Science fleeting thoughts

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Quizatzhaderac
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Re: Science fleeting thoughts

Postby Quizatzhaderac » Tue Dec 11, 2018 7:20 pm UTC

Eebster the Great wrote:But Avogadro's constant is silly because it does not relate two units, just one: the mole. So instead of defining everything in terms of the second and physical constants, we define almost everything in terms of the second and constants and one thing as an integer.
Avogadro's constant is not an integer.

With perfect instruments, we could take 12 grams of pure carbon and count the number of atoms, but we can't. We also can't count out 6.022000 X 10^23 atoms exactly.

Although we can easily conceive of both quantities with the same unit (but different scale), when we actually are measuring stuff we need to remember that we're making an inference when we try to go between macroscopic and atomic measurements.
The thing about recursion problems is that they tend to contain other recursion problems.

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Re: Science fleeting thoughts

Postby Eebster the Great » Tue Dec 11, 2018 9:05 pm UTC

The whole point of this discussion is that the SI units have been redefined. The mole is now defined by SI as follows:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.


Thus 1 mol = 602 214 076 000 000 000 000 000 exactly.

(I mean, technically these new units don't come into effect until May 20, but they've already been approved, so it's just a matter of time.)

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Re: Science fleeting thoughts

Postby Quizatzhaderac » Tue Dec 11, 2018 10:26 pm UTC

Oh, right you are.
The thing about recursion problems is that they tend to contain other recursion problems.

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Re: Science fleeting thoughts

Postby Soupspoon » Wed Jan 02, 2019 2:35 pm UTC

(I am the last poster in the place I might have otherwise put this, so choosing here, in lieu of a completely new thread.)

While we're waiting for additional post-Ultima Thule data being assembled (and the alien structures being paintshopped out, for public consumption), don't ignore the Japanese moonshot.

Ganbatte kudasai!

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Re: Science fleeting thoughts

Postby Sableagle » Wed Jan 02, 2019 4:05 pm UTC

Soupspoon wrote:(I am the last poster in the place I might have otherwise put this, so choosing here, in lieu of a completely new thread.)

While we're waiting for additional post-Ultima Thule data being assembled (and the alien structures being paintshopped out, for public consumption), don't ignore the Japanese moonshot.

Ganbatte kudasai!

Link is to Chinese moonshot.

When I saw the picture at the top of the article I thought for a moment that Japan had come up with a clever way to reduce costs by miniaturising the probe. Seeing that it was a 1:8 scale model of Chang'e-4 was disappointing.
Oh, Willie McBride, it was all done in vain.

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Re: Science fleeting thoughts

Postby DavidSh » Wed Jan 02, 2019 8:19 pm UTC

Just saw the latest press conference from the New Horizons team. It appears Ultima Thule is a contact binary. The grey-scale pictures look like a snowman, except that (1) the color images show a reddish hue, and (2) it's a lot darker than any snow I would want to be associated with.

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Re: Science fleeting thoughts

Postby Soupspoon » Thu Jan 03, 2019 6:45 am UTC

Sableagle wrote:Link is to Chinese moonshot.
Lack of sleep, and maybe a bit of traditional occidental "they're all the same to me". I was so proud to remember some actual Japanese (that wasn't "watashi wa neku desu, nyo"), as well.


When I saw the picture at the top of the article I thought for a moment that Japan had come up with a clever way to reduce costs by miniaturising the probe. Seeing that it was a 1:8 scale model of Chang'e-4 was disappointing.
Given we could almost see the flashing on the little plastic wheels, I think it was overkill to have someone dust it in a cleanroom suit (I thought, myself, at that point). Seemed strange in the context of the Japanese, but maybe not so much now that my xenoidentification error is uncovered. ;)

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Re: Science fleeting thoughts

Postby jaap » Sat Jan 05, 2019 8:04 am UTC

Sableagle wrote:
Soupspoon wrote:(I am the last poster in the place I might have otherwise put this, so choosing here, in lieu of a completely new thread.)

While we're waiting for additional post-Ultima Thule data being assembled (and the alien structures being paintshopped out, for public consumption), don't ignore the Japanese moonshot.

Ganbatte kudasai!

Link is to Chinese moonshot.

When I saw the picture at the top of the article I thought for a moment that Japan had come up with a clever way to reduce costs by miniaturising the probe. Seeing that it was a 1:8 scale model of Chang'e-4 was disappointing.


A very interesting feature of the Chinese mission is the orbit of the communications satellite around the L2 Lagrange point.
http://www.planetary.org/blogs/guest-blogs/2018/20180615-queqiao-orbit-explainer.html

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Re: Science fleeting thoughts

Postby Quizatzhaderac » Mon Jan 07, 2019 6:58 pm UTC

Sableagle wrote:... I thought for a moment that Japan had come up with a clever way to reduce costs by miniaturising the probe. Seeing that it was a 1:8 scale model of Chang'e-4 was disappointing.
On that subject, does anyone know what the limiting factor is on making space probes smaller? Putting the same functionality into a smaller mass is of such obvious benefit that I imagine there's a good reason each probe isn't one centimeter smaller.
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Re: Science fleeting thoughts

Postby Soupspoon » Mon Jan 07, 2019 7:48 pm UTC

Onboard power would be one factor. Decrease the size and the output of the cell(s) you can use reduces, with fewer watts (by way of volts and/or amps, depending on what you sacrifice). And they're likely to to have the same thickness of casing/internal partitioning, eating up more 'power volume', with non-power structure and skin. Applies to RTGs as much as other cells. Not that it would be win-win to scale it up, indefinitely, for a given tech (apart from launch costs), for various reasons. You'd have to scale up the solar (PV) panels more to make it worth more 'electrical storage space'. (And I imagine that if you don't watch out, doubling up and doubling up a RTG either in scale or by banking more units together will start to create something that, while maybe staying subcritical by keeping spot density down, does start to go through the prompt phase, requiring extra shielding. Or something.)

Structural strength is another, with the frame (or hull) thickness needing to be thick enough to not snap/crush under operational (or at least launch) pressures. May increase in the proportion of the decreasing volume.

And some instrumentation may be tied to a certain physical size for various reasons. Circuitry made from finer and finer electrical circuits may have unwanted signal responses that can't be designed out, and in the radiation-soup of space you need 'chunkier' electronics than on Earth to harden them against spurious or damaging effects.


The plan (albeit still very theoretical) to send many 'dust mote' ship-onna-chip probes on a beam of laser light towards our nearer stellar neighbours might have such considerations built in. Maybe the idea is that the driving laser (whether raw upon the 'chip' or pushing mostly upon a microsail) provides power enough, and being solid-state they can't break up or fold beyond a certain inbuilt design threshold. Wear and tear and damagingly spurious signals and collisions with micrometeoric material at either end of the route is probably just going to downright destroy a good proportion of the swarm we initially launched, of course.


But any given mission profile is going to have a different favourable scale. Which may or may not correlate with the capability to loft said mission, and I expect much of the scaling is fixed to "we can send up something with <this much> mass in a <this size> container, so what can we construct that conforms to that with the best predicted return on our investment in the mission?". Rather than have something that rattles around in a launcher because it's smaller than it could be, there'll be people clamouring to fit a slightly bigger/better/different/additional spectroscope unit, and/or experimental micro-cubesat makers eager to fund an effort tailor-made to fit into some cavity of the shroud, etc.

Making things smaller makes sense if you are forced to, but if you could put the intended functionality into a smaller space (when not forced to) you're probably better off putting something else in the space you saved.


Or so it seems to me, from here currently on the very notably armchair-end of the business of space-exploration. Never having got beyond an idealistic brainstorming session or three about this kind of thing (about a dubiously ambitious '90s solar-sail mission proposal that never got anywhere near a genuine engineering drawing-board) during a residential aerospace-themed agora for interested but very much amateur parties. I'm sure we have several actual engineering types hereabouts who have touched or even assembled genuine prototypes (or better) for actual spacebound hardware. Not counting you-know-who being a one-time NASA engineer himself, wherever exactly on the periphery that had him.

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Re: Science fleeting thoughts

Postby PM 2Ring » Tue Jan 08, 2019 1:50 pm UTC

Soupspoon wrote:(And I imagine that if you don't watch out, doubling up and doubling up a RTG either in scale or by banking more units together will start to create something that, while maybe staying subcritical by keeping spot density down, does start to go through the prompt phase, requiring extra shielding. Or something.)


No, you don't have to worry about that.
Plutonium 238, the main radioisotope used in modern RTGs, isn't fissile, it's a simple alpha emitter, and its daughter isotope, uranium-234, isn't fissile either, with roughly one U-234 decay per million being spontaneous fission.

Pu-238 generates 0.568W of heat per gram, so even a fairly small lump will glow red hot. Here's a photo of it doing its glowy thing.
Spoiler:
Image

The only danger in making a large lump of it is that it may melt its container. ;)

And it'd put a sizeable dent in your bank balance. AFAIK, it's not being produced at present, so it's a sellers market. Technically, it wouldn't be that hard to get it back into regular production, but it's politically a little tricky to build & operate breeder reactors these days.

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Re: Science fleeting thoughts

Postby DavidSh » Tue Jan 08, 2019 4:45 pm UTC

Another factor influencing scaling for space probes is communications. For a typical high-gain parabolic antenna, the size of the dish depends on the required gain and on the wavelength used. And, as already mentioned, the available power for communications depends on the size of the power source.

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Sea level

Postby Sableagle » Fri Jan 11, 2019 11:52 am UTC

Big G: 6.6719 * 10^-11 m^3 / s^2 kg
Earth: 5.972 * 10^24 kg
Product: 3.98445868 * 10^14 m^3 / s^2
Polar sea-level radius: 6356752 m
Equatorial sea-level radius: 6378137 m
Polar gravity: 9.860496668889 m / s^2 O!M!G! 666! The number people think is the number of the Beast because it sounds cooler than 616! FLEE!
Equatorial gravity: 9.794485788918 m / s^2 Clearly the South is closer to God than the North and we should bring back chattel slavery.
Siderial day: 86164.0905 seconds
Rate of rotation: 7.2921158579 * 10^-5 radians / s.
Centrifugal lightening at Equator: 0.033915713957 m / s^2.
Equatorial gravity minus centrifugal lightening at Equator: 9.76057007496 m / s^2.

(Text in bold is me taking the piss out of white supremacist religious fundamentalist conspiracy theorist flat-earthers.)

Gravitational potential energy being weight times height for small values of height, it's the area under the curve of effective weight plotted against radius for large heights.

Effective weight along the axis = 3.98445868 * 10^14 r^-2 N kg^-1.
Indefinite integral wrt r: -3.98445868 * 10^14 r^-1

Effective weight along an equatorial radius = 3.98445868 * 10^14 r^-2 - 7.2921158579 * 10^-5 r N kg^-1.
Indefinite integral wrt r: -3.98445868 * 10^14 r^-1 - 3.6460579590 * 10^-5 r N kg^-1.

Definite integral from 1 to 6356752 of effective weight along the polar axis:
-3.98445868 * 10^14 6356752^-1- -3.98445868 * 10^14 = 3.98445868 * 10^14 - 3.98445868 * 10^14 6356752^-1 = 398445805319268 Nm / kg.

Definite integral from 1 to 6378137 of effective weight along an equatorial radius:
(-3.98445868 * 10^14 6378137^-1 - 3.6460579590 * 10^-5 6378137 N kg^-1) - ( -3.98445868 * 10^14 - 3.6460579590 * 10^-5 N kg^-1 )
= 398445805529660 Nm / kg.

Considering I didn't have numbers accurate to that many significant figures, I should round that to at most 7 sig figs, so:
3.984458 * 10^14 at the pole;
3.984458 * 10^14 at the equator.

Cool! Figured it out.
Oh, Willie McBride, it was all done in vain.

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Re: Sea level

Postby PM 2Ring » Sat Jan 12, 2019 6:18 am UTC

Sableagle wrote:Big G: 6.6719 * 10^-11 m^3 / s^2 kg
Earth: 5.972 * 10^24 kg
Product: 3.98445868 * 10^14 m^3 / s^2

It's difficult to get high precision values for the masses of astronomical bodies because it's hard to make precise measurements of big G. But we can measure orbital periods quite well, so we have good values of the product Gm, even though we don't have good values of G and m separately. This product is called the standard gravitational parameter, and usually written as μ (lowercase mu).

From the table in Wikipedia, the μ of Earth is 3.986004418(8)×1014 m3/s2.

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Re: Science fleeting thoughts

Postby Eebster the Great » Sat Jan 12, 2019 6:28 am UTC

Sableagle's G differs from the CODATA value of 6.674 08(31) × 10-11 m3 kg-1 s-2 in the third decimal place. But it doesn't matter because the precision was not the point.

Still, that is an astonishingly precise measurement. The sun's μ is even more precisely known, at 1.327 124 400 18(9) × 1020 m3 s-2. That's eleven significant figures, only marginally less precisely known than the fine structure constant

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Re: Science fleeting thoughts

Postby Sableagle » Sat Jan 12, 2019 3:11 pm UTC

Exoplanar mining.png
Oh, Willie McBride, it was all done in vain.

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Re: Science fleeting thoughts

Postby Eebster the Great » Sat Jan 12, 2019 6:27 pm UTC

Sableagle wrote:Exoplanar mining.png

The negative 270 degree temperature might be a bummer.

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Re: Science fleeting thoughts

Postby poxic » Sat Jan 12, 2019 6:34 pm UTC

"Frostbite sets in at 0.004 seconds. Please dress adequately."
In everyone's life, at some time, our inner fire goes out. It is then burst into flame by an encounter with another human being. We should all be thankful for those people who rekindle the inner spirit.
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Re: Science fleeting thoughts

Postby DavidSh » Sat Jan 12, 2019 7:00 pm UTC

Eebster the Great wrote:
Sableagle wrote:Exoplanar mining.png

The negative 270 degree temperature might be a bummer.

Where are you getting that number from?
What I notice is that (1) the pits seem to be of different depths, and this might mean surface air pressures are significantly different, and (2) the "ice" must be incredibly strong in order to be able to support a cliff edge thousands of miles high. Would we be likely to be able to bore a tunnel through it? Maybe we need the equivalent of space elevators, and travel across the surface (in a hard vacuum). It may matter what we are using for a sun in this scenario.

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Re: Science fleeting thoughts

Postby Soupspoon » Sat Jan 12, 2019 7:14 pm UTC

Eebster the Great wrote:
Sableagle wrote:Exoplanar mining.png

The negative 270 degree temperature might be a bummer.

Is that Kelvin, or Rankine?

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Re: Science fleeting thoughts

Postby Eebster the Great » Sun Jan 13, 2019 4:39 am UTC

DavidSh wrote:
Eebster the Great wrote:
Sableagle wrote:Exoplanar mining.png

The negative 270 degree temperature might be a bummer.

Where are you getting that number from?
What I notice is that (1) the pits seem to be of different depths, and this might mean surface air pressures are significantly different, and (2) the "ice" must be incredibly strong in order to be able to support a cliff edge thousands of miles high. Would we be likely to be able to bore a tunnel through it? Maybe we need the equivalent of space elevators, and travel across the surface (in a hard vacuum). It may matter what we are using for a sun in this scenario.

The suns are presumably inside the pits, since they have to produce a day-night cycle somehow. So on the top of the ice, you are basically out of range of all the suns. Once you get beyond the range of significant conductive heating, you will be close to absolute zero. (The lack of air might be another challenge.)

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Re: Science fleeting thoughts

Postby ijuin » Sun Jan 13, 2019 8:28 am UTC

If air pressure is adequate above the ice, then high-efficiency aircraft would be workable—either nuclear powered stratospheric jets or zeppelins could make the flight within days (supersonic) to weeks (zeppelin).

If, however, the conditions are near-vacuum, then building a maglev rail line across the ice becomes a better prospect. With no air, a perfectly flat surface, and no such thing as escape velocity, such a train (with onboard nuclear reactor) could accelerate to tens of kilometers per second. Even better would be if such trains can somehow be run without laying down the tens of thousands of kilometers of rail first.

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Perspective and curvature

Postby Sableagle » Mon Jan 14, 2019 8:05 pm UTC

In response to: https://www.youtube.com/watch?v=Z3b1E2JBz8w
I say "very near" the sphere because normal human experience doesn't get far from the surface. https://www.youtube.com/watch?v=d7pfDzgI0MI

Code: Select all

The horizon's not an axis, though. It's a flat circle. Well, very nearly a circle. A city on a flat plane has three axes: north-south, east-west and up-down. A sphere or spheroid world has three axes as well: one

north-south through the poles and two through the equator at ... well, wherever you like, really. 0° to 180° and 90°W to 90°E would be an obvious choice, but you could define locations relative to axes that run 45°E to

135°W and 45°W to 135°E if you prefer. If you want coordinates relative to a point within the city or on the surface, for the flat plane city you just choose another place to call zero and for the spheroid world you

could choose axes parallel to those three but they'd be some awkward directions tilted relative to the surface, so it's more usual to pick a radius and the north-south and east-west tangents through that point. This

means using "locally level north and south," not "towards very near Polaris and quite near Sigma Octantis." The horizon is none of these. Two parts of it run north-south and two parts run east-west, but the whole thing

isn't a straight line at all. On or very near a sphere, it's a flat circle, level from your point of view, centred almost twice your elevation below you.
 
To keep this simple, for my sake as much as for everyone else's, I'll still go with a simple sphere for the maths, and to incorporate a bit of refraction something like standard refraction into the calculations I'll

call the radius 7200 km, not the 6371.912 km at Madeira. If you want to imagine this as a RL situation, imagine lines of ships, passing near Paul do Mar in Madeira. I'll centre my axes there, and call that 0, 0, 0.
Note that I'm using 0.1° on the 7200 km sphere Earth appears to be due to refraction, not 0.1° on Earth's surface.
 
Observers 20, 40, 80 and 160 m above sea level there will be at:
0, 0,  +20;
0, 0,  +40;
0, 0,  +80;
0, 0, +160;
 
Next up, horizon distances: the horizon is a set of points on the surface where the tangents point to the observer. For our observers,
7200000 / 7200020 = cos (0.1350472911°); ( 7200020^2 - 7200000^2 )^0.5 = 16970.5745 m;
7200000 / 7200040 = cos (0.1909854896°); ( 7200040^2 - 7200000^2 )^0.5 = 24000.0333 m;
7200000 / 7200080 = cos (0.2700936444°); ( 7200080^2 - 7200000^2 )^0.5 = 33941.2198 m;
7200000 / 7200160 = cos (0.3819683267°); ( 7200160^2 - 7200000^2 )^0.5 = 48000.2667 m;
 
Now let's have ship positions, and ship sizes. The Titanic having been 32 m from keel to top of bridge, I'll call these ships 10 m from waterline to gunwales, 20 m from waterline to top of superstructure and 40 m from

waterline to top of funnel.
A north-south line of ships 0.1° apart and passing 0.1° west of there will be at:
Waterline:                                           Gunwale:                                             Top of superstructure:                               Top of funnel:
    0           , 12566.3642344678,  -10.9662243286;     0           , 12566.3816877515,   -0.9662395594;     0           , 12566.3991410351,   +9.0337452097;     0           , 12566.4340476025,  +29.0337147480;
12566.3642344678, 12566.3450948054,  -21.9324319546; 12566.3816877515, 12566.3625480625,  -11.9324624163; 12566.3991410351, 12566.3800013196,   -1.9324928780; 12566.4340476025, 12566.4149078337,  +18.0674461985;
25132.6901896109, 12566.2876758766,  -54.8310214278; 25132.7250961250, 12566.3051290539,  -44.8310975820; 25132.7600026392, 12566.3225822312,  -34.8311737362; 25132.8298156675, 12566.3574885859,  -14.8313260446;
37698.9395862210, 12566.1919778562, -109.6618925333; 37698.9919458593, 12566.2094309006,  -99.6620448416; 37699.0443054976, 12566.2268839450,  -89.6621971497; 37699.1490247742, 12566.2617900338,  -69.6625017661;
50265.0741453232, 12566.0580010357, -186.4248782469; 50265.1439579262, 12566.0754538940, -176.4251371703; 50265.2137705291, 12566.0929067523, -166.4253960940; 50265.3533957351, 12566.1278124690, -146.4259139407;
62831.0555882923, 12565.8857458233, -285.1197447351; 62831.1428536473, 12565.9031984424, -275.1201407347; 62831.2301190023, 12565.9206510615, -265.1205367344; 62831.4046497123, 12565.9555562996, -245.1213287337;
75396.8456369697, 12565.6752127436, -405.7461913562; 75396.9503548109, 12565.6926650703, -395.7467548926; 75397.0550726520, 12565.7101173970, -385.7473184289; 75397.2645083344, 12565.7450220504, -365.7484455017.
    ^                                                    ^                                                                      ^                                  ^
    |                                                Increasing following sine curve                                        Decreasing following cosine curve      |
    |                                                                                                                                                              |
    `----------------------- Increasing difference between these is due to the ship leaning away as it goes over the curve ----------------------------------------'
 
Now that we have their cartesian coordinates, we can calculate the linear distances to them fairly simply:
Distance = ( north coord^2 + west coord^2 + (observer elevation - up coord)^2 )^0.5
We can also calculate the angle of depression of each point from each observer:
Angle = arcsin ( ( north coord^2 + west coord^2 )^0.5 / distance )

Waterline:
From 20 m elevation:                From 40 m elevation:                From 80 m elevation:                From 160 m elevation:
12566.4023881285 m, 0.1411888385°   12566.4675875655 m, 0.2323769617°   12566.6934763000 m, 0.4147492146°   12567.5271841032 m, 0.7794648152°
17771.5586666983 m, 0.1351909335°   17771.6171110335 m, 0.1996708643°   17771.8015219543 m, 0.3286290454°   17772.4404211928 m, 0.5865341127°
^^^^^ Just beyond the horizon.      28099.3362028799 m, 0.1933649809°   28099.4996667946 m, 0.2749258247°   28099.9974108116 m, 0.4380438392°
                                    ^^^^^ Beyond the horizon.           39738.5857622457 m, 0.2734588316°   39739.0481049328 m, 0.3888016360°
                                                                        ^^^^^ Beyond the horizon.           51813.1595515705 m, 0.3830847510°
                                                                                                            ^^^^^ Beyond the horizon.

Gunwale:
From 20 m elevation:                From 40 m elevation:                From 80 m elevation:                From 160 m elevation:
12566.3991781838 m, 0.0955944165°   12566.4484622760 m, 0.1867828284°   12566.6425211432 m, 0.3691563517°   12567.4125758859 m, 0.7338772638°
17771.5625675898 m, 0.1029507846°   17771.6097580455 m, 0.1674308176°   17771.7716615213 m, 0.2963894478°   17772.3655443235 m, 0.5542963932°
28099.2899985941 m, 0.1321937874°   28099.3432604570 m, 0.1729745497°   28099.4924893102 m, 0.2545355071°   28099.9617638960 m, 0.4176539967°
39738.3685145754 m, 0.1725320076°   39738.4337723820 m, 0.2013683339°   39738.5944850290 m, 0.2590406659°   39739.0366965878 m, 0.3743836382°
                      ^^^^^ Beyond and below the horizon. ^^^^^         51812.7079322725 m, 0.2835624441°   51813.1656174077 m, 0.3720266017°
                                                                        Just below horizon    ^^^^^         64076.8582643136 m, 0.3890755559°
                                                                                                                                  ^^^^^ 0.0071° below horizon

Top of superstructure:
From 20 m elevation:                From 40 m elevation:                From 80 m elevation:                From 160 m elevation:
12566.4039259667 m, 0.0500000000°   12566.4372946648 m, 0.1411885852°   12566.5995233845 m, 0.3235631478°   12567.3059237807 m, 0.6882889097°
17771.5720954455 m, 0.0707106602°   17771.6080320080 m, 0.1351907543°   17771.7474379476 m, 0.2641497520°   17772.2963018745 m, 0.5220584123°
28099.3077325504 m, 0.1118033535°   28099.3538768335 m, 0.1525841312°   28099.4888706079 m, 0.2341451816°   28099.9296756631 m, 0.3972641051°
39738.3948523860 m, 0.1581138108°   39738.4550773180 m, 0.1869501425°   39738.6057242550 m, 0.2446225074°   39739.0278046575 m, 0.3599656331°
   Below the horizon. ^^^^^         51812.5565648161 m, 0.2282716016°   51812.7313680138 m, 0.2725042286°   51813.1736132553 m, 0.3609684553°
                                       Below the horizon. ^^^^^            Below the horizon. ^^^^^         64076.8801327480 m, 0.3801338515°
                                                                                                                                  ^^^^^ 0.0018° above horizon

Top of funnel:
From 20 m elevation:                From 40 m elevation:                From 80 m elevation:                From 160 m elevation:
12566.4372946649 m, -.0411885852°   12566.4388325474 m, 0.0500000000°   12566.5374003731 m, 0.2323759485°   12567.1164887024 m, 0.5971100245°
17771.6080320080 m, 0.0062305660°   17771.6214607864 m, 0.0707106607°   17771.7158414653 m, 0.1996701479°   17772.1746884954 m, 0.4575817477°
28099.3538768335 m, 0.0710225757°   28099.3857859662 m, 0.1118033535°   28099.4923095533 m, 0.1933645278°   28099.8761752932 m, 0.3564841950°
39738.4550773180 m, 0.1292774790°   39738.5052365095 m, 0.1581138108°   39738.6357520264 m, 0.2157862194°   39739.0175700471 m, 0.3311296081°
51812.5565648162 m, 0.1840387640°   51812.6246663738 m, 0.2061551828°   51812.7840295419 m, 0.2503878295°   51813.1953949781 m, 0.3388521749°
   Below the horizon. ^^^^^            Below the horizon. ^^^^^         64076.4726961245 m, 0.3622530392°   64076.9285514668 m, 0.3622504620°
                                                                           Below the horizon. ^^^^^         76439.0074158925 m, 0.3940841926°
                                                                                                               Below the horizon. ^^^^^

Well, that sure disappeared from the bottom up, from each elevation of observer, with higher observers being able to see further.


What would it LOOK like, though, for people who don't like all those digits? Well, I can answer that with the help of some more numbers.
Bearing to ship = arctan ( west coord / north coord ) west of north.
From the 80 m elevation with horizon angle 0.2700936444°:
90.000000° 0.4147492146° 0.3691563517° 0.3235631478° 0.2323759485°
44.999956° 0.3286290454° 0.2963894478° 0.2641497520° 0.1996701479°
26.564946° 0.2749258247° 0.2545355071° 0.2341451816° 0.1933645278°
18.434783° 0.2734588316° 0.2590406659° 0.2446225074° 0.2157862194°
14.036018° xxxxxxxxxxxxx 0.2835624441° 0.2725042286° 0.2503878295°
11.309647° xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx 0.3622530392°


Ship over horizon.gif


Huh. That looks a lot like ...

Image

... that (or it would if I'd gone with every 0.01° instead of only every 0.1°).
Oh, Willie McBride, it was all done in vain.

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Soupspoon
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Re: Science fleeting thoughts

Postby Soupspoon » Tue Jan 15, 2019 2:25 pm UTC

(Unrelated to previous post, just thought this needed a moment or three of pondering.)
Image

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poxic
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Re: Science fleeting thoughts

Postby poxic » Tue Jan 15, 2019 3:38 pm UTC

I so hope that will get built. It will be the stupidest science project ever, where stupidest = most awesome way of smashing rocks (er, particles) together to see what pieces come flying out.

Also, my first fiew attempts at spelling "pieces" came out more or less "pies". It would be double plus awesome if the giant rock smasher happened to spontaneously produce pies.

Or cake. I am dessert-interdenominational.
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Thesh
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Re: Science fleeting thoughts

Postby Thesh » Tue Jan 15, 2019 3:58 pm UTC

And one day we will build one in space that will make that look like a child's toy.

Spoiler:
"Well, so far everything we've seen with the Dyson Megacollider is predicted by the standard model."
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doogly
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Re: Science fleeting thoughts

Postby doogly » Tue Jan 15, 2019 3:59 pm UTC

It's probably more important to get a linear collider next though. Hopefully that thing happens.
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Re: Science fleeting thoughts

Postby Sableagle » Tue Jan 15, 2019 6:58 pm UTC

Well, I'm glad they're not building it in California or nearer Napoli.
Oh, Willie McBride, it was all done in vain.


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