What are the uncertainty values for my corrected magnitudes?

  • #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]
 
Physics news on Phys.org
  • #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.
 
Back
Top