| --- Log opened Sun Nov 22 00:00:41 2015 |
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| 03:53 | <@Thalass|arduinoing> | Am I correct that the number of daylight hours a particular location on a planet (ie: this one) receives will vary with the sin() of the axial tilt of the planet? |
| 04:13 | <@Thalass|arduinoing> | I'm trying to boil the seasonal variation in daylight hours into a duty cycle (0 to 1) that will vary during the course of a given number of days (the year). For the purposes of indoor greenhouse control. |
| 04:14 | <&McMartin> | Is axial tilt the right physical constant? |
| 04:14 | <@Thalass|arduinoing> | The default parameters would be a 365 day year, and 24 hour day, but I figure if I'm going to work this out there's no reason I couldn't experiment with shorter years (supposedly a shorter day and year will speed up plant growth), and lead to the possibility of, say, simulating a martian year in a box. >.> |
| 04:16 | <@Thalass|arduinoing> | You may be right. I'm looking at this now: http://mathforum.org/library/drmath/view/56478.html |
| 04:16 | <&McMartin> | That wasn't a challenge, it was a question. |
| 04:18 | <&McMartin> | That said, hm |
| 04:18 | <&McMartin> | Axial tilt shouldn't alter the amount of sunlight hitting the planet as a whole. |
| 04:18 | <&McMartin> | It will make your latitude matter more for seasons though! |
| 04:24 | <~Vornicus> | higher axial tilt increases the variation in daylight as seasons change. |
| 04:24 | | * Thalass|arduinoing nods |
| 04:25 | <&Derakon> | Think about a planet with a 90° tilt. |
| 04:25 | <&McMartin> | Oh, you did say "a point on the planet" |
| 04:25 | <&Derakon> | At that point your "day" lasts half the year followed by a half-year "night". |
| 04:25 | <&Derakon> | (if you're at the pole, that is) |
| 04:25 | <&McMartin> | Er, no? |
| 04:25 | <&Derakon> | Whereas if you're at the equator then you have a constant twilight instead. |
| 04:25 | <&McMartin> | at 90 degrees you're either day forever or night forever, right? |
| 04:25 | <&McMartin> | Oh wait, no, you're right. |
| 04:26 | <&Derakon> | Day forever / night forever requires tidal locking, I believe. |
| 04:26 | <~Vornicus> | If you have 90deg tilt, everywhere is like the poles |
| 04:26 | <@Thalass|arduinoing> | Playing with the equation in the first response linked above gets me 7.78 hours for a 23.5° declination (so, summer solstice), and 4.21 hours for winter. With 6 hours for a declination of 0 (equinox, I suppose). This seems to be half what I would expect! :P |
| 04:26 | <@Thalass|arduinoing> | This is using 46 degrees latitude. |
| 04:27 | <&Derakon> | Vorn: I don't tihnk that's accurate. Think about an equatorial location for such a planet. |
| 04:27 | <&Derakon> | I mean, it's not eternal twilight like I said. |
| 04:27 | <&Derakon> | So I wasn't right either~ |
| 04:27 | <&McMartin> | I keep trying to imagine that and I end up imagining something that's tidally locked, like Luna. |
| 04:28 | <&Derakon> | I mean, imagine the planet when its axis of rotation passes through its star. At that point the equatorial location will have very oblique sunlight at all times. |
| 04:28 | <~Vornicus> | Well, okay, for the -- half a degree or so latitude along the pole it'll be permanent twilight |
| 04:28 | <&Derakon> | At pi/2 radians, though, they'll have a full day and full night. |
| 04:29 | <~Vornicus> | Der: that's not -- |
| 04:29 | <~Vornicus> | no, that's not how the axial tile works |
| 04:29 | <&McMartin> | Thalass: I can't get the physics straight in my head here, so this will complicate picking math |
| 04:29 | <&Derakon> | How do you mean? The planet's spin is about an axis that is flat with respect to the ellipse of the planet's orbit, right? |
| 04:29 | <&McMartin> | It feels like in the extreme raw day length matters too |
| 04:29 | <~Vornicus> | Axial tilt is for the most part relative to the galaxy |
| 04:30 | <~Vornicus> | So a 90deg axial tilt will only twice a year have the axis go through the sun |
| 04:30 | <&Derakon> | Right, yes. |
| 04:30 | <&Derakon> | And at those times it will experience neither night nor day. |
| 04:30 | <&Derakon> | Then, a quarter of a year later (pi/2 radians), it will experience equal day and night. |
| 04:31 | <&Derakon> | (On the equator) |
| 04:31 | <&Derakon> | I think part of our problem here is lacking the terminology needed to communicate clearly what we mean~ |
| 04:32 | <@Thalass|arduinoing> | aie. I should really read things before typing. I missed a "2". >.< |
| 04:33 | <&Derakon> | ...actually, a 90° tilt planet will experience equal day/night everywhere twice a year and either total day or total night (or on the equator, that weird twilight thing) twice a year. |
| 04:33 | <&McMartin> | Which means whatever's going on sin probably isn't the right value. |
| 04:33 | <&Derakon> | Clearly we should use tangent instead~ |
| 04:33 | <&McMartin> | sind(90) = 1 |
| 04:35 | <&Derakon> | sind? |
| 04:35 | <&Derakon> | Oh, degrees instead of radians. |
| 04:36 | <@Thalass|arduinoing> | the rough equation used on that website is 24*(2cos^-1(-tan(declination) * tan(latitude)))/360 |
| 04:36 | <&McMartin> | Oops, yeah, sorry |
| 04:37 | <&Derakon> | Inverse cosine of a negative tangent, eh? |
| 04:37 | <@Thalass|arduinoing> | Though that falls apart when you head too far north or south, it seems. |
| 04:38 | <@Thalass|arduinoing> | using a latitude of 67° gives an error, 66 gives 22.3 hours. |
| 04:38 | <@Thalass|arduinoing> | But, for my purposes, this works nicely. |
| 04:39 | <@Thalass|arduinoing> | Remove the 24 at the front, and it spits out a number between 0 and 1. Now to make the declination oscillate over the course of the "year" |
| 04:40 | <&Derakon> | Wobbling planet? |
| 04:40 | | * Derakon ponders a supervillainous plan to install a gigantic gyroscope at the center of the Earth. |
| 04:40 | <&Derakon> | It will take the heroes some time to even figure out what that would do. |
| 04:40 | <@Thalass|arduinoing> | apparent movement of the sun over the year - solstice to solstice and back. |
| 04:41 | <@Thalass|arduinoing> | I'm probably using the wrong names for things here. Maths is not my strong skill >.< |
| 04:41 | <&McMartin> | I think this is my new "A Swiftly Tilting Planet: How It Should Have Started" |
| 04:41 | <@Thalass|arduinoing> | heh |
| 05:00 | <~Vornicus> | Thal: the reason it falls apart is because for declination + latitude >= 90deg gives tan(dec) * tan(lat) > 1, which means acos doesn't work |
| 05:01 | <~Vornicus> | But that's also the reason that you get all daylight all the time: 66.5deg is the arctic circle... |
| 05:08 | | Derakon is now known as Derakon[AFK] |
| 05:25 | <~Vornicus> | so if decl + lat > 90deg you'll just say that you're above the arctic circle, which means youre solstice day is 24h |
| 05:31 | <@Alek> | wait, the core isn't a gyroscope already? >_> |
| 05:32 | <~Vornicus> | whole fuckin' planet's a gyroscope |
| 05:32 | <@Alek> | the axis is slowly precessing in a small circle, isn't it? |
| 05:33 | <@Alek> | Polaris is only the North Star for now, ISTR Draconis was it like 90k years ago or some such. |
| 05:34 | | * Alek doesn't remember nearly enough from high-school astronomy class. :/ |
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| 05:39 | | * Thalasleep nods at Vorn |
| 05:39 | <@Thalasleep> | That's kinda what I thought. |
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| --- Log closed Mon Nov 23 00:00:57 2015 |