Ay 20 – Stellar Properties From Afar
Problem 2
Primary author: Joanna Robaszewski
Secondary author: Cassi Lochhaas
Abstract
This problem attempts to estimate the luminosity of the sun based on the temperature of a light bulb.
Introduction
Luminosity is a measure of how much energy a star emits per time. It is a conserved quantity and does not depend on how far away the observer is from a particular star.
Questions and Results
Remembering that there are about 1*107 ergs/s for every watt, we can convert our light bulb power output to cgs units. 100 watts = 1*109 ergs/s. Our skin is a good thermometer so as we move our hand closer to the light bulb, we should be able to tell when it feels as if we are sitting in direct sunlight. For me, this distance was about 4 centimeters. We can then set up a proportionality of power over surface area, keeping in mind that luminosity is equivalent to power, and the distance between the sun and the Earth is 1 AU = 1.5 * 1013 cm:
The official value for the luminosity of the sun, as given by Wolfram Alpha, is 3.8 * 1033 ergs/s. So our value has a percent error of 63%, but at least it is the correct order of magnitude.
correct order of magnitude is quite impressive considering the only things you need are a lightbulb and your hand!
ReplyDeletehow did you get the efficiency of the lightbulb?
also, here's a subtle point: were you measuring temperature, or infrared flux, with your hand? the way to tell the difference is that flux is directional - for instance when you stand outside on a sunny day with your palms open to the sun, your palms will feel warmer than the backs of your hands due to the infrared flux.
Professor Johnson gave us a value for the efficiency of the light bulb in class.
ReplyDeleteIn that case, I think I was measuring infrared flux with my hand, because the back of my hand, which I had facing the light bulb, was warmer than my palm.