye only, and then your left eye only. You will notice that your thumb appears to change its position with respect to a distant background (see diagram below). In fact, if you did this with an object at various distances, you will notice that its apparent shift in position decreases with distance. You can start to see how an astronomer might use this to determine distances.

Parallax final
The diagram shows the view of your thumb from your left and right eye. Modified from Wikimedia Commons.

If we observed a star from two different points on Earth’s orbit we would see an apparent shift in its position with respect to other more distance background stars. This shift is maximized if we make two observations six months apart, since this would correspond to viewing a star from opposite sides of Earth’s orbit. One half of this apparent shift is called the parallax angle. The units used are degrees with a sixtieth of a degree called an arcminute and a sixtieth of an arcminute an arcsecond. For example:

1° 34’ 3”

This tells us that an object has a parallax angle of one degree, 34 arcminutes, and 3 arcseconds. We are now ready to understand the definition of a parsec.

Modified from Wikimedia Commons
Annular parallax due to shifting of Earth on its yearly orbit. Modified from Wikimedia Commons.

The diagram shows the position of Earth six months apart on its orbit, along with corresponding lines of sight to a nearby star. We can imagine building a right triangle with one leg as the Earth-Sun distance, one as the distance of the star from our Sun, and the hypotenuse. Using a little bit of trigonometry, it can be shown that:

Eq 2

Where theta is the parallax angle (half the total shift in position). Since the angles involved are small, we can approximate the tangent of theta as simply theta. Finally, we define the parsec as the distance to an object with a parallax angle of one arcsecond (1”). This distance is about 3.26 light years. So, with some unit conversion, we can relate the distance to an object and its parallax angle as:

Eq 1

Where “d” is in parsecs and theta in arcseconds. So, it appears Han Solo is confusing a unit of distance for a unit of time (but see this).

The nearest star, Proxima Centauri, is 4.24 pc away, which means it has a parallax angle of less than 1 arcsecond. Note that the human eye has an angular resolution of only 1 arcminute, so we are unable to detect this apparent shift without the aid of a telescope. Below is a table of distances to various astronomical objects from the Sun:

Object Astronomical Units (AU) Light Years Parsecs (pc)
Earth 1 1.581 x 10-5 4.848 x 10-6
Jupiter 5.203 8.227 x 10-5 2.522 x 10-5
Pluto 39.482 6.243 x 10-4 1.914 x 10-4
Polaris (North Star) 2.801 x 107 433 133
Proxima Centauri 268,136.44 4.24 1.30

Using parallax, astronomers have been able to map out numerous objects in the Milky Way galaxy. The European Space Agency launched the satellite Hipparcos in 1989. Over its three and a half year mission, it measured the motion and parallax of over 100,000 stars in our galaxy with high precision (~2 milliarcsec). Another 2.5 million stars were added with lesser precision by 2000. The successor to Hipparcos, Gaia, was launched in 2013 and can measure parallax with an even higher precision in the microarcsecond range. It will be able to generate a 3-D map of over 1 billion objects in the Milky Way including stars, exoplanets, and even asteroids in our solar system.

Exoplanets

Exoplanets: An Introduction

Artist impression of a planet orbiting the star Alpha Centauri B. Credit: ESO/L. Calçada/Nick Risinger (skysurvey.org)
Artist impression of a planet orbiting the star Alpha Centauri B. Credit: ESO/L. Calçada/Nick Risinger (skysurvey.org)

The realization that planets outside of our solar system are common has sparked a huge interest in planet hunting, with the prize being the detection of an Earth or near Earth-sized planet in the habitable zone of another star. But how do astronomers find these distant worlds? How do they figure out their size, mass, atmospheric composition among other things? In a series of blog posts, I will investigate these questions and more in this new and exciting field of astronomy.

Characterizing and detecting exoplanets is a very new field of astronomy. Throughout the 20th century, astronomers attempted to find these planets. While some reports would be later confirmed, many were either controversial or could be explained by other phenomena. It wasn’t until the closing decades of the 20th century that the necessary technology had been refined enough to detect exoplanets with confidence. These advancements, along with the successful detection of an exoplanet orbiting the main sequence star 51 Peg, created a surge of interest in exoplanet research starting in the mid-1990s. For a more detailed overview see Perryman (2012).

So why have these planets only been discovered in the last two decades? In short, because detecting them either directly or indirectly is hard. If we tried direct detection, like taking a picture of one of these guys through our telescope, we run into several problems.

Let’s use our solar system as an example. It is well-known that the planets in our solar system are tiny compared to our Sun. Jupiter’s radius is about one-tenth that of the Sun. Now that doesn’t seem bad, but place it at its orbital distance away from the Sun at about 778 million kilometers and then imagine trying to look at it with your telescope from tens or even hundreds of light years away (one light year is about 9 trillion kilometers). The difference between the size of the planet and the distance we observe from it is enormous, making it hard to resolve any image we might take of a planet.*

But our troubles don’t end here! We conveniently ignored the fact that our Sun is very bright compared to the planets. We see planets because of the light they reflect from the Sun, which can be on the order of one billionth of its brightness. Things are better in the infrared range, but this is a non-starter. While several planets have been directly imaged, it’s not an efficient or easy way of detecting exoplanets.

This leaves us with indirect detection, which is by far the best way to date of finding these planets. Indirect detection involves looking for signs that a star is being influenced by an unseen planet. This could be a slight periodic dimming of a star as a planet moves in front of it or changes in its position due to gravitational tugs from an orbiting planet. Here I present a brief list of ways exoplanets can be detected:

Astrometric Method

All bodies with mass exert a gravitation force on other bodies with mass. This means that planets and stars will tug at each other, which causes them to orbit around a common center of mass. The tug on a star by a planet is rather small, but with precise enough measurements, it is possible (at least in principle) to detect small changes in the star’s position by these tugs. In practice this technique is difficult to implement with today’s technology. So far, only one exoplanet detected by this method has been confirmed (see here and here).

Sun Barycenter
Motion of the barycenter (center of mass) of the solar system relative to the Sun. From Wikimedia Commons

Doppler Method

Until recently, most exoplanets were detected by this method. As noted above, orbiting planets cause the parent star to wobble about the system’s center of mass. This actually has an interesting effect on the light that we observe from the star. If we looked at the spectral lines of the star, we would notice that they shift periodically as the star moves toward us (blue shift) and away from us (red shift). This shifting is known as the Doppler Effect. By detecting these small shifts, we can infer that an exoplanet is orbiting the star. We’ll go into more detail about this method in a different post.

Gravitational  Microlensing 

This method relies on the interaction between light and objects with large mass as described by General Relativity. This technique uses the fact that light is deflected around objects with mass. In effect, the object acts as lens, which distorts the light from the source while also focusing it. This means that we could detect this lensing caused by a planet orbiting a star. The technique does require good alignment between the star, planet, and the line of sight of the observer in order to work effectively. About three dozen exoplanets have been discovered with this technique.

Pulsar Timing

Pulsars are very dense rotating stars almost entirely composed of neutrons with a radius of about 12 kilometers. These stars regularly emit radio waves in pulses which are detectable here on Earth. These pulses act as a clock and the timing between them can be measured. Changes in distance between a pulsar and Earth cause the pulses to arrive at different times. Deviations in these times might signal the presence of an unseen companion influencing the motion of the pulsar. Only a hand full of exoplanets have been detected using this method. The earliest detection occurred in 1992 with the discovery of two planets around the star PSR B1257+12 followed by a third in 1994.

Transit Photometry

Since the launch of the Kepler Space Telescope in 2009, more exoplanets have been detected by this method than any other. As a planet moves in front of a star it blocks a small portion of the star’s light causing a small decrease in brightness. We can detect planets by measuring these periodic dips in brightness.

The Future

So, where does exoplanet research go from here? From the very beginning, exoplanet research has been driven by the quest for discovering another habitable planet besides our own. This requires unparalleled precision in our methods of detection and the ability to identify exoplanets with environments conducive to life. Facilities like the European Southern Observatory’s HARPS spectrograph, are leading the charge in developing technologies capable of detecting Earth sized analogs. The launch of the Kepler Space Telescope resulted in a huge increase in exoplanet detections (see the graph below) generating a lot of data. This data consists of over 1,000 confirmed candidates and 3,600 unconfirmed candidates all of which need to be analyzed and followed-up with further observations. The Kepler data is large enough that astronomers can start figuring out what types of solar system configurations exist and at what frequency they occur. The James Webb Space Telescope, which is scheduled to launch in the fall of 2018, will help characterize planetary atmospheres. All in all the coming decade will be an exciting time for exoplanet research.

Exoplanet Detections
The transit method has become the dominant means of detection today. Note the large increase in exoplanet detections by this method after Kepler’s launch. The most up-to-date graphs can be found here.

References:
Michael Perryman. Astrobiology. October 2012, 12(10): 928-939.doi:10.1089/ast.2011.0784.

*More precisely, the angular separation between the two is small making it difficult to resolve an exoplanet from its star. This situation is only exacerbated when atmospheric effects are added which plague ground based telescopes.

Student Life

My First Telescope

Last weekend I ordered an 8 inch Dobsonian from Orion Telescopes and Binoculars for just under $400 which isn’t bad as far as telescopes go. I’ve always wanted one of my own, but it wasn’t until the last couple of months that I looked into one seriously. After all, what is an astronomer without his scope? To my surprise the Dob was delivered by Wednesday afternoon—that is some speedy delivery! The entire thing came in two boxes: one with the optical tube and the other with the mount which required some assembly. Where better to assemble your first telescope than at your local university’s observatory?

Me unboxing the telescope.
Me unboxing the telescope inside the campus observatory.

My friend Dustin, who is an astrophotographer, helped me unbox and collimate the telescope. While we worked on that some of my peers were using the campus observatory to try and detect an exoplanet by transit photometry. Here’s the telescope put together:

DSC09224

Around midnight we moved it outside of the observatory to align the guide scope and try out a few targets. Some of the objects we looked at included Saturn, the Ring Nebula (M57), and the Hercules Globular Cluster (M13). We also looked at several stars such as the famous Double Double in the constellation Lyra.

For the interested reader here are the telescope specs:

Primary mirror diameter: 203 mm
Primary mirror focal length: 1200 mm
Focal ratio: f/5.9
Focuser: 2″ and 1.25″ eyepieces with adapter
Guide scope: EZ Finder II (reflex sight)
Tube dimensions: 46.5” x 9.25”
Total weight: 41 lbs