from the July 22 issue?

All places have, on average, the same amount of daylight (12 hours a day, setting aside possible technical quibbles having to do with twilight and the like). Southern states have more than the northern ones during the winter, but less during the summer.

Why do people use bar charts when they should use scatter plots?

And yes, the image is 'way too big!

in the fall and winterthat you get more hours of sunlight as you move south, although you indeed get more energy from sunlight over the year as you move towards the equater.There's an interesting mathematical problem here.

On a planet where the axis of rotation is parallel to the axis of the orbit, the equater gets a certain amount of sunlight but the poles get essentially none [considering the sun to be a point and considering the planet to not have a refractive atmosphere]. Such a planet is said to have an inclination of zero degrees.

On a planet where the axis of rotation is in the

planeof the orbit, the poles get a certain amount of sunlight, the same amount as the equater gets on the zero inclination planet, and the equater gets less, so the poles get more than the equater. Such a planet has an inclination of ninety degrees.The amount of sunlight reacing the pole and reaching the equater is a continuous monotonic function of the inclination, so there must be a unique inclination where the poles and the equater get the same amount of sunlight. Can anyone figure out that inclination? Can anyone figure out whether, on such a planet, the intermediate latitudes get that same amount of sunlight, or more, or less?

-dk

A nitpick to a nitpick. I love it. Professor Volokh should have written, "All places have, on average, the same

~~amount~~durationof daylight. . . ."Defining "equator" to be the place farthest from the axis of rotation on the planet and the planet's period of rotation to be << than the period of revolution (orbit)...

If by "amount" you mean "duration" of sunlight, then any non-zero inclination will yield the same average hours of sunlight per year for any location (A pole, equatorial position, otherwise), just like on Earth.

If by "amount" you mean "energy" of sunlight, then a 90-degree axis of rotation (axis of rotation in plane of orbit) yields the same average intensity (energy/unit area) throughout the year for each pole and any equatorial location. Any lesser inclinations increase the equatorial location's average energy at the expense of the polar locations'.

This is wrong if we are speaking of total sunlight energy per year at a particular location. Are you wanting the calculation for both poles' duration or energy combined?

combinedyearly sunlight energy from both poles was equal to any given equatorial position's, it's 26.565 degrees.Of course the poles get one "day" a year of 6 months length.

above the arctic circle gets some winter days with no daylight, just a twilight, and some summer days with the sun continuously in the sky.

It says "

Statessouth of Topeka get more [intense] daylight. . . ." This is true because there are no states south the of equator. But I don't know why the paper mentioned Topeka.As a webmaster back in the days when I wrote my html using notepad and my traffic consisted of ppl who were 99% dialup at 28.8 or slower......

Why is the original image that large to begin with?

You're forcing ppl to download, in bytes, an image larger than what they are displaying on their screen.

Photoshop, or whatever imageing software you prefer, can shrink such an image

beforeyour users download it.I know that broadband is rampant these days but bandwidth is still not infinite. Never post an image larger than one size smaller than your average users screen resolution. Back in my day that was 800x600, (which meant 640x480 for "large" images), and I never posted images that large. Just thumbnails with links if I thought the image warrented such.

Just a thought...

Taking as a source "Thermal Environmental Engineering", Threlkeld, 2nd Ed., and using information on sun angles, Equation 13.3 states:

sin(B) = cos(l)cos(h)cos(d) + sin(l)sin(d)

Where:

B is the sun's altitude angle

l is the latitude angle

h is the sun's hour angle

d is the sun's angle of declination

At sunrise/sunset, B = zero, so:

h = arccos[-tan(l)tan(d)]

Thus, for a given angle of declination (which varies with the season) the hour of sunrise/sunset DOES vary with latitude "l". This means that in turn, the length of day-lit period also varies, on a given day, as one travels from south to north.

This is correct, the length of day does vary by lattitude for any given non-equinox day on Earth. The answer, however, states that

on average(taken over at least a year) every location gets the same amount (~12 hours) of sunlight, which is also true.