NavList:

Hello Meg. I would answer your fundamental question, "How has our knowledge of the Polynesian Celestial Navigation system helped to develop modern Star based navigation," this way: not at all. The Polynesian system of celestial navigation, and the western system of celestial navigation, are two completely different animals. 

The western system is a collection of techniques that a navigator uses to determine his or her location, i.e., latitude and longitude, on the surface of the Earth. (Or above it, if the navigator is in an aircraft). The navigator then uses that information to figure out to get to where they want to go. (E.g., how far is it to the destination, in which direction, how far and in what direction have they already travelled, etc., etc.) The western system is one that can be learned quite quickly, and with some diligent practice, the navigator can become reasonably adept in short order. Celestial navigation, as practised by Polynesian navigators, is more of a "in which direction, and how long does it take, to get from one place to another" proposition. By means of years of experience, together with knowledge garnered from more experienced navigators, the Polynesian navigator knows that, at a certain time of year, a star, or group of stars, will appear in the evening sky, or at midnight, or morning sky, in the direction of Island B, as seen from Island A. (Or you keep that star on your starboard beam, or port quarter, etc.) The Polynesian navigator integrates that celestial navigation information with other cues, e.g., the colour of the sea, the direction of the predominant swell, cloud formations, the flight patterns of sea birds, etc., etc., to stay on course, and know how far along they are. This requires years of learning, and impressively prodigious feats of memory.

It's somewhat analogous to the different approaches to a navigating in a big city applied by a tourist, and by a taxi driver. The tourist looks around for street signs, or a landmark, opens Google maps, or asks Siri, whatever, to figure out where they are. That's the equivalent of the western navigator fixing their position by observing celestial bodies. Then they would look at a paper map, or use a smartphone app, or a GPS device to figure out how to get from where they are to where they want to be. The taxi driver (and I have London, England's famous taxi drivers in mind here), by dint of experience, knows where they are, and again, from years of driving and study, just knows how to get from where they are to wherever it is their fare wants to go. That's the essence of the Polynesian navigator's technique, as I understand it. 

1. How popular is celestial navigation?

It is mostly a hobby activity pursued by individuals with a predilection for esoteric and arcane technology and practices. However, the US Navy has reintroduced celestial navigation training for its bridge watchkeeping officers, per this National Public Radio article from February, 2016:

https://www.npr.org/2016/02/22/467210492/u-s-navy-brings-back-navigation-by-the-stars-for-officers And even NASA is experimenting with the use of sextants in space; see this article on NASA's website: https://www.nasa.gov/mission_pages/station/research/experiments/2692.html

Some of the hobbyists are yachtsmen and women, and other mariners, who enjoy doing things the old-fashioned way. 

2. How trustworthy is Celestial navigation as a main type of navigating?

A knowledgeable, skilled navigator can determine his or her position within a nautical mile or so, given favourable conditions and serviceable equipment. So, the real question might be, how trustworthy is the navigator who's doing the celestial navigation for you?

3.  What type of technology is used in Celestial Navigation?

The sextant itself is a precision instrument, that requires advanced (i.e., post Industrial Revolution) metallurgical, milling/machining, glass-making, lens-grinding, and manufacturing techniques. An accurate source of time is required. (Note that time can be determined  through a specialized celestial navigation technique.) A scientific calculator, or access to various mathematical tables to facilitate the solution of spherical trigonometric formulas are required, together with a source of astronomical data tailored for celestial navigation purposes, i.e., a nautical almanac such as the one published jointly by the US Naval Observatory, and Her Majesty's Nautical Almanac Office. (There is a whole other pile of technology behind the production of the almanacs.) Lastly, some means of electronically or manually plotting the results of the calculations is needed. 

4. What type of people are involved with Celestial Navigation?

Just about anyone with an interest, the time, and access to the equipment. 

5. Currently, how much do we as a population know about Celestial navigation?

I'm not sure if you're asking what proportion of the population knows about celestial navigation, or how well-developed or mature are the underlying theories, and the techniques employed.

If it's the former, I would hazard a guess that only a very small proportion of the population could even hazard a guess as to what celestial navigation is. It has always been a niche skill set, peculiar to blue water sailors, surveyors, and navigators of long-range aircraft. And thanks to the proliferation of radio aids to navigation - in particular, global navigation satellite systems (of which the American GPS is the most widely known, in the West, at least), celestial navigation is a skill set which is fast disappearing, much like the ability to drive vehicles with manual transmissions.

If it's the latter, then I would say it's a very mature method of navigation. Its origins are millennia old, but it really came into its own in the late 18th century, when manufacturing techniques were able to produce very precise navigation instruments that do not differ greatly from today's sextants, and thanks to  Johannes Kepler and the mathematician-astronomers who followed in his footsteps, the ability to produce precise and accurate predictions of the future positions of those celestial bodies useful for celestial navigation purposes, and who developed the mathematical techniques to turn observations of those bodies into a latitude and longitude.

6. How accurate is this knowledge?

Again, I'm not sure I understand the question, but I will answer, very accurate. The astronomical data published in the almanacs (or that can be generated in one's own computer, with the right software) is extraordinarily precise, and accurate. The limiting factor is the precision of the sextant, and the skill of the navigator. In practice, a good navigator, under nominal conditions, can determine their position within a nautical mile. 

7. What sort of techniques are used in celestial navigation?

There are hundreds if not thousands of books that answer that question. But very, very basically it comes down to using the sextant to measure the elevation above the horizon of some celestial body[ies], and that information plus the time of the observation is used to solve a spherical trigonometry problem that results in a position on the Earth's surface. A less commonly technique is to measure the angular separation between the moon and some other suitable celestial body, applying some math to determine Greenwich Mean Time, thus obviating the need for a chronometer or some other accurate source of GMT (e.g., a radio time signal). GMT can be compared to local time (which can be ascertained by celestial observation) and longitude determined. Latitude can be determined by observing the meridian passage of some celestial body, typically the sun or the moon. 

8. Do you know of any techniques that were developed from the Polynesians?

And incorporated in Western celestial navigation? No. 

9. How much to you know about Polynesian celestial navigation?

Only that which I've gleaned from reading books like We, The Navigators (Lewis, D.H., 1972), and following the exploits of groups like the Polynesian Voyaging Society.