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How does inverse square law of gravity relate to the inverse square law of electromagnetic radiation (e.g. illumination)? How come gravity and EMR propagate identically even though they are different forces?
An inverse square law is a mathematical relationship in which the strength or intensity of a physical quantity decreases as the square of the distance from its source increases. This means that as the distance increases, the strength or intensity decreases exponentially.
In the case of gravity, the inverse square law states that the force of attraction between two objects is inversely proportional to the square of the distance between them. This means that the force decreases as the distance between the objects increases, and can be calculated using the equation F = Gm1m2/d2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between them.
In the case of EMR, the inverse square law states that the intensity or power of the radiation decreases as the square of the distance from the source increases. This means that the farther away an object is from the source of radiation, the less radiation it will receive. This is why, for example, the sun's rays feel less intense the farther away you are from it.
Some common examples of inverse square laws include: the intensity of sound from a loudspeaker, the strength of a light bulb's illumination, and the gravitational pull between celestial bodies. In all of these cases, the strength or intensity decreases as the distance from the source increases.
Inverse square laws are important in science because they help us understand and predict how physical quantities, such as gravity and EMR, behave. They also allow us to make accurate calculations and models for various phenomena, from the movement of planets to the spread of light and sound. Understanding inverse square laws is crucial for many fields of science, including physics, astronomy, and engineering.