Stellar Properties from Afar

Acknowledgements to Eric, Tommy

How many 100W light bulbs would it take to match the power output of the Sun?  I asked a number of non-astrophysics friends here at Caltech for an estimate.  Most gave a guess in the trillions, with a couple people guessing less and a few guessing more.  Let's find out.

Let's begin by finding the luminosity of the sun.  Luminosity is power.  No, that's not some slogan out of a George Orwell novel, it just says that luminosity is the energy output of a star in a given amount of time - power.  We can estimate the Sun's luminosity using no more than a 100W light bulb and our sense of temperature.  Using these resources, we discover that we have to hold our hand at about 5 cm away from the bulb for the temperature to feel comparable to a hot day.  Using this measurement, we can set up the following proportion and calculate the Sun's luminosity,

where L is the luminosity.  Also note that we multiplied the 100W power of the bulb by 0.1, which is the efficiency.  100W is the input power, but the bulb itself only outputs about 10W.  Also, since the temperature felt at a given distance from a luminous power source is dependent on flux, we square the distances in the denominator.  From this proportion, we calculate the Sun's luminosity to be on the order of 10^26 Watts.  That's a lot!  This means that it would take 10^25, or 10 million billion billion bulbs (each with the 0.1 efficiency) to shine as brightly as the Sun.


What other properties of the Sun can we calculate from the luminosity?  Here are just a couple.


Surface Temperature
Using the luminosity of the sun, we can calculate the flux at the surface by dividing by the Sun's surface area.

Using the Sun's actual luminosity, we calculate the flux at the surface to be 6.3E10 ergs/cm^2/s.
Assuming the Sun is a blackbody, we can calculate the surface temperature using this handy dandy formula.

We calculate an effective temperature of 5780K.


Solar Constant
The Solar constant is the flux of the Sun measured at the Earth.  Using the above formula for flux in terms of luminosity, we can calculate the Solar constant if we replace R with one astronomical unit.  We get 1.4E6 erg/cm^2/s.