1. How can the earth's orbital diameter be used to measure the distance to a 4.22 ly star?

2. Originally Posted by ivy
How can the earth's orbital diameter be used to measure the distance to a 4.22 ly star?
This sounds a bit like a homework problem, so I'll simply suggest that you do a little homework of your own, using the title of your thread as a search term. After learning about parallax, consider drawing a diagram of the earth at different positions of its orbit, with a distant object drawn on the same picture. Try to work out the geometry quantitatively to get the answer to your question.

Good luck, and feel free to post back for more hints if you get stuck along the way.

3. The distance of 4.22 ly is more than one million times larger than the earth's orbital diameter. Is not the parallax distance of the earth's orbital diameter to short of a distance to measure the distance to a 4.22 ly star? (since the resolution of the Hubble that is the most powerful telescope known to man .1 arcsec)

4. Originally Posted by ivy
The distance of 4.22 ly is more than one million times larger than the earth's orbital diameter. Is not the parallax distance of the earth's orbital diameter to short of a distance to measure the distance to a 4.22 ly star? (since the resolution of the Hubble that is the most powerful telescope known to man .1 arcsec)

Yes, the Hubble's resolution is indeed that value. It may surprise you that the achievable resolution for a parallax-based distance measurement can be considerably better than implied by a simple calculation based on the individual instrument's resolution. One key is the improvements conferred by averaging over many measurements, and over a large field of many stars. Somewhat more sophisticated algorithms than simple averaging are used in practice, but you get the idea. Parallactic resolution achieved with the Hipparcos satellite is as good as 0.001 arcsec, and there are plans (with Gaia) to improve that already-impressive figure by about 3 orders of magnitude.

5. How can the Hipparcos that has a diameter of 1 ft be more powerful than the Hubble that has a diameter of 8 ft? Also, the Hipparacos was launch in 1989 before the Hubble and the James Webb telescope has a diameter of 22 ft and a resolution of .1 arcsec.

6. Originally Posted by ivy
How can the Hipparcos that has a diameter of 1 ft be more powerful than the Hubble that has a diameter of 8 ft? Also, the Hipparacos was launch in 1989 before the Hubble and the James Webb telescope has a diameter of 22 ft and a resolution of .1 arcsec.
You are comparing apples to neutrons. Hipparcos was not intended to image objects per se, but to perform precision astrometry. It is not a question of "more powerful" or "less powerful." It is a question of which platform better measures parallax. Hubble wasn't designed for that function.

The wikipedia article, https://en.wikipedia.org/wiki/Hipparcos, provides more detail, as well as citations of references with much more detail.

7. For a 4.22 ly star, using a/c = cos θ where a is the parallax reference distance (earth's orbital diameter) and c is the distance to the 4.22 ly star and θ is the resolution forms (1.4 x 10^10 m) / (4 x 10^16 meters) = a/c. When a/c --> 0, a/c = θ; consequently, θ = 3.5 x 10^-7 degree or .00126 arcsec which is less than the .002 resolution of the Hipparacos telescope (https://en.wikipedia.org/wiki/Hipparcos) (From Hipparchus to Hipparcos: Measuring the Universe).

8. Originally Posted by ivy
For a 4.22 ly star, using a/c = cos θ where a is the parallax reference distance (earth's orbital diameter) and c is the distance to the 4.22 ly star and θ is the resolution forms (1.4 x 10^10 m) / (4 x 10^16 meters) = a/c. When a/c --> 0, a/c = θ; consequently, θ = 3.5 x 10^-7 degree or .00126 arcsec which is less than the .002 resolution of the Hipparacos telescope (https://en.wikipedia.org/wiki/Hipparcos) (From Hipparchus to Hipparcos: Measuring the Universe).
Yes, I read the full article, which is why I cited it. If you read it more carefully, you will find the following:

Originally Posted by wikipedia
Originally targeting the observation of some 100,000 stars, with an astrometric accuracy of about 0.002 arc-sec, the final Hipparcos Catalogue comprised nearly 120,000 stars with a median accuracy of slightly better than 0.001 arc-sec (1 milliarc-sec).
That is, they achieved twice the accuracy originally targeted. The median accuracy achieved is thus sufficient to make the measurement in your original scenario.

9. The Hipparacos' mirror has a diameter of 11 inches and resolution of .001 arcsec yet the Hubble's mirror diameter is 7.9 ft and has a resolution of .1 arcsec. The Hipparacos is a reflection telescope that mirror is eight times small than the Hubble's reflection mirror yet 100 time more powerful. You state "Hipparcos was not intended to image objects" but astrometry (the measurement of a star's location) requires an image of the star using a telescope that resolution (power) is determine by the size of the mirror. How can a mirror that is eight time smaller than the Hubble's mirror produce a resolution that is 100 times more powerful since both the Hipparacos and Hubble are reflection space telescopes?

10. Originally Posted by ivy
The Hipparacos' mirror has a diameter of 11 inches and resolution of .001 arcsec yet the Hubble's mirror diameter is 7.9 ft and has a resolution of .1 arcsec. The Hipparacos is a reflection telescope that mirror is eight times small than the Hubble's reflection mirror yet 100 time more powerful. You state "Hipparcos was not intended to image objects" but astrometry (the measurement of a star's location) requires an image of the star using a telescope that resolution (power) is determine by the size of the mirror. How can a mirror that is eight time smaller than the Hubble's mirror produce a resolution that is 100 times more powerful since both the Hipparacos and Hubble are reflection space telescopes?

Good luck.

11. How did astronomers measure the distance to a 4.22 ly star using parallax before 1989?

12. Originally Posted by ivy
How did astronomers measure the distance to a 4.22 ly star using parallax before 1989?
When I calculate things, I get quite different numbers to yours. The parallax for a 4.22 ly distance is nearly 1 arc-second by my reckoning, so quite accurate measurements at that distance are possible with instruments capable of tenths of arc-second resolution angles. Hipparcos should be able to provide accurate distance measures out to a couple of orders of magnitude greater distances.

Upgrades to signal-processing software has given Hubble tens of microarc-second resolution, enabling measurements of distances out to another order of magnitude.

13. Originally Posted by tk421
When I calculate things, I get quite different numbers to yours. The parallax for a 4.22 ly distance is nearly 1 arc-second by my reckoning
I'm surprised nobody mentioned the parsec

14. The Hipparcos was launched in 1989 and the Hubble in 1990; therefore, the question is: How did astronomers measure the distance to a 4.22 ly star using parallax before 1989 without using the Hubble or Hipparcos?

15. Originally Posted by ivy
The Hipparcos was launched in 1989 and the Hubble in 1990; therefore, the question is: How did astronomers measure the distance to a 4.22 ly star using parallax before 1989 without using the Hubble or Hipparcos?
So now you are asking a different question to your original one.

There have been great advances in networked computers over the last couple of decades. A company called Google has a tool that helps people like you. Click here: LMGTFY

I recommend reading the Australia Telescope National Facility page.

16. The Australia Telescope National Facility page does not describe the measurement of a 4.22 ly star using parallax before 1989.

17. Originally Posted by ivy
The Australia Telescope National Facility page does not describe the measurement of a 4.22 ly star using parallax before 1989.
You are being aggressively lazy, so this will be my last attempt at educating you.

The page actually shows much more than you have bothered to think about. It shows the historical evolution of capabilities over the centuries of development. There is a chart that shows the ability of parallax to measure a 4.22ly-distant star was available by the mid-19th century, and to measure it well by the early 20th century. Perhaps you have not bothered to correct the maths error I pointed out earlier. In any case, you need to get off your arse and actually read the flippin' page in its entirety. Your intellectual laziness, combined with an apparent dogmatic belief that such measurements could not have been made, have blinded you to simple facts. All I can do is lead you to knowledge, and that I have done. Whether or not you choose to learn is up to you.

18. How did astronomers measure the distance using parallax to a 4.22 ly star using the La Silla telescope (.3 arcsec). If you cannot determine the distance to a 4.22 ly star or any star in the stellar universe, before 1998, then astronomy is a hoax.

19. Originally Posted by ivy
astronomy is a hoax.
OK. You've caught us out. There are no stars or planets.

Although, apparently there are still idiots.

20. Originally Posted by ivy
How did astronomers measure the distance using parallax to a 4.22 ly star using the La Silla telescope (.3 arcsec). If you cannot determine the distance to a 4.22 ly star or any star in the stellar universe, before 1998, then astronomy is a hoax.
It probably has something to do with the fact the the parallax of a 4.22 ly distant star is in the order of .78 arcsec, which is over twice that of the La Silla telescope resolution. Then add in the fact that when you give the parallax for an object, you are giving the angle as seen across the radius of the Earth's orbit, while the actual measurement is made over the diameter. Thus the angular shift that the telescope measures for the star is twice that of the listed parallax. This means that that LA Silla telescope has over 5 times the resolution needed to measure the parallax for a 4.22 ly distant star.

21. Originally Posted by Doctorevil
I was looking at an astronomer book and it said that the lower the arcsec value the greater the resolution but the above post suggests that the greater the value of the resolution the greater the resolution and power of the telescope.
You are "ivy" aren't you.

22. Originally Posted by Strange
You are "ivy" aren't you.
precisely

23. Normally, this troll only create a new name after being banned. Maybe he just got confused here.

 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Forum Rules