A little ‘light’ reading on the subject of the inverse square law

Naturally Hot

After the fashion of that great song by the Black Eyed Peas, the lyrics that ask, “Where is the love?” regarding the claims by the climate alarmists of anthropogenic climate warming, a question arises: From where comes the heat? What heat? The heat that is attributed to global warming, global flooding, famines, worldwide catastrophic deaths, etc.

Let’s look away from atmospheric CO₂, ozone holes, and gas stoves, Joe Biden’s theoretical enemy to mankind, except for the gas stoves in his favorite restaurants.

What do you know about the inverse square law? You live with it. You experience it. But you probably never thought about it.

Here is a video that explains the physics, by using the light source of an ordinary light bulb.

Thinking Three Dimensionally

Imagine a sphere with a diameter of 2 feet. A 1-foot-candle power light source is precisely in the center of the sphere.

The light intensity on the inner surface of this 2-foot sphere will uniformly be 1 foot-candle.

Find the area of the spheres.
Surface Area Formula = 4⫪r²
If radius (r) = 1 ft., then r² = 1
Surface area is: 4 X ⫪ X 1 = 12.56637061 ft²
If radius (r) = 2 ft., then r² = 4
Surface area is: 4 X ⫪ X 4 = 25.13274123 ft²
If radius (r) = 3 ft., then r² = 9
Surface area is: 4 X ⫪ X 9 = 113.0973355 ft²

Considering the spheres’ surface area:

Calculate the intensity of light at a prescribed distance:
S = source strength in foot candles
4⫪r² = Surface area of the target
r = radius of the sphere or distance between S and the surface in question

• A sphere 2 feet in diameter has a radius of 1 foot. The light of a 1-foot-candle source in the center of the sphere will bathe the entire surface of this sphere with one foot-candle of luminance.
• A sphere 4 feet in diameter has a radius of 2 feet. The light of a 1-foot-candle source in the center of the sphere will bathe the entire surface of this sphere with 0.07957747157 foot-candle of luminance. [1/12.56637061 = 0.07957747157 foot-candle]
• A sphere 6 feet in diameter has a radius of 3 feet. The light of a 1-foot-candle source in the center of the sphere will bathe the entire surface of this sphere with 8.841941285 X 10^-3 foot-candle of luminance. [1/113.0973355 = 8.841941285 X 10^-3 foot-candle]

Calculating line-of-sight diminution of the light:

Another perspective assumes uniform luminosity in all directions from the source.

All manner of energy obeys the inverse square law, including sound waves, light waves, radar, sunshine, infrared and ultraviolet radiation.

Food for Thought

The temperature of the core of the earth is approximately 12,140 °F (7,000 °C). The part of the Sun we call its surface – the photosphere – is a relatively cool 10,000 °F (5,500 °C). 

For a perspective on temperature these temperatures, consider the melting point of cast iron at 2,060-2,200 °F (1,127-1,204 °C)

The Takeaways

• The sun is not the only source of heat.
• The inner core of the earth is hotter than the surface of the sun.
• Heat energy from a given source diminishes as a function of the inverse square law.

John White
Rockwall, Texas