Tech/Inverse-square law

Inverse-square law

Inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity.

The inverse-square law generally applies when some force, energy, or other conserved quantity is evenly radiated outward from a point source in three-dimensional space. As the emitted radiation gets farther from the source, it is spread out over an area that is increasing in proportion to the square of the distance from the source. Hence, the intensity of radiation passing through any unit area (directly facing the point source) is inversely proportional to the square of the distance from the point source.

Radar energy expands during both the signal transmission and the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range.

Formula

In mathematical notation the inverse square law can be expressed as an intensity (I) varying as a function of distance (d) from some centre. The intensity is proportional to the reciprocal of the square of the distance thus:

${\text{intensity}}\ \propto \ {\frac {1}{{\text{distance}}^{2}}}\,$

It can also be mathematically expressed as: ${\frac {{\text{intensity}}_{1}}{{\text{intensity}}_{2}}}={\frac {{\text{distance}}_{2}^{2}}{{\text{distance}}_{1}^{2}}}$

or as the formulation of a constant quantity: ${\text{intensity}}_{1}\times {\text{distance}}_{1}^{2}={\text{intensity}}_{2}\times {\text{distance}}_{2}^{2}$

Occurrences

Electrostatics

The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as Coulomb's law. The deviation of the exponent from 2 is less than one part in 1015

$F=k_{\text{e}}{\frac {q_{1}q_{2}}{r^{2}}}$

Light and other electromagnetic radiation

The intensity (or illuminance or irradiance) of light or other linear waves radiating from a point source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source, so an object (of the same size) twice as far away receives only one-quarter the energy (in the same time period).

Heliocentric Model - lights in the sky

Using the inverse square law of light and the heliocentric assumptions of the distance to the moon (and that the moon is reflecting sunlight), you can calculate that the moon's surface would have been 1 trillion times brighter than the sun when viewed from the earth. Why are there so few people in academia that point out this obvious fraud?

Some people incorrectly state that the inverse square law is only valid for "point sources of light" (like the sun). The moon, however, in the Heliocentric Model is not a point source of light, so they claim the inverse square law of light equation has been misapplied and the numbers are not valid on that basis alone.

They claim that flat earthers do not account for the atmospheric scattering and reflecting of light before it reaches the surface of the earth. There are claims that the moon has no atmosphere, so all the light that hits it, reaches the surface. NASA fan boys claim only about 12% of light that hits it is reflected. For comparison, the Earth reflects about 30% of the light that reaches its surface, and only about 56% of sunlight makes it to the surface.

However one thing to consider, If you make the sun a "point light source" then you have no way to explain the seasons on the earth which requires a directional light source with all rays coming in parallel. A "point light source" is also the same assumption required to determine the distance of the sun and planets in the first instance. They also use this "point light source" assumption to have calculated the radius of the earth in the days of eratosthenes. This doesn't work for eclipses though does it? In these cases they switch back to the "point light source" to explain why the umbra of the eclipse isn't 1000 miles wide. This is what you would expect from a directional light source, unfortunately it just doesn't happen because the sun is not what they are telling you it is.