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

[mokeejoe5]

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

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Can someone please explain to me where I'm going wrong?

 

[sophiecentaur]

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)

 

[phyzguy]

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?

 

[mfb]

Another example where proper units everywhere would have made the mistake obvious.

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.

 

[pmacias]

Hello,

First of all, it is great that you are trying to calculate the luminosity of the sun. However, I would like to point out that the steps you have mentioned are not entirely accurate. Let me explain:

1. The value of 1630 Watts/m2 is the solar constant, which is the amount of solar radiation received per unit area at the Earth's distance from the sun. This value is not the luminosity of the sun.

2. The apparent magnitude is a measure of how bright an object appears to an observer on Earth. It is not directly related to the luminosity of the sun.

3. The equation you have used to calculate the brightness at Earth's distance, 1/(1.496*10^11)^2, is correct. However, this value only represents the brightness of the sun at Earth's distance, not its luminosity.

4. The surface area of the sun divided by 4.468*10^-23m2 is not equal to the number of 1630 Watt sections. This step is not necessary in calculating the luminosity of the sun.

5. Finally, the value of 2.21*10^44 Watts that you have obtained is not the luminosity of the sun. This value is much higher than the actual luminosity of the sun, which is approximately 3.828*10^26 Watts.

To accurately calculate the luminosity of the sun, you will need to use the Stefan-Boltzmann law, which states that the luminosity of a star is proportional to its surface area and temperature raised to the fourth power. You will also need to know the radius and temperature of the sun.

I hope this helps clarify where you may have gone wrong in your calculation. Keep up the scientific curiosity!