Excepting the closer stars, it seems that determining distances of stars is at best educational guess work. Has there ever been any consideration of placing an observatory upon the planet Pluto, or somesuch place, for the express purpose of determining stellar parallax with a considerably larger radius? How many stars can have their distances measured with a reasonable degree of certainty, and to what distance limit? Has the distance of any cepheid variable ever been verified by trigonometric parallax? Though I've asked the latter question a number of times, I have yet to receive what I consider a definite answer.
You're right, in that distance measurements are extremely difficult in astronomy. Usually, we are happy if we can find the distances to distant objects to within a factor of two! At present, there are no plans to set up an observatory on Pluto or another distant planet, although the Voyager spacecraft are sending back some parallax data from beyond the solar system, and the Hipparcos satellite was specifically designed to seek out precise parallaxes.
Before the Hipparcos sattelite, there were about 50 stars whose distances were measured to within 1% accuracy using ground-based telescopes, out to a distance of about 10 light-years. Distances to about 1000 stars within 50 light-years were known to within 10% accuracy. Before Hipparcos, no Cepheid distances could be determined directly using the parallax method, but had to be measured using an intermediate method known as the "Cluster Method," in which the bulk motion of a cluster of stars is used to obtain their distance.
Thanks to Hipparcos satellite, distances to a handful of Cepheids are now known directly. Hipparcos was able to measure the parallaxes for 400 stars within 30 light years to 1% accuracy, and 28,000 stars within 300 light years to 10% accuracy. About 7 or 8 Cepheids are among these, including the North Star, Polaris.
Could you elaborate how the Hipparcos satellite works. Does it revolve around the sun like a planet but at a greater distance than Earth?
Hipparcos orbited the Earth in a roughly geosynchronous orbit, but was equipped with hyper-accurate instrumentation and was therefore able to obtain parallax measurements of unprecedented accuracy.
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.
For more info on the Hipparcos satellite and distance measurements, see the Hipparcos home page.
July 2015 update: In December 2013 a new space telescope called GAIA was launched, with the mission objective of making a 3D map of the galaxy. This telescope will be able to measure stellar distances much more accurately, and for much more distant stars than Hipparcos. Although the data from this mission has not been analyzed and released yet, you can read all about the mission and how the telescope works here.
This page updated on July 18, 2015.