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Illustration of the use of interferometry in the optical wavelength range to determine precise positions of stars. Courtesy NASA/JPL-Caltech
Illustration of the use of interferometry in the optical wavelength range to determine precise positions of stars. Courtesy NASA/JPL-Caltech

Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of the Solar System and our galaxy, the Milky Way.

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Transcription

Oh. Hey! Sorry, I don’t mean to be rude. I’m just trying to figure out how far away my thumb is. How? Parallax. Centuries ago, people thought the stars were holes in a huge crystal sphere, letting through heavenly light. It wasn’t clear just how big the sphere was, but it was pretty dang big. I have some sympathy for them. By eye, and for all intents and purposes, the stars are infinitely far away. If you drive down a road you’ll see trees nearby flying past you, but distant mountains moving more slowly. The Moon is so far it doesn’t seem to move at all compared to nearby objects — and it’s easy for your brain to think it’s much closer, smaller, and actually following you, which is a bit creepy. Sometimes people even think it’s a UFO tailing them. Finding the distance to something really far away is tough. It’s not like you can you can just pace off the distance. Or can you? The ancient Greeks knew the Earth was round and there are lots of ways to figure that out. For example, ships sailing over the horizon seem to disappear from the bottom up, as you’d expect as they slip around the Earth’s curve. But how big is the Earth? Over 2000 years ago, the Greek philosopher Eratosthenes figured it out. He knew that at the summer solstice, the Sun shone directly down a well in the city of Syene at noon. He also knew that at the same time, it was not shining straight down in Alexandria, and could measure that angle. There’s a legend that he paid someone to pace off the distance between the two cities so he could find the distance between them. But more likely he just used the numbers found by earlier surveying missions. Either way, knowing the distance and the angle, and applying a little geometry, he calculated the circumference of the Earth. His result, a little over 40,000 km, is actually amazingly accurate! For the very first time, humans had determined a scale to the Universe. That first step has since led to a much, much longer journey. Once you know how big the Earth is, other distances can be found. For example, when there’s a lunar eclipse, the shadow of the Earth is cast on the Moon. You can see the curve of the Earth’s edge as the shadow moves across the Moon. Knowing how big the Earth is, and doing a little more geometry, you can figure out how far away the Moon is! Also, the phases of the Moon depend on the angles and distances between the Earth, Moon, and Sun. Using the size of the Earth as a stepping stone, Aristarchus of Samos was able to calculate the distances to the Moon and the Sun as well as their sizes. That was 2200 years ago! His numbers weren’t terribly accurate, but that’s not the important part. His methods were sound, and they were used later by great thinkers like Hipparchus and Ptolemy to get more accurate sizes and distances. They actually did pretty well, and all over a thousand years before the invention of the telescope! And I think it also says a lot that these ancient thinkers were willing to accept a solar system that was at least millions of kilometers in size. But at this point things got sticky. Planets are pretty far away and look like dots. Our methods for finding distances failed for them. For a while, at least. In the 17th century, Johannes Kepler and Isaac Newton laid the mathematical groundwork of planetary orbits, and that in turn made it possible, in theory, to get the distances to the planets. Ah, but there was a catch. When you do the math, you find that measuring the distances to the other planets means you need to know the distance from the Earth to the Sun accurately. For example, it was known that Jupiter was about 5 times farther from the Sun than the Earth was, but that doesn’t tell you what it is in kilometers. So how far away is the Sun? Well, they had a rough idea using the number found by the Greeks, but to be able to truly understand the solar system, they needed a much more accurate value for it. To give you an idea of how important the distance from the Earth to the Sun is, they gave it a pretty high-falutin’ name: the astronomical unit, or AU. Mind you, not “an” astronomical unit, “the” one. That’s how fundamental it is to understanding everything! A lot of methods were attempted. Sometimes Mercury and Venus transit, or cross the face of the Sun. Timing these events accurately could then be used to plug numbers into the orbital equations and get the length of an AU. Grand expeditions were sent across the globe multiple times to measure the transits, and didn’t do too badly. But our atmosphere blurs the images of the planets, putting pretty big error bars on the timing measurements. The best they could do was to say the AU was 148,510,000 km -- plus or minus 800,000 km. That’s good, but not QUITE good enough to make astronomers happy. Finally, in the 1960s, astronomers used radio telescopes to bounce radar pulses off of Venus. Since we know the speed of light extremely accurately, the amount of time it takes for the light to get to Venus and back could be measured with amazing precision. Finally, after all these centuries, the astronomical unit was nailed down. It’s now defined to be 149,597,870.7 kilometers. So there. The Earth orbits the Sun on an ellipse, so think of that as the average distance of the Earth from the Sun. Knowing this number unlocked the solar system. It’s the fundamental meterstick of astronomy, and the scale we use to measure everything. Having this number meant we could predict the motions of the planets, moons, comets, and asteroids. Plus, it meant we could launch our probes into space and explore these strange new worlds for ourselves, see them up close, and truly understand the nature of the solar system. And it’s even better than that. Knowing the Astronomical Unit meant unlocking the stars. We have two eyes, and this gives us binocular vision. When you look at a nearby object, your left eye sees it at a slightly different angle than your right eye. Your brain puts these two images together, compares them, does the geometry, and gives you a sense of distance to that object. And you thought your teacher lied when she said math was useful in everyday life. We call this ability depth perception. You can see it for yourself by doing the thumb thing: as you blink one eye and then the other, your thumb appears to shift position relative to more distant objects. That shift is called parallax. The amount of shift depends on how far apart your eyes are, and how far away the object is. If you know the distance between your eyes — we’ll call this the baseline — then you can apply some trigonometry and figure out how far away the object is. If the object is nearby, it shifts a lot; if it’s farther away, it shift less. It works pretty well, but it does put a limit on how far away we can reasonably sense distance with just our eyes. Stars are a bit beyond that limit. If we want to measure their distance using parallax, we need a lot bigger baseline than the few centimeters between our eyes. Once astronomers figured out that the Earth went around the Sun rather than vice-versa, they realized that the Earth’s orbit made a huge baseline. If we observe a star when the Earth is at one spot, then wait six months for the Earth to go around the Sun to the opposite side of its orbit and observe the star again, then in principle we can determine the distance to the star, assuming we know the size of the Earth’s orbit. That’s why knowing the length of the astronomical unit is so important! The diameter of Earth’s orbit is about 300 million kilometers, which makes for a tremendous baseline. Hurray! Except, oops. When stars were observed, no parallax was seen. Was heliocentrism wrong? Pfft, no. It’s just that stars are really and truly far away, much farther than even the size of Earth’s orbit. The first star to have its parallax successfully measured was in 1838. The star was 61 Cygni, a bit of a dim bulb. But it was bright enough and close enough for astronomers to measure its shift in apparent position as the Earth orbited the Sun. 61 Cygni is about 720,000 astronomical units away. That’s a soul-crushing distance; well over 100 trillion kilometers! In fact, that’s so far that even the Earth’s orbit is too small to be a convenient unit. Astronomers came up with another one: The light year. That’s the distance light travels in a year. Light’s pretty fast, and covers about 10 trillion kilometers in a year. It’s a huge distance, but it makes the numbers easier on our poor ape brains. That makes 61 Cygni a much more palatable 11.4 light years away. Astronomers also use another unit called a parsec. It’s based on the angle a star shifts over the course of a year; a star one parsec away will have a parallax shift of one arcsecond—1/3600th of a degree. That distance turns out to be about 3.26 light years. As a unit of distance it’s convenient for astronomers, but it’s a terrible one if you’re doing the Kessel Run. Sorry, Han. The nearest star to the sun we know of, Proxima Centauri, is about 4.2 light years away. The farthest stars you can see with the naked eye are over a thousand light years distant, but the vast majority are within 100 light years. Space-based satellites are used now to accurately find the distance to hundreds of thousands of stars. Still, this method only works for relatively nearby stars, ones that are less than about 1000 light years away. But once we know those distances, we can use that information on more distant stars. How? Well, like gravity, the strength of light falls off with the square of the distance. If you have two stars that are the same intrinsic brightness—giving off the same amount of energy—and one is twice as far as the other, it will be ¼ as bright. Make it ten times farther away, it’ll be 1/100th as bright. So if you know how far away the nearer one is by measuring its parallax, you just have to compare its brightness to one farther away to get its distance. You have to make sure they’re the same kind of star; some are more luminous than others. But thanks to spectroscopy, we can do just that. A star’s distance is the key to nearly everything about it. Once we know how far it is, and we can measure its apparent brightness, we can figure out how luminous it is, how much light it’s actually giving off, and its spectrum tells us its temperature. With those in hand we can determine its mass and even its diameter. Once we figured out how far away stars are, we started to grasp their true physical nature. This led to even more methods of finding distances. The light given off by dying stars, exploding stars, stars that literally pulse, get brighter and dimmer over time. All of these and more can be used to figure out how many trillions of kilometers of space lie between us and them. And we see stars in other galaxies, which means we can use them to determine the actual size and scale of the Universe itself. And all of this started when some ancient Greeks were curious about how big the Earth was. Curiosity can take us a great, great distance. Today you learned that ancient Greeks were able to find the size of the Earth, and from that the distance to and the sizes of the Moon and Sun. Once the Earth/Sun distance was found, parallax was used to find the distance to nearby stars, and that was bootstrapped using brightness to determine the distances to much farther stars. Crash Course Astronomy is produced in association with PBS Digital Studios. Head over to their YouTube channel to catch even more awesome videos. This episode was written by me, Phil Plait. The script was edited by Blake de Pastino, and our consultant is Dr. Michelle Thaller. It was directed by Nicholas Jenkins, edited by Nicole Sweeney, the sound designer is Michael Aranda, and the graphics team is Thought Café.

Contents

History

Concept art for the TAU spacecraft, a 1980s era study which would have used an interstellar precursor probe to expand the baseline for calculating stellar parallax in support of Astrometry
Concept art for the TAU spacecraft, a 1980s era study which would have used an interstellar precursor probe to expand the baseline for calculating stellar parallax in support of Astrometry

The history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession. In doing so, he also developed the brightness scale still in use today.[1] Hipparchus compiled a catalogue with at least 850 stars and their positions.[2] Hipparchus's successor, Ptolemy, included a catalogue of 1,022 stars in his work the Almagest, giving their location, coordinates, and brightness.[3]

In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magnitudes and star color; furthermore, he provided drawings for each constellation, which are depicted in his Book of Fixed Stars. Ibn Yunus observed more than 10,000 entries for the Sun's position for many years using a large astrolabe with a diameter of nearly 1.4 metres. His observations on eclipses were still used centuries later in Simon Newcomb's investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn.[4] In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within approximately 20 minutes of arc.[5]

In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, with a precision of 15–35 arcsec.[6] Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using the "observational clock" he invented.[7] When telescopes became commonplace, setting circles sped measurements

James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earth's axis. His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel, the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni.

Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, mostly by use of the filar micrometer. Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines[8] and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond. This technology made astrometry less expensive, opening the field to an amateur audience.[citation needed]

In 1989, the European Space Agency's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. Operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions, parallaxes, and proper motions of 118,218 stars were determined with an unprecedented degree of accuracy. A new "Tycho catalog" drew together a database of 1,058,332 to within 20-30 mas (milliarcseconds). Additional catalogues were compiled for the 23,882 double/multiple stars and 11,597 variable stars also analyzed during the Hipparcos mission.[9]

Today, the catalogue most often used is USNO-B1.0, an all-sky catalogue that tracks proper motions, positions, magnitudes and other characteristics for over one billion stellar objects. During the past 50 years, 7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec.[10]

Applications

Diagram showing how a smaller object (such as an extrasolar planet) orbiting a larger object (such as a star) could produce changes in position and velocity of the latter as they orbit their common center of mass (red cross).
Diagram showing how a smaller object (such as an extrasolar planet) orbiting a larger object (such as a star) could produce changes in position and velocity of the latter as they orbit their common center of mass (red cross).
Motion of barycenter of solar system relative to the Sun.
Motion of barycenter of solar system relative to the Sun.

Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions. It is instrumental for keeping time, in that UTC is essentially the atomic time synchronized to Earth's rotation by means of exact astronomical observations. Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way.

Astrometry has also been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere.[11] NASA's planned Space Interferometry Mission (SIM PlanetQuest) (now cancelled) was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of the nearest solar-type stars. The European Space Agency's Gaia Mission, launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets,[12] it can also be used to determine their mass.[13]

Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics. By measuring the velocities of pulsars, it is possible to put a limit on the asymmetry of supernova explosions. Also, astrometric results are used to determine the distribution of dark matter in the galaxy.

Astronomers use astrometric techniques for the tracking of near-Earth objects. Astrometry is responsible for the detection of many record-breaking Solar System objects. To find such objects astrometrically, astronomers use telescopes to survey the sky and large-area cameras to take pictures at various determined intervals. By studying these images, they can detect Solar System objects by their movements relative to the background stars, which remain fixed. Once a movement per unit time is observed, astronomers compensate for the parallax caused by Earth's motion during this time and the heliocentric distance to this object is calculated. Using this distance and other photographs, more information about the object, including its orbital elements, can be obtained.[14]

50000 Quaoar and 90377 Sedna are two Solar System objects discovered in this way by Michael E. Brown and others at Caltech using the Palomar Observatory's Samuel Oschin telescope of 48 inches (1.2 m) and the Palomar-Quest large-area CCD camera. The ability of astronomers to track the positions and movements of such celestial bodies is crucial to the understanding of the Solar System and its interrelated past, present, and future with others in the Universe.[15][16]

Statistics

A fundamental aspect of astrometry is error correction. Various factors introduce errors into the measurement of stellar positions, including atmospheric conditions, imperfections in the instruments and errors by the observer or the measuring instruments. Many of these errors can be reduced by various techniques, such as through instrument improvements and compensations to the data. The results are then analyzed using statistical methods to compute data estimates and error ranges.[citation needed]

Computer programs

In fiction

See also

References

  1. ^ Walter, Hans G. (2000).
  2. ^ Kanas, Nick (2007). Star maps: history, artistry, and cartography. Springer. p. 109. ISBN 0-387-71668-8.
  3. ^ p. 110, Kanas 2007.
  4. ^ Great Inequalities of Jupiter and Saturn
  5. ^ Lankford, John (1997). "Astrometry". History of astronomy: an encyclopedia. Taylor & Francis. p. 49. ISBN 0-8153-0322-X.
  6. ^ Kovalevsky, Jean; Seidelmann, P. Kenneth (2004). Fundamentals of Astrometry. Cambridge University Press. pp. 2–3. ISBN 0-521-64216-7.
  7. ^ Tekeli, Sevim (1997). "Taqi al-Din". Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Kluwer Academic Publishers. ISBN 0-7923-4066-3.
  8. ^ CERN paper on plate measuring machine USNO StarScan
  9. ^ Staff (1 June 2007). "The Hipparcos Space Astrometry Mission". European Space Agency. Retrieved 2007-12-06.
  10. ^ Kovalevsky, Jean (1995).
  11. ^ Nature 462, 705 (2009) 8 December 2009 doi:10.1038/462705a
  12. ^ ESA - Space Science - Gaia overview
  13. ^ "Infant exoplanet weighed by Hipparcos and Gaia". 20 August 2018. Retrieved 21 August 2018.
  14. ^ Trujillo, Chadwick; Rabinowitz, David (1 June 2007). "Discovery of a candidate inner Oort cloud planetoid" (PDF). European Space Agency. Archived (PDF) from the original on 26 October 2007. Retrieved 2007-12-06.
  15. ^ Britt, Robert Roy (7 October 2002). "Discovery: Largest Solar System Object Since Pluto". SPACE.com. Retrieved 2007-12-06.
  16. ^ Clavin, Whitney (15 May 2004). "Planet-Like Body Discovered at Fringes of Our Solar System". NASA. Archived from the original on 30 November 2007. Retrieved 2007-12-06.

Further reading

  • Kovalevsky, Jean; Seidelman, P. Kenneth (2004). Fundamentals of Astrometry. Cambridge University Press. ISBN 0-521-64216-7.
  • Walter, Hans G. (2000). Astrometry of fundamental catalogues: the evolution from optical to radio reference frames. New York: Springer. ISBN 3-540-67436-5.
  • Kovalevsky, Jean (1995). Modern Astrometry. Berlin; New York: Springer. ISBN 3-540-42380-X.

External links

This page was last edited on 18 November 2019, at 19:45
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