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 Subject: astronomy Category: Miscellaneous Asked by: mongolia-ga List Price: \$20.00 Posted: 16 Nov 2003 05:57 PST Expires: 16 Dec 2003 05:57 PST Question ID: 276376
 ```When distances are quoted to Astronomical Objects I would like to know what would be the approximate error in the distance give? I am obviously not looking for an exact measurement but lets say it could a guide( 1cm , 1 metre, 1 kilometre, 100000 kilometre, one tenth of a light year, 1 light year, 100 light years etc) Here are some specific objects wher I would like to know the accuracy of the distance measured: - Moon - Pluto - Neptune - Proxima Centauri - The star Rigel - Globular Cluster in Hercules - Androemda Galaxy - A Galaxy in the Virgo group - The quasar 3c273 Thanks Mongolia For an extended object such as a star cluster or Galaxy , I would be looking for the accuracy to a particular point or perhaps star within the object.``` Request for Question Clarification by techtor-ga on 16 Nov 2003 07:00 PST ```Hello Mongolia, May I know if you mean distances of the objects you listed from the earth, or from another point?``` Clarification of Question by mongolia-ga on 19 Nov 2003 12:56 PST ```To clarify I would say for stellar objects (e.g. a globular cluster) it could be to the central point of the sun. It could also be to the centre of teh earth at a specific point in time. If we know the distance to Proxima centauri for example to such an accuracy that the earth's point in its orbit around the sun would make a difference ,then of course I would talking about the distance at a specific point in time. It if serves to simplfly the issue then perhaps it should be to the cental point of the sun. Regarding the issue brought by the commentor , I would of course be looking at the latest and what is considered the most accurate method. If different methods of measuring a distance yield different answers, this in of itself would determine the error in the measurement of the distance. I fully accept that ther is a certain subjectivity in answering this question. Mongolia``` Clarification of Question by mongolia-ga on 22 Nov 2003 05:21 PST `any progress on this?` Request for Question Clarification by techtor-ga on 22 Nov 2003 08:42 PST ```Hello Mongolia, Your question proved to be more difficult that I thought. I haven't found any web pages discussing accuracy of astronomical distances since it does not seem to be a very popular topic for discussion these days. I'll keep on looking though.``` Request for Question Clarification by techtor-ga on 22 Nov 2003 08:58 PST ```I had forgotten to mention, what makes this difficult for me (on the premise that you are looking for the margin of error in the recorded measurements) is that bodies in space do not have perfectly circular orbits, so the distance of one body from another actually varies, and there seems to be no definite standard to use in getting the margin of error. I doubt if even average distance is hard to use as a standard since the celestial bodies are in constant motion, so it seems futile to test how accurate one's distance measurement is. If you're looking for something about the accuracy of the methods used to measure distance, I haven't found anything yet on it. If I can't, perhaps someone else with a better knowledge of astronomical metrics can.```
 Subject: Re: astronomy Answered By: hlabadie-ga on 23 Nov 2003 08:49 PST Rated:
 ```The distance to the Moon has been measured by Lunar Laser Ranging, utilizing lasers that are transmitted through telescopes on Earth to reflectors that had been placed on the lunar surface by Apollo astronauts and a Russian lunar lander. The distances have been calculated so precisely that fractional differences in centimeters have been measured. The Moon is receding from the Earth at a rate of 3.8 cm per year. Gravitational and Relativistic Physics (GRP) http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html "Ranging has provided the most accurate technique available for measuring the Moon's rotation and orbit. It has also determined that the length of an Earth day has distinct small-scale variations. Also observed are crustal plate drifts on Earth. Measurements show that the Moon is moving away from the Earth at a rate of about 3.8 centimeters per year. Laser ranging has also made possible a wealth of new information about the dynamics and structure of the Moon." ILRS Satellite Missions LUNAR http://ilrs.gsfc.nasa.gov/satellite_missions/list_of_satellites/lunar.html Distances to the inner planets of the Solar System have been determined by radar ranging, in a manner similar to that used in laser ranging of the moon. The distances to the outer planets Neptune and Pluto are such that traditional means of measurement by triangulation are used. Observations from widely spaced Earth observatories provide parallax measurements from which the distances to the most distant planets can be calculated. Calculations are based upon tables for planetary ephemerides, the most accurate being produced by the Jet Propulsion Laboratory, which directs many interplanetary missions and must have precise figures by which navigation of spacecraft can be accomplished. The margin of error for the planets Neptune and Pluto are such that respective errors of 4000 and 10000 km are normal. The Solar System http://heasarc.gsfc.nasa.gov/docs/cosmic/solar_system_info.html "Pluto, normally the most remote planet, has an average distance of 5,913,520,000 km from the Sun." [...] "One of the most accurate ways to measure the distances to the planets is by bouncing radar off them, or sending a spacecraft there, which can send a radio signal back to the Earth that can be timed. Radar is essentially microwave electromagnetic radiation (microwaves fall under the radio spectrum). Since electromagnetic radiation, in all of its forms, is light, we know that radar travels at the speed of light - 3 x 10^5 km/s. We know that a distance traveled is equal to the time it takes to travel that distance, times the velocity used to travel that distance (x=vt). If we bounce radar off a planet, and measure the time it takes the signal to get there and back, we can use this information to calculate the distance of the planet. In the absence of spacecraft or radar, one can, in principle, use triangulation to measure the distance to a planet. That is, measure the celestial position of a planet from two different points on Earth simultaneously; knowing the difference in the angles that were measured, and the distance between the two points on Earth, the distance to the planet can be calculated. Even with modern technology, this is not trivial - even with a baseline of 10,000 km (about as long a baseline that is possible on Earth), the angular offset at two sites must be measured to be accurate to 4 seconds of arc (1/450th of the diameter of a full moon) to achieve ~10% accuracy in the distance to Venus, our nearest neighbor." Radar http://starchild.gsfc.nasa.gov/docs/StarChild/questions/radar.html "This method has been used in one form or another to determine the distances to all of the planets in our solar system (except Pluto, which we have not visited)." Description of JPL Solar System Ephemeris http://www.gb.nrao.edu/~rfisher/Ephemerides/ephem_descr.html Help for EPHEMERIS http://www-mipl.jpl.nasa.gov/vicar/vicar201/html/vichelp/ephemeris.html "One method of describing the accuracy of the positions provided in DE403 is to consider the angles between various ephemeris objects as viewed from Earth. If the two objects observed are taken from the list (Sun, Mercury, Venus, Mars, Moon) the angles computed from the ephemeris positions are accurate to one or two milli-arcsecond.(This assumes all appropriate corrections are applied for light time, stellar aberration, and relativistic effects to the ephemeris derived positions.) If you add the barycenter of Jupiter to this list, uncertainty in ephemeris derived angles may grow to a few hundredths of an arcsecond. Adding Saturn, Uranus and Neptune will raise the uncertainty level to approximately 0.1 arcseconds. Finally, adding Pluto to the list raises the observable errors to 0.3 arcseconds for the present and increasing into the future. Radial distances to the centers of objects follow a similar trend. The radial distances between the inner objects of the solar system as computed via the ephemeris are accurate to 1 to 2 km. The distance between the Earth and the Jupiter Barycenter is accurate to better than 10 km. The uncertainty in the distances to Saturn, Uranus and Neptune are approximately 1000, 2000 and 4000 km respectively. For Pluto, the radial distance from earth may be in error up to 10000 km for the present and growing into the future." New Accuracy Levels for Solar System Ephemerides http://www.bdl.fr/sympo/abstracts/Standish.txt The JPL HORIZONS http://ssd.jpl.nasa.gov/horizons.html "The JPL HORIZONS /On-Line/ Solar System Data and Ephemeris Computation Service provides access to key solar system data and flexible production of highly accurate ephemerides for solar system objects (163000+ asteroids and comets, 128 natural satellites, 9 planets, the Sun, L1, L2, select spacecraft, and system barycenters)." The Hipparcos Space Astrometry Mission http://astro.estec.esa.nl/Hipparcos/ The Hipparcos and Tycho-1 Databases ftp://cdsarc.u-strasbg.fr/pub/cats/I/239/ The Tycho-2 Database http://www.astro.ku.dk/~erik/Tycho-2/ The Guide Star Catalog ftp://adc.gsfc.nasa.gov/pub/adc/superseded/1/1220/ Based upon the observations of the European Space Agency's (ESA) High Precision Parallax Collecting Satellite (HIPPARCOS), within 30 light years of Earth, the accuracy of distance measurements is about 1 per cent. Within 150 ly, the accuracy is about 5 per cent. Within 300 ly, the accuracy is about 10 per cent. Beyond those distances, however, the error and be as high as 50 percent, the greater the measured distance from our solar system. Extremely large distances are calculated by measuring the Doppler shift of spectra, and this requires an accurate value for the Hubble constant. The different means by which a value for the Hubble constant can be determined can yield differing numbers, and thus differing results from the calculations for distance can result. The standard means of getting a value is to find some distant object to which a reasonably firm distance can be attached. Choosing such an object is, however, contentious. One generally accepted means uses Cepheid variable stars. This method is itself disputed, however, by some astronomers, because of the underlying assumptions, themselves of doubtful validity. A second method relies upon masers, and has fewer assumptions. It gives a significantly different value. There is no agreement on the better method. Therefore, even distances within the Milky Way galaxy have a large margin of error built into them. Distances to the Sun and Stars http://www.uwgb.edu/dutchs/CosmosNotes/distance.htm "Hipparcos worked by observing stars through two telescopes aimed 58 degrees apart. The light from the two telescopes was merged into a detector with a fine grid of wires. As the satellite rotated, different stars passed through the field of view of each telescope and blinked on and off as the stars passed across the grid of wires. These observations allowed extremely accurate relative positions of the stars to be determined. The relative positions of all the stars could then be combined into an extremely accurate catalog of star positions across the entire sky. For 118,000 selected stars, Hipparcos measured their parallax accurate to .001 second of arc. That's the apparent diameter of a quarter at a distance of 5000 kilometers, or putting a quarter in New York and viewing it from San Francisco. It's also the amount the hair on a person a meter away appears to grow in one second. A secondary mission named Tycho measured another million stars to an accuracy of "only" 0.01 second." [...] "Accuracy Level Earth-Based Data Hipparcos Data 1 percent 50 stars 10 light years 400 stars 30 light years 5 percent 100 stars 20 light years 7,000 stars 150 light years 10 percent 1000 stars 50 light years 28,000 stars 300 light years" [...] "When we say that the bright star Deneb is 1600 light years away, for example, the distance is an estimate based on its brightness and spectral type. The distance could easily be 25% larger or smaller. Deneb is still too far away for even Hipparcos to measure accurately." [...] "Cepheid Variables The cluster method works out to a thousand light years or so. Fortunately, within that distance are stars that give us a yardstick to distant galaxies. These are the Cepheid Variables. Cepheids are named for a star in the constellation Cepheus, the first star of this type discovered, but the most famous Cepheid, and also the nearest, is Polaris, the Pole Star. Polaris is about 300 light years away and varies in brightness too slightly to be obvious to the unaided eye. Before Hipparcos, the distance to Cepheids had to be determined indirectly by the cluster method, but now the distances to several have been determined directly." Cosmic Yardsticks: Pulsing Stars Unlock Universe's Secrets http://www.space.com/scienceastronomy/astronomy/pulsing_cepheids_000927-2.html "Astronomers calculate the Hubble Constant by observing the "Doppler shift" in the color of light galaxies emit, determining how fast galaxies are moving away from us. Then, they combine that with the distances to those galaxies, as measured using Cepheid stars. Existing methods have a 30-percent to 50-percent margin of error for measuring the distance to a single Cepheid, although measuring numerous Cepheids sharply reduces that margin, Lane said. The new method now has a 15-percent maximum error margin for measuring distance to one Cepheid, but that should drop to less than 3 percent when the method is used with bigger, advanced interferometers, he added." The Distance to the Galactic Center http://www.astrophys-assist.com/educate/distance/distance_gc.htm "The distance between the Sun and the Galactic Center, referred to as R_o , is an important one. Many of the measured parameters of galactic objects such as distance, mass and luminosity are directly related to R_o , which has an estimated value of 8.0 kilo parsecs (~26,000 light years), with a standard error of about 0.5 kilo parsecs." [...] "Salim and Gould expect to be able to determine R_o to an accuracy within 4% as early as the year 2002. While this is indeed an improvement over the current standard of error, it is a slight one. Nonetheless, the astronomical community awaits their results." NASA's measure of the universe questioned http://www.floridatoday.com/space/explore/stories/1999b/060299h.htm "A technique using a radio-telescope is a "golden ruler" for measuring cosmic distances and calls into question the conclusions announced by astronomers using the Hubble Space Telescope who were supported by the National Aeronautics and Space Administration, a researcher said Tuesday. "Ours is a direct measurement, using geometry, and is independent of all other methods of determining cosmic distances," said Jim Herrnstein of the National Radio Astronomy Observatory. "It is the most precise distance ever measured to a remote galaxy."" [...] "He said the new technique shows a 15 to 20 percent margin of error in the results announced last week by a NASA team led by Wendy Freedman of the Carnegie Institute of Washington. The NASA team using the space telescope said last week that it had successfully achieved the goal of measuring within an uncertainty of only 10 percent the speed at which the universe is expanding, a value called the Hubble constant. Herrnstein said this calculation is off by 15 to 20 percent. He based his conclusion on the difference in calculated distance to a specific galaxy using his technique compared with the calculation method used by the NASA group." [...] "But Herrnstein said the technique using Cepheids is far less accurate than his new method that directly measures the motion of gas around a galaxy. NGC 4258 is surrounded by a rotating cloud of gas. Within this gas cloud is water vapor, which tends to amplify radio signals. This creates radio "hot spots" called masers. The orbital speed of masers between NGC 4258 and Earth was measured in 1994, and again every few months over the following three years. By determining the speed at which the masers were moving, the astronomers created a triangle with the first maser position at one angle, the latest position at a second angle, and the galaxy center at the third angle. Measuring the angles gives the distance. The distance to NGC 4258 was calculated at 23.5 million light years, with an accuracy to within 4 percent. This distance has been calculated using the Cepheid star technique at 27 to 29 million light years. Herrnstein said that the distance measure using Cepheid stars is based on a series of assumed values, such as the distance to the Large Magellanic Cloud, a galaxy neighbor to the Milky Way. These assumed values, said Herrnstein, have a greater margin of error than does the direct measuring technique he is using." Astronomers dispute NASA gauge of universe's age http://seti.sentry.net/archive/public/1999/6-99/0085.html Quasar 3C273 http://www.ne.jp/asahi/stellar/scenes/object_e/3c273.htm Thus, the margins of error: Moon - fractional centimeters Neptune and Pluto - thousands of kilometers Proxima Centauri (4.22 ly) - ~ 1 per cent The star Rigel (910 ly) - greater 10 per cent less 25 percent Globular Cluster in Hercules (There are four globular clusters in Hercules, the nearest, M13, is 13000 ly from the Sun: M93 is 25000 ly away: 6229 is 102000 ly distant.) - margin of error greater than 25 per cent Spiral Galaxy in Andromeda, M31 (~2 million ly) - greater than 25 per cent A Galaxy in the Virgo group (3000 galaxies, ~65 million ly) - greater than 25 per cent The Quasar 3C273 (~2.5 billion ly) - greater than 25 per cent, possibly as much as 40 percent SEARCH TERMS ://www.google.com/search?q=astronomical%20distances%20margin%20error&sourceid=mozilla-search&start=0&start=0&ie=utf-8&oe=utf-8 ://www.google.com/search?q=lunar+laser+ranging&btnG=Google+Search&hl=en&lr=&ie=UTF-8&oe=utf-8&safe=off ://www.google.com/search?q=high+precision+parallax+collecting+satellite&btnG=Google+Search&hl=en&lr=&ie=UTF-8&oe=utf-8&safe=off ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=utf-8&safe=off&q=planetary+ephemerides&btnG=Google+Search ://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=utf-8&safe=off&q=radar+ranging+planets&btnG=Google+Search ://www.google.com/search?q=quasar%203c273&sourceid=mozilla-search&start=0&start=0&ie=utf-8&oe=utf-8 hlabadie-ga``` Request for Answer Clarification by mongolia-ga on 12 Dec 2003 15:30 PST ```I am very impressed with your comprehensive answer. (I will rate it shortly) However I must say I am surprised by the huge uncertainy for anything beyond the moon. Regarding Neptune I would have thought it's distance would have been known within a few tens of miles considering it has been visited by a spaceprobe and that that Radar ranging should be possible. When one considers a star like Rigel (which in our Backyard in cosmological terms) a error measurement between 10% and 25% sounds very large. However again thank you for the effort you have put into my question Regards Mongolia``` Clarification of Answer by hlabadie-ga on 12 Dec 2003 16:41 PST ```As regards Neptune, it is at the outer limits of direct measurement within the Solar System, and navigation to the planet naturally entails numerous corrections in the flight path of spacecraft, both for errors in measurement and for gravitational perturbance. An error of only 4000 km at that distance on a first estimate is not excessive, I think. It is an average, I believe. With respect to Rigel, the problem is the minute differences detectable in parallax. HIPPARCOS demonstrates that even a relatively near stellar object is still a very great distance away, and the difficulty in measuring distance with even a very precise instrument above the atmosphere is challenging. hlabadie-ga``` Clarification of Answer by hlabadie-ga on 13 Dec 2003 05:02 PST ```Planet Neptune: diameter, distance from Sun Information about the planet Neptune http://www.the-solar-system.net/planet-neptune/neptune-fact-sheet.html To give the margin of error some perspective, 4000km is less than the radius of the Earth and less than 1/12th of the diameter of Neptune. In other words, if one aimed at the center of Neptune from Earth, one could miss one's target by 4000 km and still hit Neptune by a comfortable margin. Put a different way, 4000km is only 1125000th of the average distance of Neptune from the Sun, a remarkably small fraction. "Neptune's Diameter: 49,528 km, 3.9 Earth Diameters" [...] "Neptune Orbital parameters Semimajor axis (10^6 km) 4,495.06 Sidereal orbit period (days) 60,189 Perihelion (10^6 km) 4,444.45 Aphelion (10^6 km) 4,545.67" hlabadie-ga```

 ```mongolia... Since you are asking for the accuracy of the measurements it would also help to know "as measured by whom, and/or by what method?", since different sources for these measurements will no doubt reflect different degrees of error, possibly based, in part, on different methods of measurement.```
 ```The distance to the moon has been measured so accurately by laser that it is known that it is receding from the Earth at rate of 3.8 cm per year. Measurements of the distance of the planets from the Earth are made with radar and by triangulation. Naturally, those distances have a greater margin of error. Distances to nearby stars (within 300 light years) have been measured by satellites using parallax techniques. Within 30 light years of Earth, the accuracy of distance measuresments is about 1 per cent. Within 150 ly, the accuracy is about 5 per cent. Within 300 ly, the accuracy is about 10 per cent. Beyond those distances, the error can vary by 20-40 per cent. hlabadie-ga```
 ```Thank you for the tip and the rating. hlabadie-ga```
 ```The distance to the moon has been measured (repeatedly) plus or minus one part per billion. Using these baselines and computers, the distance to the Moon can calculated for any date and time (in the last 100 years) to better accuracy than one part per million. Perhaps one part per million is also available for Neptune and all the other planets except Pluto. Error for Pluto may be about one percent. Perhaps 2% for the three stars in the Centarii system. Probable error increases with distance, but we all but surely have the decimal point in the right place. Neil```