# The star that changed the cosmos: M31-V1

## The distance to M31

To compare my results for the distance to M31 directly to Hubble’s, I needed to use Shapley’s faulty calibration of the period-luminosity relationship. Curiously, Hubble has adjusted this graph to produce the absolute magnitude at the maximum, rather than the mean absolute magnitude as originally suggested by Leavitt and used in virtually all other calibrations. Hubble said it believes its peak magnitude readings are more reliable than those obtained during the weaker parts of the cycle. Based on this graph, the logarithm of my period of 31.91 days gave an absolute magnitude for the maximum of M31-V1 of -3.6.

Once you have an object’s absolute magnitude and corresponding apparent magnitude, it’s simple to calculate its distance using an equation called distance modulus: m – M = 5[log10(d/10)], where m is the apparent magnitude, M is the absolute magnitude, and d is the distance in parsecs. (One parsec equals 3.26 light-years.) Solving this equation for d yields d = 10(m-M+5)/5.

My values for m and M gave a distance of 275,423 parsecs, or 897,879 light years – very close to Hubble’s published value of 900,000. With that, I had achieved my goal. Despite the faulty calibration, I had also proven that M31 is so far away that it must be a separate galaxy.

I was extremely happy that my result was so close to Hubble’s. The difference was only 2,121 light years. Then, re-reading the 1929 Hubble publication, I noticed something remarkable. Although Hubble did not show its apparent and absolute maximum magnitude values, it did give their difference: m – M = 22.2. This was precisely the value I had obtained! This could only mean that Hubble got exactly the same distance: 897,879 light-years. He simply rounded to 900,000 light years in his paper. Now I was delighted. I had done in my garden what Hubble had done at Mount Wilson, with exactly the same result.

However, this result is incorrect because it is based on an incorrect calibration of the period-luminosity relationship. Since 1929, as technology has improved, the calibration has been revised. This greatly increased the calculated distance to M31. With the advent of the HST, that number is now 2.537 million light-years away.

## A memorable business

With that, I declared the project a great success. Following in the footsteps of Hubble was an exhilarating experience that I will definitely remember for the rest of my life. Above all, I am amazed that I, a simple amateur astronomer using equipment in my backyard, have been able to replicate a feat that was accomplished less than a century ago by the greatest astronomer in the world using the greatest world telescope.

It is a testament to amateur astronomy as a hobby. Do you want to be an archaeologist or an amateur paleontologist? Good luck gaining access to an Egyptian tomb or T. rex fossil bed to conduct your own research projects. These precious materials are reserved exclusively for professionals.

This is not the case with amateur astronomy. All astronomers have unlimited access to the same crucial resource: the entire sky above us. And with that, the sky really is the limit of what we hobbyists can do.

## Up to date

One of HST’s main goals was to accurately determine the distances of 10 Cepheids in the Milky Way by measuring their trigonometric stellar parallaxes – something that can only be done from space – to produce a calibration with unparalleled precision. precedent for the period-luminosity relation.

The equation for the period-luminosity relationship using HST calibration is: M = (–2.43 + 0.12)[log10(P)-1.0] – (4.05 + 0.02), where M is the absolute magnitude and P is the period.

Using my data with HST calibration, how close can I get to the currently accepted distance of M31? My period of 31.91 days gives an absolute magnitude of -5.27 using this calibration. Then the distance modulus gives a distance of 776,247 parsecs or 2.531 million light years.

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