Calculate the uncertainty of the distance to the clusters?

[rikpotts]

Hi,
Im sorry to make my first post a question but I am going mad trying to sort my problem. I've looked in all kinds of places for my answer but it never seem so to be there.
Im in my 3rd year of an OU Physics degree, and currently writing up a report on some observations I made of star clusters in mallorca.
Ive got to a point where I am throwing apparent magnitude, absolute magnitude and interstellar extinction into an equation giving the distance in parsecs.
My absolute mag and interstellar extinction is of fixed value but my apparent mag has an uncertainty associated with a reading from a chart.

How do I calculate the uncertainty of the distance to the clusters?
ie my apparent mag is 13+- 1. Do I Calculate d/pc for mag = 12, 13 and 14 and go from there... or is there another way.

I know somewhere in all my books and notes will be a one line answer to this but I cannot find it anywhere. All my uncertainty notes go on about standard deviation. standard error, combining uncertainties etc...

Please help! I've got this report, 1 textbook to read and 2 exams all in the next 3 weeks!

Many Thanks
Rik

 

[Nereid]

Welcome to Physics Forums rikposts!

I hope that your star clusters were in Andromeda, or Sextans, or Gemini; the only 'star clusters' I can imagine being in 'mallorca' aren't normally measured with apparent magnitudes

It's not clear from your post just what you've done, nor what you have to work with, so I'll assume something like the following:
- you measured the apparent magnitude of some stars in a cluster
- each measurement has some kind of error (what kind?)
- you have a value for the interstellar extinction between us and the cluster
- you have a table of the absolute magnitudes of the stars whose apparent magnitudes you measured
- you have a formula which contains apparent mag, absolute mag, and extinction as inputs; it gives distance as an output.

Am I close?

It seems to me you can take each star that you observed and calculate an estimate of the distance to that star. If you have 100 stars, all of which you assume to be in your cluster, then you will get 100 different estimates of the distance.

On the other hand, you have measured apparent magnitudes and some kind of error. Let's suppose these are 1 sigma errors, and there are no systematic effects. For one star (apparent magnitude), you can apply your formula and calculate three estimated distances: mean, +1 sigma, -1 sigma. You can then say that you estimate the star to be at a distance of x +y -z (1 sigma).

I suggest that you read your uncertainty notes again, after getting clear in your own mind a) what sort of answer you're trying to get, and b) what sort of uncertainties ('errors') you have in your input data.