What-if 0010: "Cassini"

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Max™
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Re: What-if 0010: Cassini

Postby Max™ » Wed Sep 05, 2012 3:48 am UTC

I hurt my neck trying to contort into the right angle to see that... damn you, it was just getting better too!
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jtboofle
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Re: What-if 0010: Cassini

Postby jtboofle » Wed Sep 05, 2012 4:07 am UTC

SlyReaper wrote:I don't get it. Whining isn't a British stereotype at all. We do orderly queues, apology, posh accents, and stiff upper lips. I don't know where you got whining from.


Weather.

You're very good sports about most things. I suspect you could chop an Englishman's arm off without him complaining over anything more than the challenge of learning to drink tea with the other hand, but you people have a problem with weather.

I remember hopping off the plane at Heathrow and hearing about the bloody heat wave on the entire drive back to town. It started raining about 20 minutes after we got to the flat, at which point my hosts started whining about the rain.

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Re: What-if 0010: Cassini

Postby armandoalvarez » Wed Sep 05, 2012 4:55 am UTC

Cassini seems to have deliberately targeted Spanish-speaking America, huh? (well, Argentina and I guess Puerto Rico have been spared from the Antarctic chill). Not that South/SE Asia got off any easier, but it's weird that the new Antarctica looks almost exactly like a map of the Spanish language in the Americas.
EDIT: With a little more thought, I hereby propose that in order to keep half the human population from living in uninhabitable frozen wasteland, we give Antarctica to the people of the Indian subcontinent. We transfer the people what was SE Asia to what was formerly the Australian desert. And we give inland Alaska, the Canadian territories, and the former Greenland ice sheet to the Spanish speaking world. I figure this will get most of the newly frozen population into inhabitable countries with the least number of natives displaced (and the fewest miles traveled compared to, for example, sending the Mexicans to Antarctica).
My apologies to the current inhabitants of the countries I just gave away, but it's better than shoving the entire displaced population in Antarctica.

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Re: What-if 0010: Cassini

Postby mhwilking » Wed Sep 05, 2012 5:01 am UTC

You had me at "...the final, fatal broadcast of A Prairie Home Companion." Oh, but it were true.

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Re: What-if 0010: Cassini

Postby PM 2Ring » Wed Sep 05, 2012 6:34 am UTC

Here's a link to a cropped, rotated & scaled version of a Cassini projection of Earth from Wikipedia. Obviously, the colours aren't correct for Randall's scenario, but it's bigger than his map and the lines are neater. :)

Image

This file can be used as the source data for my HTML/JavaScript Globe animation program, so you can see this globe rotating in your Web browser. This program has been tested in FireFox and Konqueror, but it should run in the latest version of Internet Explorer, and any browser that supports the Canvas element.

For security reasons, your browser may not allow scripts to access the pixel data of images on the local hard drive, or on domains different from the domain where the script is hosted. If that is the case, your browser will pop up a dialog asking you to give it explicit permission.

Code: Select all

<!DOCTYPE html>
<html>
<head>
<title>Globe</title>
<meta http-equiv="Content-Script-Type" content="text/javascript">
<style type="text/css">
body{ background-color: #404040 }
h4, hr, a {color: #fa8 }
p { color: #ff8 }
p.centered{ text-align: center }
span {font-size: large; color: #fa8 }
th, h3 { text-align: center; font-size: large; color: #fa8 }
input { width: 90px; }
table { color: #ff8;
 border: solid;  border-color: #fa8
}

</style>
<script type="text/javascript">
var srcMap, mapname =
    //'images/EarthColour_2048.jpg',
    'http://maps.jpl.nasa.gov/pix/jup0vss1.jpg',
    srcpix, octx, ocanvasData, pixels,
    iwidth, iheight, owidth, oheight,
    rad = 180, iscale = 1.25,
    blur = 0.65, gamma = 0.75,
    delay = 50, delta = 0, ddelta = 1, go = false, timeout;

function byId(id) { return document.getElementById(id); }

//Create a canvas element
function make_canvas(w, h)
{
    var c = document.createElement('canvas');

    c.setAttribute('width', w);
    c.setAttribute('height', h);
    return c;
}

//Do Gaussian blurring from src image / canvas into canvas context ctx.
// Mixing ratio: 0 <= r <= 1. 0=Not blurred, 1 = fully blurred
function drawBlurredImage(ctx, src, r)
{
    ctx.globalAlpha = 1 - 12*r/16;
    ctx.drawImage(src, 0, 0);
    if (r == 0)
        return;

    ctx.globalAlpha = 2*r/16;
    ctx.drawImage(src, -1, 0); ctx.drawImage(src, 1, 0);
    ctx.drawImage(src, 0, -1); ctx.drawImage(src, 0, 1);

    ctx.globalAlpha = 1*r/16;
    ctx.drawImage(src, -1, -1); ctx.drawImage(src, 1, -1);
    ctx.drawImage(src, -1, 1); ctx.drawImage(src, 1, 1);
}

// Get canvas pixel data from context ctx
function get_pixels(ctx, ox, oy, w, h)
{
    try
    {
        try
        {
            //Attempt to read canvas data
            var imgd = ctx.getImageData(ox, oy, w, h);
        }
        catch (e)
        {
            //Ask user to give us permission to read canvas data
            netscape.security.PrivilegeManager.enablePrivilege("UniversalBrowserRead");
            var imgd = ctx.getImageData(ox, oy, w, h);
        }
    }
    catch (e)
    {
        var msg = "Unable to access Canvas image data: " + e;

        alert(msg);
        throw new Error(msg);
    }
    return imgd;
}

function init()
{
    set_inputs();
    init_globe();
}

function init_globe()
{
    owidth = 2 * rad; oheight = owidth;
    iheight = Math.floor(iscale * oheight);
    iwidth = 2 * iheight;

    init_ocanvas();
    init_image();
}

function init_ocanvas()
{
    var ocanvas;

    //Set up display canvas
    ocanvas = document.getElementById('outcanvas');
    if (!ocanvas.getContext)
        return alert("Sorry, I can't set up the canvas!");

    ocanvas.width = owidth;
    ocanvas.height = oheight;

    octx = ocanvas.getContext('2d');
    octx.fillStyle = "rgba(64,64,64, 255)";
    octx.fillRect(0, 0, owidth, oheight);
    ocanvasData = get_pixels(octx, 0, 0, owidth, oheight);
    pixels = ocanvasData.data;
}

//Load source map image & wait for image to finish loading before proceeding
function init_image()
{
    //Load globe lat-long map
    srcMap = document.createElement('img');
    srcMap.src = mapname;
    srcMap.onload = init_map;
}

function init_map()
{
    var i, tmpCanvas, tmpCtx, srcCanvas, srcCtx;
   
    //var sc = Math.max(iwidth / srcMap.width, iheight / srcMap.height);

    //Scale source image to final size
    tmpCanvas = make_canvas(iwidth, iheight);
    tmpCtx = tmpCanvas.getContext('2d');
    tmpCtx.scale(iwidth / srcMap.width, iheight / srcMap.height);
    tmpCtx.drawImage(srcMap, 0, 0);

    //Create the source canvas
    srcCanvas = make_canvas(iwidth, iheight);
    srcCtx = srcCanvas.getContext('2d');

    //Do Gaussian blurring on scaled source image
    drawBlurredImage(srcCtx, tmpCanvas, blur)

    //Get pixel data from scaled blurred source map
    srcpix = get_pixels(srcCtx, 0, 0, iwidth, iheight).data;

    if (gamma != 1.0)
    {
        function do_gamma(p) { return Math.floor(255*Math.pow(p/255, gamma)); }

        //On each pixel, do gamma correction
        for (i=0; i<srcpix.length; i+=4)
        {
            srcpix[i] = do_gamma(srcpix[i]);
            srcpix[i+1] = do_gamma(srcpix[i+1]);
            srcpix[i+2] = do_gamma(srcpix[i+2]);
        }
    }
    draw();
}

//Project from lat-long form to orthographic
function draw()
{
    var i, j, ko, ki, u, v, r, pi = Math.PI,
    y, oy = oheight / 2, oy2 = oy * oy, ox = owidth / 2;

    for (j=0; j<oheight; j++)
    {
        y = j - oy;
        v = Math.floor(iheight * (0.5 + Math.asin(y / oy) / pi));
        r = Math.floor((Math.sqrt(oy2 - y*y)));
        for (i=1-r; i<r-1; i++)
        {
            u = Math.floor(iwidth * (2 - 0.5 * Math.acos(i/r) / pi) - delta) % iwidth;
            ki = 4 * (u + iwidth * v)
            ko = 4 * (ox + i + owidth * j);
            pixels[ko++] = srcpix[ki++];
            pixels[ko++] = srcpix[ki++];
            //pixels[ko++] = srcpix[ki++];
            pixels[ko] = srcpix[ki];
        }
    }
    octx.putImageData(ocanvasData, 0, 0);
    delta = (delta + iwidth + ddelta) % iwidth;
}

function timer()
{
    if (go)
    {
        draw();
        timeout = window.setTimeout("timer()", delay);
    }
}

//Toggle timer
function pause()
{
    if(go = !go)
    {
        timer();
        byId('ipause').value = "Pause";
    }
    else
    {
        window.clearTimeout(timeout);
        byId('ipause').value = "\xA0Play\xA0\xA0";
    }
}

//Set input value fields from Javascript global vars
function set_inputs()
{
    byId('ipause').value = "\xA0Play\xA0\xA0";
    byId('imap').value = mapname;
    byId('irad').value = rad;
    byId('iiscale').value = iscale;
    byId('iblur').value = blur;
    byId('igamma').value = gamma;
    byId('idelay').value = delay;
    byId('iddelta').value = ddelta;
}

//Update Javascript global vars from input value fields
function update()
{
    //Pause while changing vars
    go = true;
    pause();

    mapname = byId('imap').value;
    rad = byId('irad').value - 0;
    iscale = byId('iiscale').value - 0;
    blur = byId('iblur').value - 0;
    gamma = byId('igamma').value - 0;
    delay = byId('idelay').value - 0;
    ddelta = byId('iddelta').value - 0;

    delta = 0;
    init_globe();
    pause();
}

</script>
</head>
<body onload="init();">
<p class="centered">
<canvas id="outcanvas">
If you can read this, your browser does not support the HTML5 Canvas.
</canvas>

<p>
<input type="button" id="ipause" onclick="pause();">

<table>
<th colspan="4">Parameters</th>
<tr> <td> Map    <td colspan="3"> <input type="text" id="imap" style="width: 260px"> </tr>
<tr> <td> Radius <td> <input type="text" id="irad">
 <td> Scale  <td> <input type="text" id="iiscale"> </tr>
<tr> <td> Blur   <td> <input type="text" id="iblur">
 <td> Gamma  <td> <input type="text" id="igamma"> </tr>
<tr> <td> Delay  <td> <input type="text" id="idelay" onchange="delay=this.value-0">
 <td> Delta  <td> <input type="text" id="iddelta" onchange="ddelta=this.value-0"> </tr>

<tr> <td colspan="2"> <input type="button" id="update" value="Update" onclick="update();"> </tr>
</table>

<hr>

<h3>Globe</h3>
<h4>by PM 2Ring</h4>
<p>
This JavaScript / HTML program creates animated globe images from planet and moon map images in equirectangular format. This is the usual format that NASA uses for its map images: a full planet (or moon) image in this format is twice as wide as it is tall. The program can read image files from an Internet URL, or from your hard drive. The map image data is scaled, blurred and gamma corrected before being orthogonally projected. The projection function uses no interpolation, so it runs reasonably fast, but the downside is that the resulting image is a bit "sparkly", especially on the left &amp; right edges. This can be alleviated by playing with the scale of map image data, and by the use of blurring.<br><br>

For security reasons, your browser may not allow scripts to access the pixel data of images on the local hard drive, or on domains different from the domain where the script is hosted. If that is the case, your browser will pop up a dialog asking you to give it explicit permission. The original version of this script doesn't do anything dodgy; obviously I can make no claims about any modified scripts that are built from it...<br><br>

The image processing &amp; display utilizes the HTML5 Canvas element, so it may not work on older browsers.<br>

<h4>Parameters</h4>
<p>
<span>Map:</span> The URL or file name of the equirectangular map image file, which should be a JPEG, PNG, or GIF file (or any other format your browser can display directly). If you wish to use a local file, you can give its name relative to the directory you are running this script from, or you can give the file name in absolute form by specifying the name as a file:// URL. The default value for this parameter is a JPL / NASA URL for a map of Jupiter; there are various other maps in the <a href="http://maps.jpl.nasa.gov/pix/">same directory</a>.<br><br>

<span>Radius:</span> The radius (in pixels) of the globe image.<br><br>

<span>Scale:</span> This controls the scaled size of the source map, relative to the globe image: a scale of 1 makes the map the same height as the globe. A scale around 1 gives the best results. If the scale is too large, the globe will be too sparkly; if it's too small, the globe will get pixelated. The scale also controls the speed that the globe turns: the larger the scale, the slower the rotation.<br><br>

<span>Blur:</span> How much blurring to apply. 0 = no blurring, 1 = maximum blurring.<br><br>

<span>Gamma:</span> Gamma correction factor. This affects the brightness of the image. Gamma values less than 1 make it brighter, greater than 1 make it darker. Gamma must be greater than zero.<br><br>

<span>Delay:</span> The time delay between frames, in milliseconds, not counting processing time. The default of 50 should be adequate. If you try to speed it up or slow it down too much the resulting animation may be jerky.<br><br>

When you change the parameters to new values, hit the Update button to tell the program to regenerate the data with the new values. The delay parameter can be modified without using the Update button (just hit enter after changing the delay value), but changes to the other parameters require the map data to be recalculated; the Update button allows you to change multiple parameters without the calculations being redone for every single change.<br><br>

To keep this program as simple and compact as possible, there is NO error checking performed on any parameter values entered, so if you enter weird values outside the acceptable range, expect weird results. :)<br>

<hr>
</body>
</html>

Just save the text in the Code box to a .html file on your HD and then load it into your browser to read the instructions. The page will load showing its default image: a globe of Jupiter, courtesy of NASA. (FWIW, I posted an earlier version of this program in the xkcd Coding forum).

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Re: What-if 0010: Cassini

Postby Soeroah » Wed Sep 05, 2012 7:23 am UTC

I'm probably missing something really obvious, but I'm totally unable to work out how Australia seems to be flipped 90 degrees in the opposite direction to the other continents.


Or in the picture there http://upload.wikimedia.org/wikipedia/commons/b/bd/Cassini_projection_SW.jpg is it just that, due to globes, Australia also belongs above the upper-right greenry...south?...of Old Asia?

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Re: What-if 0010: Cassini

Postby Angelastic » Wed Sep 05, 2012 8:00 am UTC

keithl wrote:We will not receive that last segment of Prairie Home Companion. Much of the NPR network is collected and distributed by satellite, and most of the geosynchronous satellites will be in the wrong place in the sky, with the wrong polarizations on the transponders. If the equatorial GEO belt is rotated along with the equator, then the satellites stop working, not merely useless.
Yeah, I was a bit disappointed that the radio thing turned out to be a quick reference to some show I've never heard of, rather than something interesting about satellite positions. Thanks for filling that in. :)
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Re: What-if 0010: Cassini

Postby flicky1991 » Wed Sep 05, 2012 8:19 am UTC

SlyReaper wrote:I don't get it. Whining isn't a British stereotype at all.

You're from England and haven't heard of the stereotype of British people complaining about everything? That's weird - I have. Maybe it's more of a London thing.
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Re: What-if 0010: Cassini

Postby AvatarIII » Wed Sep 05, 2012 1:14 pm UTC

flicky1991 wrote:
SlyReaper wrote:I don't get it. Whining isn't a British stereotype at all.

You're from England and haven't heard of the stereotype of British people complaining about everything? That's weird - I have. Maybe it's more of a London thing.


My experience of the stereotype is that English people tolerate things and whine about them instead of taking action.

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Re: What-if 0010: Cassini

Postby J Thomas » Wed Sep 05, 2012 1:46 pm UTC

keithl wrote:We will not receive that last segment of Prairie Home Companion. Much of the NPR network is collected and distributed by satellite, and most of the geosynchronous satellites will be in the wrong place in the sky, with the wrong polarizations on the transponders. If the equatorial GEO belt is rotated along with the equator, then the satellites stop working, not merely useless


You are assuming the satellites will be rotated along with the planet? But if the planet is rotated 90 degrees and then spun up with the axis in the same direction as it was before, and the moon is left alone and the satellites are left alone, then they'd still be there and the only problem would be most of the ground stations are now in the wrong places.
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Re: What-if 0010: Cassini

Postby mathmannix » Wed Sep 05, 2012 2:13 pm UTC

I'm surprised nobody has mentioned that the new South Pole is basically the Galapagos Islands... poor frozen giant turtles!!!

At first I was confused why Randall chose this particular alternate 90-degree shift... after all, there are, of course, infinitely many possibilities. Assuming that the questioner intended the poles to move, which makes more sense than the "wait six hours" response that I so enjoyed, then the poles could be anywhere along our current equator, right? I realized that it seemed a good choice to take the new equator to be the Prime Meridian / 180-degree meridian, but my first impulse was that the new north pole should be 0 degrees, 0 degrees (off the African coast of Ghana, Gabon, Equatorial Guinea (naturally), etc.) and the South Pole should be 0 degrees, 180 degrees (in a rather remote section of the Pacific, approximately midway from Hawaii to Australia or New Guinea, and closer to the countries of Nauru and Tuvalu.)

Anyway, I think the new map would look more or less like this:

earth3.jpg


At least Antarctica would be the same as in Randall's idea...
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Re: What-if 0010: Cassini

Postby another josh » Wed Sep 05, 2012 2:34 pm UTC

Now, arbitrarily choose another meridian to be the new equator and repeat. Really, the choice of using the current Prime Meridian is based on an arbitrary choice made some centuries ago.

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Re: What-if 0010: Cassini

Postby AvatarIII » Wed Sep 05, 2012 3:00 pm UTC

the reason that Randall chose that specific way to rotate the globe, is simply because a map projection for the new globe already existed.

also I get what you are implying mathmannix, but your edited map doesn't make sense.

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Re: What-if 0010: Cassini

Postby mathmannix » Wed Sep 05, 2012 4:04 pm UTC

I know I didn't make the projection look accurate (South America should be smaller and not go all the way to the top, Asia should be larger, etc.) but it was just to get a general feel for the positions.
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Re: What-if 0010: Cassini

Postby Red Hal » Wed Sep 05, 2012 5:23 pm UTC

The "prime-meridian is new equator" seems to generate more habitable land, on account of passing through both oceans. I wonder if there is a better one? Hmm, here's an interesting thought experiment; if the object is to maximise habitable land, which would be the best equator to choose? Also, would that change if one were not constrained to a great circle passing through the current poles? To wit, if one could choose any great circle to become the new equator, which would maximise habitable land?
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Re: What-if 0010: Cassini

Postby Jackpot777 » Wed Sep 05, 2012 6:56 pm UTC

It looks like the best place for the International date Line is between Australia and New Zealand, and (the former) Antarctica. Meaning a nice population-dense place to stick the new Meridian through would be Gothenburg, Sweden. Maybe Oslo, Norway would be better .

Image

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Re: What-if 0010: Cassini

Postby hthall » Wed Sep 05, 2012 7:20 pm UTC

ech wrote:
edmeserve wrote:Randall didn't take into consideration that the spin of the planet distorts the shape from a sphere to an oblate spheroid.
The oceans are pulled toward the equator by centrifugal force of the spin, causing the ocean to be as much as 5 miles higher than at the poles.
http://bigthink.com/strange-maps/475-th ... tood-still

If the the Prime Meridian were now the equator, the oceans would "pool-up" and submerge parts of Northern Canada (and Alaska), Europe, Western Africa. Places like the Carribean would see an increase in land mass.

No, I don't think this would be an issue in the scenario under consideration. The Earth's spin causes the equator—and the ocean—to bulge now, and it would do likewise on Cassini. Both the crust and the water would be similarly deformed; I don't think anyone would notice.


The oblate spheroid was my first thought as well. Considering the upheaval that we now see whenever the earth's crust stretches or compresses by a few feet, the result of the crust pulling apart by about 40 miles total along its new equator, and compressing by the same amount at the poles, not to mention the sloshing shift of the underlying magma, to relax to its equilibrium shape would be … noticeable.

We'll just assume that this is all describing circumstances after a few thousand years' worth of cataclysmic earthquakes and volcanoes have quieted down a bit.
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Re: What-if 0010: Cassini

Postby J Thomas » Wed Sep 05, 2012 8:07 pm UTC

hthall wrote:
ech wrote:
edmeserve wrote:Randall didn't take into consideration that the spin of the planet distorts the shape from a sphere to an oblate spheroid.
The oceans are pulled toward the equator by centrifugal force of the spin, causing the ocean to be as much as 5 miles higher than at the poles.
http://bigthink.com/strange-maps/475-th ... tood-still

If the the Prime Meridian were now the equator, the oceans would "pool-up" and submerge parts of Northern Canada (and Alaska), Europe, Western Africa. Places like the Carribean would see an increase in land mass.

No, I don't think this would be an issue in the scenario under consideration. The Earth's spin causes the equator—and the ocean—to bulge now, and it would do likewise on Cassini. Both the crust and the water would be similarly deformed; I don't think anyone would notice.


The oblate spheroid was my first thought as well. Considering the upheaval that we now see whenever the earth's crust stretches or compresses by a few feet, the result of the crust pulling apart by about 40 miles total along its new equator, and compressing by the same amount at the poles, not to mention the sloshing shift of the underlying magma, to relax to its equilibrium shape would be … noticeable.

We'll just assume that this is all describing circumstances after a few thousand years' worth of cataclysmic earthquakes and volcanoes have quieted down a bit.


Or maybe something that can rotate the earth 90 degrees against its axis and spin it up on a new axis can also subtly reshape it so those effects are no so lethal.
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Re: What-if 0010: Cassini

Postby Tass » Wed Sep 05, 2012 9:12 pm UTC

Jackpot777 wrote:It looks like the best place for the International date Line is between Australia and New Zealand, and (the former) Antarctica. Meaning a nice population-dense place to stick the new Meridian through would be Gothenburg, Sweden. Maybe Oslo, Norway would be better .


Now you could make this prime meridian the new equator. Find a new obvious date line and repeat.

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Re: What-if 0010: Cassini

Postby PM 2Ring » Thu Sep 06, 2012 2:30 am UTC

another josh wrote: Really, the choice of using the current Prime Meridian is based on an arbitrary choice made some centuries ago.


No, the current Prime Meridian as an international standard is relatively recent.
International Meridian Conference wrote:The International Meridian Conference was a conference held in October 1884 in Washington, D.C., in the United States to determine a prime meridian for international use. The conference was held at the request of U.S. President Chester A. Arthur. The subject to discuss was the choice of "a meridian to be employed as a common zero of longitude and standard of time reckoning throughout the world" (Proceedings of the 1884 International Meridian Conference, page 7). It resulted in selection of the Greenwich Meridian as an international standard for zero degrees longitude.

Twenty-five nations, represented by 41 delegates, participated in the conference

[...]

The French did not adopt the Greenwich meridian until 1911.

Although two delegates, including Sandford Fleming, proposed the adoption of standard time by all nations, other delegates objected, stating that it was outside the purview of the conference, so neither proposal was subjected to a vote. Thus the conference did not adopt any time zones, contrary to popular belief.


Also see http://en.wikipedia.org/wiki/Prime_meridian#History for various historical meridians. For example, a line through the Azores (~ 25°W) was used by Ptolemy, and it continued to be commonly used until the middle ages.

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Re: What-if 0010: Cassini

Postby keithl » Thu Sep 06, 2012 8:43 pm UTC

J Thomas wrote:
keithl wrote:We will not receive that last segment of Prairie Home Companion. Much of the NPR network is collected and distributed by satellite, and most of the geosynchronous satellites will be in the wrong place in the sky, with the wrong polarizations on the transponders. If the equatorial GEO belt is rotated along with the equator, then the satellites stop working, not merely useless


You are assuming the satellites will be rotated along with the planet? But if the planet is rotated 90 degrees and then spun up with the axis in the same direction as it was before, and the moon is left alone and the satellites are left alone, then they'd still be there and the only problem would be most of the ground stations are now in the wrong places.


I was unclear. I intended to describe two possibilities - either the satellites stay fixed in space (as the earth suddenly pivots at 0N 0E), or they turn with the (former) equator. As you say, the first puts the satellites in the wrong position in the sky for all the bolted-down dish antennas. To see GEO, our antennas would need their elevation changed, at least.

Assuming the satellites stay fixed in space, the same relay satellites would be visible from the US - centered around longitude 95W, we just rotated down 90 degrees (A different story if we rotate over the pole 90 degrees). However, the transponders on the satellites (which are very carefully positioned in the factory, to point at the right places on the ground) would now be pointed uselessly. The US transponders would now be pointed at western China, and South American transponders would mostly be pointed at the Atlantic. There are no transponders now pointed at the southwest Pacific between 65 and 41 south, the new US contiguous state latitudes. I suppose the satellites could be rotated 180 degrees and repositioned in orbit, so their north-pointing transponders are now south-pointing.

If the GEO orbit rotates also, the satellites are now in a polar orbit, and the earth rotates under their ground track. That would make it impossible for fixed high-gain antennas to stay pointed at them. Keeping their solar arrays pointed at the sun and also balanced against tidal gradients would be difficult, probably beyond their capabilities.

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Re: What-if 0010: Cassini

Postby J Thomas » Thu Sep 06, 2012 10:18 pm UTC

keithl wrote:I was unclear. I intended to describe two possibilities - either the satellites stay fixed in space (as the earth suddenly pivots at 0N 0E), or they turn with the (former) equator. As you say, the first puts the satellites in the wrong position in the sky for all the bolted-down dish antennas. To see GEO, our antennas would need their elevation changed, at least.


When you explain it in detail, I can look back at what you said the first time and see it clearly. I think the flaw was in my reading more than your writing. Sorry about that.
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Re: What-if 0010: Cassini

Postby Rotherian » Thu Sep 06, 2012 10:24 pm UTC

I might be wrong, but shouldn't the Cassini projection be applied after the 90 degree rotation about the x-axis occurs? Unless I'm mistaken, any globe projection (Cassini, Mercator, Waterman, etc.) should apply to the globe in the state in which the projection is attempting to display. So, in the globe form, the positions would be approximately like the following (at 6-hour intervals)*:

ImageImageImageImage

*Obviously, I didn't feel like recoloring them, but the projection should be based upon something similar to those.
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Re: What-if 0010: Cassini

Postby Max™ » Thu Sep 06, 2012 11:37 pm UTC

Like I said, that planetocopia site covers a lot of that stuff, it's great, besides the furry bits in the ecological hypothesizing.
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Re: What-if 0010: Cassini

Postby Rotherian » Fri Sep 07, 2012 1:03 am UTC

Max™ wrote:Like I said, that planetocopia site covers a lot of that stuff, it's great, besides the furry bits in the ecological hypothesizing.


It does, but instead of using the PM as the new equator, the person decided to go with the N&S poles completely within ocean areas. This wouldn't be the case since both poles would consist primarily of land.
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Re: What-if 0010: Cassini

Postby Max™ » Fri Sep 07, 2012 2:14 am UTC

There are other versions too, one where pacific coast was equatorial, one where siberia was an ice cap.

Very interesting explorations all in all, worth checking out if you liked the idea in this what-if.
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Re: What-if 0010: Cassini

Postby rmsgrey » Fri Sep 07, 2012 1:43 pm UTC

Rotherian wrote:I might be wrong, but shouldn't the Cassini projection be applied after the 90 degree rotation about the x-axis occurs? Unless I'm mistaken, any globe projection (Cassini, Mercator, Waterman, etc.) should apply to the globe in the state in which the projection is attempting to display.


The point being made is that the Mercator-ish (I'm not an expert on cartography, so I've no idea which projection it actually is) projection showing the new geography is similar to the Cassini projection of the current arrangement.

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Re: What-if 0010: Cassini

Postby Rotherian » Sat Sep 08, 2012 12:41 am UTC

rmsgrey wrote:
Rotherian wrote:I might be wrong, but shouldn't the Cassini projection be applied after the 90 degree rotation about the x-axis occurs? Unless I'm mistaken, any globe projection (Cassini, Mercator, Waterman, etc.) should apply to the globe in the state in which the projection is attempting to display.


The point being made is that the Mercator-ish (I'm not an expert on cartography, so I've no idea which projection it actually is) projection showing the new geography is similar to the Cassini projection of the current arrangement.


The Cassini exaggerates to the N-S (as opposed to the E-W exaggeration of the Mercator, and the WTF exaggeration of the Waterman*), so the Cassini representation of the shifted axis should show the N-S exaggeration. Likewise, a Mercator projection should apply the bias after the rotation.

But I think I understand what you are saying. If I am interpreting your post correctly, you are basically saying that the relative positions in a rotated Cassini projection of the current globe are basically the same as a Mercator projection of the hypothetically rotated globe. To that, I would have to say almost. If you look closely at the second pic in my earlier post, it shows the south pole being roughly in the Gulf of Mexico and the north pole in the vicinity of India. The only projection that has been applied to those pics is whatever Google Earth uses (although I did a slight shortening of the new N-S to the pic and a slight widening to the new E-W, to simulate the oblate spheroid shape of Earth - but no more than a few pixels each way).


*Actually, TBH, Waterman (the projection) is a lot less prone to exaggeration than Waterman (the person).
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Re: What-if 0010: Cassini

Postby Himself » Sat Sep 08, 2012 5:05 am UTC

hthall wrote:
ech wrote:
edmeserve wrote:Randall didn't take into consideration that the spin of the planet distorts the shape from a sphere to an oblate spheroid.
The oceans are pulled toward the equator by centrifugal force of the spin, causing the ocean to be as much as 5 miles higher than at the poles.
http://bigthink.com/strange-maps/475-th ... tood-still

If the the Prime Meridian were now the equator, the oceans would "pool-up" and submerge parts of Northern Canada (and Alaska), Europe, Western Africa. Places like the Carribean would see an increase in land mass.

No, I don't think this would be an issue in the scenario under consideration. The Earth's spin causes the equator—and the ocean—to bulge now, and it would do likewise on Cassini. Both the crust and the water would be similarly deformed; I don't think anyone would notice.


The oblate spheroid was my first thought as well. Considering the upheaval that we now see whenever the earth's crust stretches or compresses by a few feet, the result of the crust pulling apart by about 40 miles total along its new equator, and compressing by the same amount at the poles, not to mention the sloshing shift of the underlying magma, to relax to its equilibrium shape would be … noticeable.

We'll just assume that this is all describing circumstances after a few thousand years' worth of cataclysmic earthquakes and volcanoes have quieted down a bit.


I wonder how long that would take anyway, thousands of years or millions? The oceans and the atmosphere would respond faster.
Or we could assume for these purposes, since the question here is primarily one of climate, that whatever magical force rearranged earth's crust without causing any damage also redid the equatorial bulge appropriately.

On an unrelated note, I think it's interesting that we would have a polar volcanic island arc.
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Re: What-if 0010: Cassini

Postby PM 2Ring » Sat Sep 08, 2012 7:50 am UTC

rmsgrey wrote:The point being made is that the Mercator-ish (I'm not an expert on cartography, so I've no idea which projection it actually is) projection showing the new geography is similar to the Cassini projection of the current arrangement.


Randall wrote:(An equirectangular projection, by the way. This type of equirectangular projection, centered on a north-south meridian instead of the equator, is specifically called a Cassini projection, so a good name for our alternate Earth might be "Cassini".)


FWIW, the equirectangular projection centered on the equator is known as the plate carrée projection.

An equirectangular projection shows the whole surface of the planet, unlike the Mercator. Its completeness and mathematical simplicity make it fairly easy to wrap equirectangular projection data back around the globe (as my program illustrates :) ), or to transform it into another projection. Sure, an equirectangular projection doesn't preserve distances, angles, shapes or areas, but NASA seem to like it.

Wikipedia wrote:In particular, the plate carrée has become a de facto standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.

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Re: What-if 0010: Cassini

Postby planetjay » Mon Sep 10, 2012 3:15 pm UTC

I'm not getting why everything except North America is rotated 90 degrees. Are we, as Americans, that inflexible?

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Re: What-if 0010: Cassini

Postby Thorbard9 » Mon Sep 10, 2012 3:39 pm UTC

planetjay wrote:I'm not getting why everything except North America is rotated 90 degrees. Are we, as Americans, that inflexible?


It is, sort of. On the project North America is not rotated and Europe is rotated 180 degrees. The transformation in 3D is not the same as the transformation on the 2D projection of that 3D shape.

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Re: What-if 0010: Cassini

Postby Max™ » Mon Sep 10, 2012 6:31 pm UTC

Look at how far southwest Mexico is distorted, that is due to the rotation from flattening the map in that manner.
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Re: What-if 0010: Cassini

Postby Nuxxy » Tue Sep 11, 2012 8:42 am UTC

One of the reasons I love living in South Africa. Whenever there is a disaster, we're always safe. Check out 2012.

Or don't. It was a terrible movie.

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Re: What-if 0010: Cassini

Postby Pingouin7 » Wed Sep 19, 2012 7:56 pm UTC

This would be a super cool map for a new Final Fantasy game.
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