How do I determine the uncertainty value of the star's absolute magnitude?

In summary, the homework statement has a star with an apparent magnitude of 13.73 and an uncertainty of 0.03303. The star's distance Modulus is 13.9967 and its absolute magnitude is -0.26. The distance is 6300 parsecs.
  • #1
Thomas Smith
12
0

Homework Statement


I have a star that has an apparent magnitude of 13.73 with uncertainty of 0.03303

It's distance Modulus is 13.9967 so it's absolute magnitude is -0.26

The distance is 6300 parsecs

Homework Equations


[/B]
The uncertainty on log10(d) is given by
Δ(log10)≈0.4343 Δd/d

ΔQ) = √(Δx)^2 + (Δy)^2 errors of sums or differences

The Attempt at a Solution



My guess is working out the uncertainty of d first

0.4343 x Δ/6300

d= 0.4343/6300

d=0.00007

and then the uncertainty of the absolute magnitude given by:

∆M= 0.4343 × √(0.03303)^2+(0.00007)^2) =0.0143

I'm not quite sure if this is right.
 
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  • #2
What is Δd? You seem to assume 1 pc, that is unrealistic in an astronomy context.
Thomas Smith said:
and then the uncertainty of the absolute magnitude given by:

∆M= 0.4343 × √(0.03303)^2+(0.00007)^2) =0.0143
Why did you multiply by 0.4343?
Thomas Smith said:
I'm not quite sure if this is right.
Your uncertainty on the derived absolute magnitude is smaller than the uncertainty on the measured apparent magnitude. Can that be right?
 
  • #3
mfb said:
What is Δd? You seem to assume 1 pc, that is unrealistic in an astronomy context.
Why did you multiply by 0.4343?Your uncertainty on the derived absolute magnitude is smaller than the uncertainty on the measured apparent magnitude. Can that be right?
∆d is 500 parsec sorry
 
  • #4
I've did my calculations again and got the absolute magnitude uncertainty of 0.21.

I did 0.4343 x 500/6300
∆log(d) = 0.0345
∆5log(d) = 0.0345 × 5 = 0.1725

∆M = sqaureroot of (0.033030)^2 + (0.1725)^2

∆M = 0.20553 rounded up to 0.21
 
  • #5
That looks good.

This forum supports LaTeX, by the way: ##\Delta M = \sqrt{0.033030^2+0.1725^2} = 0.2055##

How I wrote it: ##\Delta M = \sqrt{0.033030^2+0.1725^2} = 0.2055##

Edit: Fixed link
 
Last edited:
  • #6
mfb said:
This forum supports LaTeX,
Hi mfb:

The LaTeX link does not open. I get the message:
Server error
404 - File or directory not found.
The resource you are looking for might have been removed, had its name changed, or is temporarily unavailable.

I imagine you may want to correct this.

Regards,
Buzz
 
  • #7
Buzz Bloom said:
Hi mfb:

The LaTeX link does not open. I get the message:
Server error
404 - File or directory not found.
The resource you are looking for might have been removed, had its name changed, or is temporarily unavailable.

I imagine you may want to correct this.

Regards,
Buzz
Missing initial h. Should read https://www.physicsforums.com/help/latexhelp/
 

Related to How do I determine the uncertainty value of the star's absolute magnitude?

1. What is the uncertainty value of a star's absolute magnitude?

The uncertainty value of a star's absolute magnitude is a measure of the range of possible values for the star's absolute magnitude. It represents the level of confidence we have in the measured value, and takes into account any potential sources of error or variation.

2. How do I calculate the uncertainty value of a star's absolute magnitude?

The uncertainty value of a star's absolute magnitude is typically calculated using statistical methods, such as standard deviation or confidence intervals. This involves taking multiple measurements of the star's absolute magnitude and using these values to determine the range of possible values with a certain level of confidence.

3. What factors can contribute to the uncertainty of a star's absolute magnitude?

The uncertainty of a star's absolute magnitude can be influenced by a variety of factors, including observational errors, instrumental limitations, atmospheric conditions, and variability in the star's brightness. It is important to consider and account for these factors when determining the uncertainty value.

4. Is the uncertainty value of a star's absolute magnitude always the same?

No, the uncertainty value of a star's absolute magnitude can vary depending on the methods used to measure it and the specific characteristics of the star being observed. It is important to assess and report the uncertainty value for each individual measurement.

5. Can the uncertainty value of a star's absolute magnitude change over time?

Yes, the uncertainty value of a star's absolute magnitude can change over time as new data is collected and as our understanding of the star and its environment evolves. It is important to regularly reassess and update the uncertainty value as needed.

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