How Accurately Will Gaia Measure Cepheid Distances?

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In summary, the planned Gaia satellite is a successor to Hipparcos with an astrometric accuracy of 24 micro-arcseconds. It will be able to detect Cepheid variable stars in the Magellanic clouds, which are approximately 70 kiloparsecs away. Based on this distance and the accuracy of Gaia, it will not be able to accurately measure distances to these Cepheids using parallax. However, by averaging results from multiple stars, it can achieve better accuracy.
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Homework Statement



The planned Gaia satellite is a successor to Hipparcos. It will have an astrometric accuracy of 24 micro-arcseconds, and be able to detect Cepheid variable stars in the Magellanic clouds (~ 70kpc away). Estimate how accurately Gaia will determine distances to these Cepheids

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The Attempt at a Solution



I haven't really done any cosmology before so this is new to me. I've just defined a parsec in the previous question as a star 1pc away having a parallax of one arcsecond.

http://upload.wikimedia.org/wikipedia/en/a/a8/Parsec.png

I'm not sure what value this question actually wants as an answer :confused:
 
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  • #2
Take your picture and replace the base distance with the approximate distance to the Magellanic cloud. Now what is the angle. (Hint: this is really trigonometry - not cosmology).
 
  • #3
Hmm, i tried that and the angle came out as virtually 0 arc seconds
 
  • #4
You're right! It is virtually zero. But it is NOT zero. Express the answer in micro-arcseconds. This whole game is about tiny angles.
 
  • #5
ok, well converting to meters:

1AU = 149.6 x 10^9 m
70kpc = (70,000) * (3.086 x 10^16) m

Angle, say, x = 3.97 x 10^-9 degrees = 14.28 microarcseconds
 
  • #6
So given the astrometric accuracy of Gaia, will it be able to accurately measure distances on this scale using parallax?
 
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  • #7
Given that it can only(!) read to 24micro-arcseconds, no - as the calculated angle is 14.28 microarcseconds. But I'm confused at the way the question's worded - "estimate HOW ACCURATELY Gaia will determine distances to these Cepheids", I'm not sure what physical quantity it's asking for
 
  • #8
Aside from saying "not very accurately at all", I'm not sure. You could say if the true parallax is 14, Gaia could measure anything between 0 and 38, implying it's somewhere between around half the true distance and infinity. Not very satisfying, eh? If it's any consolation, if you measured LOTS of stars and averaged the results - you could do a lot better. And I think that's what they do.
 
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FAQ: How Accurately Will Gaia Measure Cepheid Distances?

What is a parsec and how is it related to distance accuracy?

A parsec is a unit of measurement used in astronomy to measure extremely large distances, particularly between celestial objects. It is equal to 3.26 light years or approximately 19 trillion miles. Distance accuracy refers to the precision of measuring these large distances, and a parsec is often used as a standard unit of measurement for its accuracy.

How is the accuracy of a parsec calculated?

The accuracy of a parsec is calculated based on the precision of the instruments used to measure it. This includes factors such as the resolution of telescopes and the accuracy of timekeeping devices. The smaller the margin of error in these measurements, the more accurate the calculation of a parsec will be.

Can a parsec be used to measure distances within our own solar system?

No, a parsec is not an appropriate unit of measurement for distances within our own solar system. It is typically used for measuring distances between stars and galaxies, as the distances within our solar system are much smaller and can be measured in units such as miles or kilometers.

What is the most precise distance that can be measured using a parsec?

The most precise distance that can be measured using a parsec is approximately 3.26 light years. This is because a parsec is defined as the distance at which an object would have a parallax angle of one arcsecond, and anything closer than that would have a larger parallax angle and therefore be measured in smaller units.

Are there any limitations to using parsecs for distance accuracy?

Yes, there are some limitations to using parsecs for distance accuracy. One limitation is that it is based on the assumption of a single observer, and as such, it may not accurately reflect the true distance between celestial objects if viewed from different perspectives. Additionally, it is not a very practical unit of measurement for distances within our own galaxy, as the use of smaller units such as light years or astronomical units would be more appropriate.

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