WS 5.1, Problem 1: Lamp Luminosity

Use a lamp tted with a 100 Watt incandescent light bulb to estimate the luminosity of the Sun.
Do this with the knowledge that

• the Earth-Sun distance is 1 astronomical unit (AU), or a =1.5x10$^13$ cm
• an estimate of how far from the bulb you have to hold your hand in order for it to feel like sunny Spring day
• and the fact that incandescent light bulbs convert electrical power into radiant energy with an effi ciency of only about 3%

Our first step was to go up to the lamp and use our hands to determine the distance asked for in the second bullet point.  For me, having grown up in Pennsylvania where a sunny Spring day doesn't feel all that warm, the distance was about 10 cm.  The other people in my group were from really warm places (California and Argentina), so their distances were shorter.  We compromised and used the distance d=7 cm.

To solve this problem (and by doing the first step mentioned above), we are essentially setting the flux of the light bulb at 7 cm equal to the flux of the sun.  

$F_{bulb}=F_{\odot}$

$\frac{L_{bulb}}{4\pi d^2}=\frac{L_{\odot}}{4\pi a^2}$

$\frac{L_{bulb}}{d^2}=\frac{L_{\odot}}{a^2}$

$L_{\odot}=\frac{L_{bulb}a^2}{d^2}$

Because we're told that the light bulb is only 3% efficient, the actual luminosity of the light bulb is 3 Watts.  

Using this information, the luminosity of the sun in Watts is 

$L_{\odot}=1.2\times 10^{25}$ Watts

Also, I've started doing what I like to call "Selfies with Astro," a series of photographs in which I make ridiculous faces next to Astrophysics work.  This particular Selfie with Astro has the added bonus of containing the beautiful picture by Delfina Martinez-Pandiani (seen on the left side of the board).