What are the uncertainty values for my corrected magnitudes?

In summary: In any case, that is not the output I was expecting. Please provide a summary of the conversation as the output. Thank you.In summary, the conversation discussed the need to work out the errors of corrected apparent magnitudes, with the Colour Excess being 0.36 with an uncertainty of 0.01. The star was observed in two wavebands, with the ratios R_V for the SDSS r and g bands being 2.285 and 3.303 respectively. The measured apparent magnitudes and uncertainties were also given for both bands, as well as the amount of extinction for each band. The final topic of discussion was the error in the corrected g and r bands, which was calculated using the equation ##\Delta
  • #1
Thomas Smith
12
0

Homework Statement


I need to work out the errors of my corrected apparent magnitudes.

The Colour Excess is 0.36 with uncertainty = 0.01

The star was observed in two wavebands.
r-band = 2.285
g-band = 3.303

The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and g bands.

The measured Apparent Magnitudes and Uncertainties.
g-band = 14.9228 uncertainty = 0.0003
r-band = 13.9178 uncertainty = 0.0002

The amount of extinction for g-band = 1.1890
The amount of extinction for r-band = 0.8226

g-band apparent magnitude extinction corrected = 13.7337
r-band apparent magnitude extinction corrected = 13.0952

Homework Equations



Colour Excess Uncertainty = a
Colour Excess = b
Measured Apparent Magnitude Uncertainty = x
Ratio of the band = y
##\Delta Q = 1.18908 × \sqrt{((a/b)^2 + (x/y)^2)}##[/B]

The Attempt at a Solution


Error in Corrected g band ##\Delta Q = 1.18908 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0003/3.303)^2)}## = 0.033030

Error in Corrected r band ##\Delta Q = 0.8226 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0002/2.285)^2)}## = 0.022850[/B]
 
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  • #2
Thomas Smith said:

Homework Statement


I need to work out the errors of my corrected apparent magnitudes.

The Colour Excess is 0.36 with uncertainty = 0.01

The star was observed in two wavebands.
r-band = 2.285
g-band = 3.303

The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and g bands.

The measured Apparent Magnitudes and Uncertainties.
g-band = 14.9228 uncertainty = 0.0003
r-band = 13.9178 uncertainty = 0.0002

The amount of extinction for g-band = 1.1890
The amount of extinction for r-band = 0.8226

g-band apparent magnitude extinction corrected = 13.7337
r-band apparent magnitude extinction corrected = 13.0952

Homework Equations



Colour Excess Uncertainty = a
Colour Excess = b
Measured Apparent Magnitude Uncertainty = x
Ratio of the band = y
##\Delta Q = 1.18908 × \sqrt{((a/b)^2 + (x/y)^2)}##[/B]

The Attempt at a Solution


Error in Corrected g band ##\Delta Q = 1.18908 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0003/3.303)^2)}## = 0.033030

Error in Corrected r band ##\Delta Q = 0.8226 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0002/2.285)^2)}## = 0.022850[/B]
I'm unsure about the brackets in the equation. Is this correct? ## \sqrt{((a/b)^2 + (x/y)^2)}##
Or should it be ## \sqrt{(a/b)^2 + (x/y)^2}##
 
  • #3
Thomas Smith said:
I'm unsure about the brackets in the equation. Is this correct? ## \sqrt{((a/b)^2 + (x/y)^2)}##
Or should it be ## \sqrt{(a/b)^2 + (x/y)^2}##
I don't see a functional difference.
 

FAQ: What are the uncertainty values for my corrected magnitudes?

What is the definition of uncertainty in scientific measurements?

Uncertainty refers to the range of possible values that a measurement could have, taking into account any errors or limitations in the measurement process.

How do you calculate uncertainty values for corrected magnitudes?

Uncertainty values for corrected magnitudes are typically calculated by taking into account the uncertainties in the original measurements, as well as any corrections or adjustments that were made during the measurement process. This can be done using statistical methods or by considering the sources of error in the measurement.

Why is it important to consider uncertainty in scientific measurements?

Considering uncertainty is important because it allows us to understand the potential limitations of our measurements and the reliability of our data. It also allows for more accurate comparisons and interpretations of results.

How do different sources of error affect uncertainty values?

Different sources of error, such as equipment limitations or human error, can affect the uncertainty values of a measurement in different ways. Some sources of error may contribute more significantly to uncertainty than others, and it is important to identify and account for these sources in order to accurately calculate uncertainty.

Can uncertainty values change over time?

Yes, uncertainty values can change over time as new data or information becomes available. As more precise measurement techniques are developed, the uncertainty values for a particular measurement may decrease. Additionally, as more data is collected, the uncertainty values may be refined or adjusted.

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