How Far are the Stars? (part 1)

Under the Milky Way
Creative Commons License photo credit: jurvetson

During a recent planetarium show, I discussed the stars of the Summer Triangle (up all night long in summer, they are still high in the west at dusk in autumn). I mentioned that Deneb, apparently dimmer than the Triangle’s other two stars Vega and Altair, is actually much larger and gives off much more light. It just seems dimmer because it’s about 100 times farther away. This prompted the question, “How can we tell how far away the stars are?”

This is a very perceptive question.  We obviously cannot directly measure the distance to a star like you might measure the height of a wall.  Neither can we use an odometer like you have in your car, since no one has been to the stars.  By doing a little trigonometry, however, we can get reliable distances to the stars nearest to us.


This animation is an example of
parallax – as the viewpoint moves
side to side, the objects closer to
the camera appear to move faster,
while the objects in the distance
appear to move slower.
Image by natejunk2004
Can’t see the Image? Click here.

This geometric way to measure distance is called parallax and you can illustrate it for yourself quite simply.  Hold your finger in front of your face.  Now close your left eye, leaving the right eye open.  Then close the right eye and open the left.  Repeat this sort of blinking several times and watch how you finger moves back and forth compared to things in the background.  Bring your finger close to your face, and repeat the experiment.  Now hold your finger at arm’s length, and repeat.  Notice how your finger seems to move farther when it is close to your face.  In fact, if you could measure how far your finger moves against the background objects, you could calculate how far it is from your face.

We can do the same thing with nearby stars. If we observe a star at a particular time of year (for example, in January) and then again six months later (in this case, in July), we can define an isosceles triangle where the base is the diameter of Earth’s orbit and the sides are the distance to the star.  The vertex angle of this triangle equals the apparent change in the star’s position due to the Earth’s yearly motion.  One half of this isosceles triangle is a right triangle where one leg is the known Earth-Sun distance (one AU, or astronomical unit), and the hypotenuse is the distance to the star. The angle opposite the one AU leg, which is one half the star’s apparent motion, is the parallax angle p.  Basic trigonometry then yields

sin p = 1 AU/ d,

where d is the distance to the star in question.  Since p is tiny for all stars, the small angle approximation sin p =p is valid.  We can define a standard distance by asking how far away a star would be if it had a parallax of one arcsecond (1/3600 degree).  Plugging d= 1 arcsecond into the equation gives us

d= 206265 AU,

where 206265 represents the conversion factor between radians and arcseconds, given that the approximation sin p =p holds only if the angle is in radians.  We have now defined the parsec, the distance at which a star has a parallax angle of one arcsecond.  It now becomes easy to determine stellar distances compared to this standard distance.  First, measure the parallax of a star in arcseconds.  Then take one over that value, and you have the distance to that star in parsecs.  By the way, although the general public prefers to think of distances to stars in light years, modern astronomers never quote them that way.  The parsec, directly related to a measurable quantity, is a much more preferable unit.  (One parsec is about 3.26 light years.)

This way of measuring distance has a limitation: most stars are too far away to have measurable parallaxes.  An imaginary sphere with a radius of one parsec centered on our Sun would contain precisely one star–the Sun.  The nearest star system to ours, that of Alpha Centauri, is 1.34 parsecs away, and therefore has a parallax of only about 0.75 arcseconds.  More distant stars have much smaller parallaxes, too small for most Earth based equipment to detect.

This began to change in 1989, however, when the European Space Agency (ESA) launched the High Precision Parallax Collecting Satellite, or Hipparcos.  The name was chosen in honor of the ancient Greek astronomer Hipparchus, who put together the first star catalog of the western world.  The first space experiment devoted to astrometry, Hipparcos catalogued 118,218 stars between 1989 and 1993.  The Hipparcos Catalogue was published in 1997.  Among its many scientific results, Hipparcos helped astronomers determine accurate proper motions (a star’s true motion through the galaxy) and was able to measure good parallaxes for stars up to about 1,000 parsecs away.

But, you may wonder, “What about stars more than a few thousand parsecs away from us? “  Keep in mind that our Galaxy is about 100,000 light years, or just over 30,000 parcsecs across.  Most stars, to say nothing of distant galaxies, are so distant that not even Hipparcos can measure their infinitesimal parallaxes.  Fortunately, there are objects known as “standard candles”–celestial objects with a known intrinsic brightness.  Comparing their intrinsic brightness with their apparent brightness in our skies lets us figure out the distances to them.  In a later post, I’ll discuss how we identify and use “standard candles” to determine distances to much more distant stars and even to other galaxies.

Vulcan? Caprica? Tatooine?

The idea that other life-bearing worlds are out there continues to fire our imaginations, as attested by the success of the recently-opened Star Trek movie, and by the critically acclaimed Battlestar Galactica series which concluded earlier this spring. 

In 1995, astronomers identified the first exoplanet around the star 51 Pegasi, nicknamed Bellerophon.  Since then, we’ve found over 300 planets around other stars.  For many years, though, we were finding only ‘hot Jupiters’ - gas giants extremely close to the host star (such as Bellerophon.)  These are not logical places to search for Mr. Spock, or for that matter any kind of life as we know it.  However, the search for extra-solar planets or exoplanets (planets around stars other than our Sun) is now entering a new phase.   As we refine our methods and our tools, we are at last beginning to find planets much smaller than Jupiter, approaching Earth in size.  And we’re starting to find some planets in the habitable zones of stars, regions where the temperature is neither too hot nor too cold for life.  Although we don’t really expect to find another Vulcan or Caprica, two recent announcements can give us some insight into how the search is done. 

In April, astronomers announced the discovery of Gliese 581 e, the fourth planet found around the star Gliese 581.  At around two Earth masses, this is the least massive planet ever found outside our solar system.  Astronomers also announced that Gliese 581 d(the third planet found in the system) is within the star’s habitable zone.  (‘A’ would designate the star itself; the planets are b, c, d, and e.)  This is star #581 in Wilhelm Gliese’s Gliese Catalogue of Nearby Stars, an effort to list all stars less than 25 parsecsfrom the Sun.  Gliese 581 is about 20 light years away, located in the constellation Libra.

Astronomers found Gliese 581′s planets using the radial velocity method.  Perhaps you are familiar with the Doppler effect, in which a sound changes in frequency when a source that had been approaching begins to move away.  We see the same effect with receding and approaching sources of light.  When a light source is receding from us, the wavelength of its light gets longer (and therefore redder.)  When a light source is approaching, the wavelength of its light gets shorter (and therefore bluer.)  The spectra of stars show dark absorption lines, indicating wavelengths of light absorbed by gases in the star.  By observing these lines over time we see that some stars show a slight redshift, then a slight blueshift, then a slight redshift….  Such a periodic variation indicates that the star is being tugged by something orbiting it.  The size and period of the tug gives us an idea of the tugger’s mass.  A mass much less than our Sun and comparable instead to Jupiter indicates a planet. 

To understand how hard it is to find Earth-sized planets this way, imagine if a crewman on Galactica had to find Earth with this method.   Our observer needs to see an entire oscillation to recognize the periodic tug of a planet, so (s)he must observe the Sun for a full year (Earth’s entire orbital period) to detect our planet.  Further, Jupiter’s tug on our Sun overwhelms Earth’s by about a factor of 12.  Any distant observer studying our own Sun’s radial velocity would probably notice only Jupiter’s influence on our Sun.  And that would take about 12 years of observing, since Jupiter takes about that long to orbit the Sun.  Finally, the observer needs to see our solar system roughly edge on, such that planets tug the Sun towards and away from the observer.  Fortunately for Starbuck et. al., Galactica has access to much better technology than we do today. 

Gliese581 is type M3V.  Here ‘V’ is the Roman numeral five, representing the fifth luminosity class, which is the main sequence of stars that includes our Sun.  ‘M3′ indicates a reddish star significantly smaller and cooler than our Sun.  In particular, Gliese 581 has less than one-third our Sun’s mass and is more than 2000K (3600 oF) cooler than our Sun.  Therefore, the habitable zone around Glises 581 is much closer to the star than ours is to our Sun.  Gliese 581 d, orbiting in that zone, orbits once in 67 Earth days.  Although Gliese 581 e takes only about 3 days to orbit its star once, is the planet closest to Earth’s mass we have yet identified.  The Gliese 581 system brings us closer to finding planets like ours and to understanding solar systems like our own.

hubble
Hubble Telescope
 © Photo credit: Xaethyx

Just days ago (May 13,) NASA announced that its Kepler telescope, launched March 6, is ready to begin observations.  This is NASA’s first mission capable of finding Earth-sized and smaller planets around stars other than our Sun.  Unlike the Hubble telescope which orbits Earth, this telescope is in orbit around the Sun.  It is roughly at Earth’s distance from the Sun, but on an orbit where it lags slightly more behind Earth’s position as time passes.  After 4 years, Kepler will be about 0.5 AU, or half the Earth-Sun distance, behind Earth on its orbit. 

Kepler will stare continuously at the same small region of the sky for three and a half years. Scientists did not want this steady gaze interrupted by day-night cycles or by passage behind the Earth, as would happen if the telescope were in Earth’s orbit.  Further, Kepler is looking at a region of space far above the plane of our solar system, so the Sun, Moon, and other solar system bodies never come near the field of view.  That area of space is also in the galactic plane roughly in the direction the Sun itself is traveling.  This means we are observing stars at the Sun’s approximate distance from the galactic core.

Kepler will detect extrasolar planets using the transit method.  This method involves looking at stars continually for long periods of time to see if the light ever gets slightly dimmer.  If the slight dimming occurs on a regular basis, it might be because a planet is orbiting the star and regularly passing in front of it from our perspective.  Such a passage is called a transit.  When a planet as small as our Earth transits its star, the star dims by only a factor of 1/10,000.  Only now, with Kepler, do we have an instrument powerful enough to detect such a tiny change in a star’s brightness.  Of course, we need to be fortunate enough to observe the planetary system edge-on, otherwise no transit will occur.  However, the chosen field of view contains about 100,000 stars, so odds are at least a few are oriented favorably. 

green-alien
 © Photo credit: stéfan

Even if we do find other Earth-sized planets, however, we are still far from  finding alien cultures, much less interacting with them as in science fiction.  Aliens in science fiction can interact because writers cheat on the laws of physics by introducing a parallel dimension.  This dimension is called ‘subspace’ in Star Trek and ‘hyperspace’ in Star Wars and Babylon 5.  To travel from one planetary system to the next, a starship leaves space, enters subspace/hyperspace, travels through that dimension, and reemerges into space at its destination.  As far as we know, however, no subspace or hyperspace exists to shorten space travel; real spacecraft must travel through space.  That makes the speed of light (300,000,000 m/s) an inviolable speed limit.  For example, nothing can travel between our system and that of Gliese 581 in less than 20 years, because Gliese 581 is 20 light years away. 

What’s more, any life we hope to find and interact with has to exist at the same time we do.  Given our short existence compared to the universe as a whole (equivalent to eight minutes out of a year), this could be the single biggest limitation on our ability to find other worlds with life. 

But even as we leave green-blooded aliens and warp drive at the theater, a quite real adventure remains before us.  No matter how much we explore and study our solar system, we cannot truly understand it until we can place it in a larger context.  The Kepler mission promises to show us more systems like our own, or to show us just how rare systems like ours are.  Either way, we will be able to appreciate our own Earth and familiar planets like never before.  I find that as thrilling as a ride with Captain Kirk.