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I am looking at data from Andrea Ghez (2005; ADS link) which states the mass of the supermassive black hole in the MW. Here's what I don't understand: She reports the value as $3.7 \times 10^6 [R_0/(8~\mathrm{kpc})]^3$ solar masses.

The part I'm not clear on is the radius/8 kpc piece. Everything else I read (except for the journal article) leaves out the radius/8 kpc stuff and just reports it as $3.7 \times 10^6$ solar masses. (I know that other values have since been determined). What is that radius/8 kpc all about?

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The largest source of error in the measurement of the black hole mass is its distance, $R_0$, which Wikipedia says is $7940\pm420$ parsec. By quoting the mass in terms of the distance, this error is isolated. So, for example, if the black hole is actually $7600$ parsec away, its mass is about $3.5\times10^6\,M_\odot$. All the other sources of error are presumably much smaller.

As for the other publications, they should really say that the black hole's mass is around $3.7\times10^6\,M_\odot$ but many popular publications don't bother with uncertainties unless they're really important.

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