Calculating Sun's Luminosity: Step-by-Step Guide

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Discussion Overview

The discussion revolves around calculating the luminosity of the Sun, focusing on the methodology and mathematical reasoning involved in the calculations. Participants explore different approaches to derive the Sun's luminosity based on the apparent magnitude and flux measurements from Earth.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant attempts to calculate the Sun's luminosity using the apparent magnitude and distance, leading to a specific numerical result.
  • Another participant suggests that the initial approach is unclear and recommends starting over with a different method that involves calculating the total power radiated based on the area of a sphere.
  • A third participant critiques the initial calculation, arguing that the method used to derive the flux is incorrect and proposes an alternative formula that relates the flux at the Sun's radius to that at Earth's orbit.
  • A fourth participant highlights the importance of using proper units throughout the calculations to avoid confusion and errors, pointing out a specific mistake in unit handling.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to calculating the Sun's luminosity, with no consensus reached on the methodology. Multiple competing perspectives on the calculations and their interpretations remain evident.

Contextual Notes

There are unresolved issues regarding the assumptions made in the calculations, particularly concerning the application of flux and the handling of units. The discussion reflects a variety of mathematical steps and interpretations that have not been fully reconciled.

mokeejoe5
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I'm trying to work out the luminosity of the sun.

1630 Watts/m2 apparent magnitude reduces with distance squared so
1/(1.496*1011)2 = 4.468*10-23m2 has the same brightness 1630 Watts from earth

Surface area of the sun divided by 4.468*10-23m2 = # of 1630 Watt sections
*1630 = 2.21*1044 Watts
    • #​

    [*]


Can someone please explain to me where I'm going wrong?
 
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It is not clear what you are trying to show. I think you are choosing a 'strange path' through your calculations. Try starting again.
Given the luminosity, measured on Earth, you can work out the total Power radiated. (Area of a sphere of radius 1.496*1011 times the Watts per m2 on Earth)
You can then work out the flux for a sphere of any radius (even the radius of the Sun)
 
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Why 1/(1.496*1011)2 ? When you do this, you are calculating how much the flux increases from the radius of the Earth's orbit to a radius of 1 meter. What you want to do instead of calculating 1/Rearth^2, is calculate Rsun^2/Rearth^2. If the flux at Earth's orbit is given by Fearth (=1630 W/m^2), then the flux at the sun's radius is given by 4 * pi * Rsun^2 * Fearth / (Rsun^2/Rearth^2) = 4 * pi * Rearth^2 * Fearth. This is the same answer that SophieCentaur gave you. Do you see?
 
Another example where proper units everywhere would have made the mistake obvious.
mokeejoe5 said:
1/(1.496*1011)2
This is 1/(1.496*1011m)2 = 4.468*10-23m-2
It does not make sense to divide the surface of sun by this value, the result would be meters to the 4th power.
 

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