Dumb physics question: "Jupiter's orbit is five times farther from the Sun than Earth's orbit, which means that the giant planet receives 25 times less sunlight than Earth."
Would the amount of energy from the sun be the square root or the cube root? I assumed the latter because space exists in three dimensions.
Total energy the star projects on a sphere is same at any radius. The formula for surface of a sphere is 4 * pi * r ^2. So if Earth was placed in Jupiter's orbit it would indeed receive 25 times less solar flux because the surface area of the sphere would be 25 times larger.
However, Jupiter's planetary radius is 11 times that of Earth (69,911 km vs 6,371). Area of the circle is pi * r^2, so Jupiter receives 121/25 ~= 5 times more total sunlight than Earth. Of course it also has 121 times larger surface area (see surface of the sphere equation above), so per square meter Jupiter does receive about 25 times less sunlight.
Every instant the sun emits a certain amount of energy. After 1 second that energy is spread across the surface of a sphere 4pi(c)^2 big. After 2 seconds it's spread across a the surface of a sphere 4pi(2c)^2. And so forth.
Or another way to look at is that that at a certain distance from the sun all the energy leaving the sun is passing through a sphere that grows that same way.
EDIT: Thanks to grn for pointing out I was confusing the constant of a sphere's volume with its area. Fixed.
A bunch of comments have explained already, but I'd recommend this wikipedia article with some helpful illustrations for anyone who's having trouble visualizing it:
It's the inverse square (not a root), because the surface of the planet is two-dimensional. Think of moving a projector screen back and forth. For a fixed aperture angle, the area projected upon will grow quadratically with distance, so the intensity (inverse area) grows inverse-quadratically.
A given amount of light emitted by the Sun is spread over a sphere of radius r. As the light propagates the radius gets bigger and bigger. The light per area is proportional to 1 / 4πr². If the radius grows 5 times then the area of the sphere grows 25 times.
>"We learn that the force between two charges, two magnetic monopoles, or two masses all follow an inverse square law, however, most of the time, the scientific reader is not made aware of an important assumption, that of being able to model these entities as point objects. If the entities cannot be reduced to a point, then, the inverse square laws cannot be applied. As I shall mathematically show, the inverse square law changes into an inverse cube law approximation for the case of dipoles. In practice, a physicist finds that most of real life applications cannot be modelled by point entities, but only by dipoles."
[+] [-] dalbasal|7 years ago|reply
[+] [-] JorgeGT|7 years ago|reply
Link to the mentioned Nature Astronomy letter: http://doi.org/10.1038/s41550-018-0442-z
[+] [-] teachrdan|7 years ago|reply
Would the amount of energy from the sun be the square root or the cube root? I assumed the latter because space exists in three dimensions.
[+] [-] TrainedMonkey|7 years ago|reply
However, Jupiter's planetary radius is 11 times that of Earth (69,911 km vs 6,371). Area of the circle is pi * r^2, so Jupiter receives 121/25 ~= 5 times more total sunlight than Earth. Of course it also has 121 times larger surface area (see surface of the sphere equation above), so per square meter Jupiter does receive about 25 times less sunlight.
[+] [-] Symmetry|7 years ago|reply
Or another way to look at is that that at a certain distance from the sun all the energy leaving the sun is passing through a sphere that grows that same way.
EDIT: Thanks to grn for pointing out I was confusing the constant of a sphere's volume with its area. Fixed.
[+] [-] wlesieutre|7 years ago|reply
https://wikipedia.org/wiki/Inverse-square_law
[+] [-] ballenarosada|7 years ago|reply
[+] [-] grn|7 years ago|reply
[+] [-] tejtm|7 years ago|reply
[+] [-] nonbel|7 years ago|reply
>"We learn that the force between two charges, two magnetic monopoles, or two masses all follow an inverse square law, however, most of the time, the scientific reader is not made aware of an important assumption, that of being able to model these entities as point objects. If the entities cannot be reduced to a point, then, the inverse square laws cannot be applied. As I shall mathematically show, the inverse square law changes into an inverse cube law approximation for the case of dipoles. In practice, a physicist finds that most of real life applications cannot be modelled by point entities, but only by dipoles."
http://blazelabs.com/inversecubelaw.pdf
[+] [-] maxxxxx|7 years ago|reply
[+] [-] rubidium|7 years ago|reply
[+] [-] letitgo12345|7 years ago|reply
[+] [-] unknown|7 years ago|reply
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