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mysearch

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Hi, I am trying to resolve a few questions concerning the measurement of cosmological distance and the determination of Hubble’s constant (H=v/d), where (v) is the recessional velocity of the source and (d) is its distance. Various sources quote Hubble’s constant with a confidence in its accuracy of less than 2%:

[tex] 70.1 \pm 1.3km/s/mpc = 2.28x10^{-18} \pm 4.23x10^{-20}m/s/m [/tex]

http://en.wikipedia.org/wiki/Hubble's_law

In practice, I am assuming that this figure is an average of a multitude of measurements associated with objects at various distances, which presumably confirm a value that is essentially constant with distance, but variable with time in an expanding universe?

My next assumption is that the velocity has to be determined from its associated redshift (z), which is related to the source and observed wavelength of light received from a given object:

[tex] z = \lambda_s - \lambda_o/\lambda_s [/tex]

The key problem with this method is determining the source wavelength, which I understand is normally addressed by using a type of star called Cepheids. If the source wavelength is known, non-relativistic velocity is determined from the simple relationship [v=zc], while a relativistic velocity requires the more complex formula:

[tex]z = (1+v/c)\gamma – 1 [/tex]

However, what is the accuracy of this method? I have seen statements suggesting that for distant objects beyond the Milky Way, the relation is less clear, since the apparent magnitude is affected by spacetime curvature. So, is the Cepheid method the primary method or are other methods, e.g. angular diameter distance, preferred in other circumstances?

Presumably, on the accuracy of (H), a cosmic horizon exists at d=c/H, where any source must be receding faster than the speed of light. Based on the excepted value of (H) and the speed of light [c], this would appear to correspond to a radial distance of 13.9 billion light-years. Does this horizon present a barrier to further observation and what is the furthest distance [d] of any accepted measurement associated with (H)?

Finally, are there any sources showing (H) against time (t)?

Would appreciate any technical clarifications on any of questions raised. Thanks

[tex] 70.1 \pm 1.3km/s/mpc = 2.28x10^{-18} \pm 4.23x10^{-20}m/s/m [/tex]

http://en.wikipedia.org/wiki/Hubble's_law

In practice, I am assuming that this figure is an average of a multitude of measurements associated with objects at various distances, which presumably confirm a value that is essentially constant with distance, but variable with time in an expanding universe?

My next assumption is that the velocity has to be determined from its associated redshift (z), which is related to the source and observed wavelength of light received from a given object:

[tex] z = \lambda_s - \lambda_o/\lambda_s [/tex]

The key problem with this method is determining the source wavelength, which I understand is normally addressed by using a type of star called Cepheids. If the source wavelength is known, non-relativistic velocity is determined from the simple relationship [v=zc], while a relativistic velocity requires the more complex formula:

[tex]z = (1+v/c)\gamma – 1 [/tex]

However, what is the accuracy of this method? I have seen statements suggesting that for distant objects beyond the Milky Way, the relation is less clear, since the apparent magnitude is affected by spacetime curvature. So, is the Cepheid method the primary method or are other methods, e.g. angular diameter distance, preferred in other circumstances?

Presumably, on the accuracy of (H), a cosmic horizon exists at d=c/H, where any source must be receding faster than the speed of light. Based on the excepted value of (H) and the speed of light [c], this would appear to correspond to a radial distance of 13.9 billion light-years. Does this horizon present a barrier to further observation and what is the furthest distance [d] of any accepted measurement associated with (H)?

Finally, are there any sources showing (H) against time (t)?

Would appreciate any technical clarifications on any of questions raised. Thanks

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