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

CC BY-SA 4.0
2021-03-22T19:53:30.823Z
The units of distance modulus are "mag". It is incorrect to quote more than 3 Sig figs in the result or more than 2 in the error bars.
ProfRob
CC BY-SA 4.0
2021-03-26T07:12:04.240Z
Alright. Thanks a lot :)
CGHA
CC BY-SA 4.0
2021-03-22T13:39:16.853Z
2021-03-22T13:39:16.853Z
slowerthanstopped
<p>This is rather a short question. As we know of;</p>
<p>Distance Modulus (DM) <span class="math-container">$\mu = 5 \log d - 5$</span></p>
<p>If <span class="math-container">$d = 168_{-14.9}^{+27.5}$</span> pc (<span class="math-container">$3\sigma$</span> value), how can I possibly compute for <span class="math-container">$\mu$</span>'s uncertainty?</p>
<p><em>P.S. Perhaps I need to multiply those <span class="math-container">$\pm$</span> values to a 'some constant'(?)</em></p>
<p>Thanks a lot and clear skies.</p>

CC BY-SA 4.0
2021-03-22T08:29:17.810Z
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
CC BY-SA 4.0
2021-03-22T08:42:39.663Z
@ProfRob  That seems applicable. ^^ Let me check.
CGHA
<distances><apparent-magnitude>
How to compute for Distance Modulus' uncertainty/ies?
CGHA
# How to compute for Distance Modulus' uncertainty/ies?

(Asked by: username_0 on 2021-03-22)

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.

**Tags:** distances, apparent-magnitude

> **Comments:**
> **username_1**: 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 $5\log d - 5$.  
> **username_0**: @username_1  That seems applicable. ^^ Let me check.  

---

## 1 answers

### Answer by username_2 on 2021-03-22. Score: 3 | Accepted answer

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.

> **Comments:**
> **username_1**: The units of distance modulus are "mag". It is incorrect to quote more than 3 Sig figs in the result or more than 2 in the error bars.  
> **username_0**: Alright. Thanks a lot :)  

---

