# Astro: Uncertainty in distance using the spectroscopic parallax method.

1. Nov 25, 2009

### knowlewj01

1. The problem statement, all variables and given/known data

The uncertainty $$\Delta$$M in the absolute magnitude for a given spectral type could be 0.25 magnitude. while the uncertainty in the apparent magnitude magnitude m, can be negligable. Give an indication of the relative uncertainty in the derived distance.

2. Relevant equations

m - M = 5 log(d) - 5

3. The attempt at a solution

I have no idea how i am going to do this, I thought that maybe rearranging to get d as the subject might be a good starting point, so:

d = 10^[$$\frac{m-M+5}{5}$$]

now maybe use a bit of quadrature?

($$\Delta$$d)^2 = $$\sqrt{((dd/dM)\Delta M)^2}$$

Anyone think they can push me in the right direction? I have a feeling that I'm doing this all wrong.

Last edited: Nov 25, 2009