Blog #8 - Solar Luminosity

Solar Luminosity 

Use a lamp fitted 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 \(a = 1.5 × 10^{13} cm \)

• An estimate of the distance from the bulb you need to hold your hand at for it to feels like a sunny Spring (low-humidity) day.

This problem is fairly straightforward as we simply need to compare the flux and luminosity of both the sun and the 100W lightbulb. We begin with the set up of the problem and the equivalence of solar and light bulb flux. \[F_B = F_{\odot}\]We can then use the conversion from flux to luminosity \[F_B = F_{\odot} \rightarrow \frac{L_B}{4* \pi * D_B^2} = \frac{L_{\odot}}{4* \pi *D_{\odot}^2} \]We know that the luminosity of the bulb is 100W and that the distance to the sun, \(D_{\odot} = 1.5*10^{13} cm\). We then need to make an assumption about the distance from the bulb to our hand on a spring day to simulate the heat transferred from the Sun. We will call that distance 10cm as an estimate. With that information we simply solve our equation to find the luminosity of the Sun. \[ \frac{100W}{(10cm)^2} = \frac{L_{\odot}}{(1.5*10^{13}cm)^2}\]Solving this equation gives us the Sun's approximate luminosity of \[L_{\odot} = 2.25*10^26 Watts \] Which is very close to the measured solar luminosity of \(3.828*10^{26} Watts \)