# How many parsecs is it when the redshift z=1

1. Jun 2, 2013

### nenyan

How to convert red shift to parsecs? Is there a simple converting equation?

2. Jun 2, 2013

### George Jones

Staff Emeritus
This depends on which concept of distance is used. See the first paragraph of the attached file.

I wrote up an answer for someone else, who specified z = 0.4. I didn't use dimensionless parameters. See the last two graphs in the attached file.

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3. Jun 2, 2013

### nenyan

very useful. thanks

4. Jun 2, 2013

### Mordred

thats one of the better quality articles I've read. Far better than some of my attempts lol. Thank you for showing it.

5. Jun 2, 2013

### Mordred

My signature first link has a handy tool called the lightcone calculator here I set stretch to 2.0 for S_upper. S=1+z. I set a randon value for lower stretch.
then I selected the columns I wanted and decimal places. Clicked linear steps.
here is the result with WMAP
flat geometry parameters.

$${\small\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&z&T (Gy)&D_{now} (Gly)&D_{then}(Gly) \\ \hline 0.500&2.000&1.000&5.8636&11.046&5.523\\ \hline 1.000&1.000&0.000&13.7872&0.000&0.000\\ \hline 1.668&0.599&-0.401&21.7987&6.249&10.425\\ \hline 2.783&0.359&-0.641&30.4437&10.300&28.660\\ \hline 4.642&0.215&-0.785&39.2497&12.776&59.303\\ \hline 7.743&0.129&-0.871&48.0918&14.267&110.467\\ \hline 12.915&0.077&-0.923&56.9418&15.162&195.824\\ \hline 21.544&0.046&-0.954&65.7934&15.698&338.212\\ \hline 35.938&0.028&-0.972&74.6452&16.020&575.729\\ \hline 59.948&0.017&-0.983&83.4973&16.213&971.932\\ \hline 100.000&0.010&-0.990&92.3494&16.328&1632.838\\ \hline \end{array}}$$

the top row has the result you want you just need to convert to parsecs.