# How to compute for Distance Modulus' uncertainty/ies?

This is rather a short question. As we know of;

Distance Modulus (DM) $$\mu = 5 \log d - 5$$

If $$d = 168_{-14.9}^{+27.5}$$ pc ($$3\sigma$$ value), how can I possibly compute for $$\mu$$'s uncertainty?

P.S. Perhaps I need to multiply those $$\pm$$ values to a 'some constant'(?)

Thanks a lot and clear skies.

• Can't you just use the upper and lower bounds of distance to calculate upper and lower bounds to distance modulus? And BTW, distance modulus is $5\log d - 5$. – ProfRob Mar 22 at 8:29
• @ProfRob That seems applicable. ^^ Let me check. – CGHA Mar 22 at 8:42

You can just use these upper and lower bounds to create an upper/lower bound for the distance modulus. The lower bound is $$168-14.9 = 153.1$$, and the upper bound is $$168+27.5 = 195.5.$$ You can calculate the distance moduli for these values to get upper and lower bounds: $$5\log(153.1) - 5 = 5.924876 \\ 5\log(195.5) - 5 = 6.455734$$ Then we calculate the distance modulus of the base value: $$5\log(168) - 5 = 6.126546$$ To get the deviations, we just subtract the distance moduli from the original. Therefore, your distance modulus is equal to $$6.126546_{- 0.20167}^{+0.329188} \text{ pc.}$$ I hope this helps. If there are any issues with my answer, please notify me.