Reference: Carroll, Bradley W. & Ostlie, Dale A. (2007), An Introduction to Modern Astrophysics, 2nd Edition; Pearson Education – Chapter 3, Problem 3.2.
The luminosity of the Sun is
On a sphere of radius centred at the Sun, the power received is therefore
which is the inverse square law for radiation from a spherically symmetric source. At the distance of the Earth, so the solar flux, known as the solar irradiance, is
This is the power received when the Sun is directly overhead, which can occur only between the tropics of Cancer and Capricorn. At my latitude of around , the highest the Sun can get in the sky occurs at noon on the summer solstice, when the Sun’s declination is around , putting it at an altitude of . The flux here is therefore
At the winter solstice, the Sun’s maximum altitude is , giving a flux of
I’ve actually measured this in my own backyard with my weather station (see the High Solar Rad graph about halfway down the page) and the numbers do check out; in June the highest recorded radiation is between 1100 and 1200 and in December it peaks at around 200.
A somewhat dated comparison is to look at the radiation emitted by an old-fashioned 100
W light bulb. In order for us to receive the solar irradiance from such a bulb, we’d need to be at a distance
More modern light bulbs such as LEDs emit just as much light as the old high-power bulbs but consume much less power (a typical LED consumes under 5 watts). This is because most of the energy in an LED goes into emitting light while in an old 100W bulb, a large portion of the energy is radiated as heat (or to be more precise, infrared radiation).