Stellar parallax

[Tzarkoth]

How accurate is this measurement for very distant objects?

Given the base length is 2 AU, presumably we are talking about looking at the same object exactly 6 months apart, given the rotation of the Earth or the orbit of satellite taking the images, and the motion of the Sun about the galactic center ... wouldn't significant errors creep into the calculations?

[Veeger]

Observations from earth based observatories were reasonably accurate for close stars but because the angles are so small, there was a practical limit to how good the measure could be (somewhere around 800 ly or less). In 1989, the Hipparcos satellite was launched which extended the base angle and allowed measurements to be 200 times more accurate then earth bound instruments.

http://www.to.astro.it/astrometry/Astrometry/HIPPARCOS.html

The upcoming Gaia mission will improve the measures even more and extend the accuracy limit to over 10,000 ly.

[ngc3314]

How accurate is this measurement for very distant objects?

Given the base length is 2 AU, presumably we are talking about looking at the same object exactly 6 months apart, given the rotation of the Earth or the orbit of satellite taking the images, and the motion of the Sun about the galactic center ... wouldn't significant errors creep into the calculations?

6 months is optimal, but other time periods can be (and are) used as long as the right baseline goes into the calculation (the projection of the baseline perpendicular to the line of sight). The solar motion drops ot because the parallax shift exhibits a sine-wave behavior (of one year period) with the relative motion of Sun and target providing a linear drift (which can be distinguished as long as the data extend much longer). The errors are generally set by the error in the parallax angle measurement itself, translating to a distance error that balloons with increasing distance. In principle, one could think about launching something like Hipparcos into a solar orbit much bigger than 1 AU (with correspondingly longer mission lifetime, but so far the gain in gong to orbit has been so large for big samples that spaceborne parallax data have come from Earth orbit.

[StupendousMan]

How accurate is this measurement for very distant objects?

Given the base length is 2 AU, presumably we are talking about looking at the same object exactly 6 months apart, given the rotation of the Earth or the orbit of satellite taking the images, and the motion of the Sun about the galactic center ... wouldn't significant errors creep into the calculations?

The answer to your first question depends on which instrument is being used to make measurements. The best ground-based single-telescope optical measurements, such as those by Greenwood, and the best space-based single-telescope optical measurements, such as those by Hipparcos, have precisions of order 1 or 2 milliarcseconds. That means that the distances derived from these measurements are "accurate" out to something like 100 to 500 pc, depending on your definition of the word "accurate." For details on that, see

http://stupendous.rit.edu/richmond/answers/parallax.txt

Note that some ground-based measurements using several telescopes and interferometry have recently started to make more precise measurements in the millimeter-wave portion of the radio spectrum. Astronomers who study star-forming regions in the Milky Way can pinpoint the location of masers to small fractions of a milliarcsecond, allowing them to measure distances out to several kiloparsecs. See

http://spiff.rit.edu/richmond/asras/mw_rot/mw_rot.html

for a short summary of some semi-recent work in this area.

If you look at some of the graphs in that summary, you'll see that astronomers can indeed take into account the motion of the Sun relative to the target objects. Plots of position versus time don't show a simple back-and-forth sinusoidal curve, but rather a sinusoidal curve on top of a linear trend. The linear trend is due to the relative motion of the Sun and the target object. Astronomers can remove this trend and make a fit to the residual sinusoidal motion, and so measure the distance accurately.

[tdvance]

FYI--not a direct answer to the question, but there is a book called "Parallax" that may be of interest--its the history of finding how far the stars are, all the things that went wrong, etc. For example, the time it takes light to go from the objective to the eyepiece of the telescope affected the measurements and had to be taken into account! It's a very interesting read.

[mugaliens]

The upcoming Gaia mission will improve the measures even more and extend the accuracy limit to over 10,000 ly.

Another consideration is that we don't measure these angles directly, which is very difficult. Rather, we simply note the relative positional differences on an exposed plate (ok, showing my age, here...), then calculating a distance based on the variance.

[StupendousMan]

FYI--not a direct answer to the question, but there is a book called "Parallax" that may be of interest--its the history of finding how far the stars are, all the things that went wrong, etc. For example, the time it takes light to go from the objective to the eyepiece of the telescope affected the measurements and had to be taken into account! It's a very interesting read.

I don't understand the effect you mention here. Can you please explain in some detail? I've done a little parallax work myself, and haven't run across this source of error in the past.

Perhaps I'm just thinking of a different name or description of this particular source of error. If you could provide more information, I might be able to figure it out.

[tdvance]

Basically, the earth moves in the time it takes the photon to go from objective to eyepiece. Thus, the telescope must be pointed, not directly at the star for the star to be centered, but a tiny amount off. The telescope used, if I remember right, was one permanently pointing straight upward (which limited the choice of star--61 Cygni was used because it passed through the field of view once per day) so it was more a timing issue than an aiming issue, but it did have the effect of inflating the "parallax"--as the motion of the earth pushed the angle one way on one side of the sun, and pushed the angle the other way on the other side of the sun. In the case of 61 Cygni, this effect was bigger than the real parallax.

[StupendousMan]

Basically, the earth moves in the time it takes the photon to go from objective to eyepiece. Thus, the telescope must be pointed, not directly at the star for the star to be centered, but a tiny amount off. The telescope used, if I remember right, was one permanently pointing straight upward (which limited the choice of star--61 Cygni was used because it passed through the field of view once per day) so it was more a timing issue than an aiming issue, but it did have the effect of inflating the "parallax"--as the motion of the earth pushed the angle one way on one side of the sun, and pushed the angle the other way on the other side of the sun. In the case of 61 Cygni, this effect was bigger than the real parallax.

Oh, I see, you are talking about the aberration of starlight.
Right.

[Veeger]

When measuring the locations of stars to milliarcsecond accuracy, astronomers must not only account for light time, but refraction by gravity in the solar system, movement of the earth, and the movement of the instrument/observer at the relevant location on earth with respect to the center of the earth. In addition and this goes without saying, the target must be well above area of atmospheric refraction. Meridian transit instruments work well for this purpose.

[ngc3314]

Oh, I see, you are talking about the aberration of starlight.

In more detail - aberration was identified by John Bradley from London, using a zenith telescope on Gamma Draconis. He was able to distinguish it from genuine parallax because, first, the phase of the angular shift is 90 degrees different between the two (maximum aberration is when the transverse velocity component is largest, when parallax shift is zero), and eventually because all stars in a small region of sky show the same pattern tracing out an ellipse (axial ratio depends on ecliptic latitude) during the year. In hindsight, this was just as strong as a sign of the Earth's orbital motion as parallax itself would eventually become (essentially, one measures the derivative of the other).

[Tzarkoth]

Thanks for the answers and the links folks. I've got a follow up question in mind but I need to reread all of the above to make sure it's not already been answered.

I've got a slightly off topic question though, looking at the sig for tdadvance, '(Bowie, MD, US, North America, Earth, Sol System, Vega region, Local Bubble, Orion arm, Milky Way Galaxy, Local Group, Virgo A Cluster, Virgo supercluster, the universe in which spock is clean shaven).'

Aren't we on the Orion spur of the Perseus arm of the Milky Way Galaxy?

[antoniseb]

Aren't we on the Orion spur of the Perseus arm of the Milky Way Galaxy?

Make a left at Arcturus, and follow the signs that say "Hospital".

[tdvance]

That's probably true, since by some reckonings, the Orion Arm is just a spur connecting the Perseus Arm to....I forgot which other arm, Saggitarius?

"Turn Left at Arcturus"--good book.

[eburacum45]

Yep. The Orion Spur, or Arm, is between the Sagittarius Arm and the Perseus Arm. On recent maps the Sagittarius Arm is shown as much smaller than the Perseus Arm; see here, for example
http://en.wikipedia.org/wiki/File:236084main_MilkyWay-full-annotated.jpg
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