APOD: Tropic of Cancer (2013 Aug 02)

[geckzilla]

There APOD monument is at 23° 27′ 6.14″ N, 121° 29′ 47.02″ E in Fengbin Township, Hualien county.

[alter-ego]

That is exactly what I was thinking. And at noon on the solstice the sun would shine straight down the structure. Like a giant solstice "clock"

Looking at the design - and something that isn't mentioned in the write-up on the day of the solstice the sun will rise framed within the monument

On the summer solstice, if one is viewing through the frame in a due west or east direction (the view in the APOD is essentially due west), the sun will not rise within the gap. It rises & sets about 26° north of the frame. However, at roughly noon, the sun will be directly over the monument. Based on the star field, the monument subtends an angle of about 50°.

Edit / Correction: The sun only rises/sets due east/west on an equinox.

[alter-ego]

There APOD monument is at 23° 27′ 6.14″ N, 121° 29′ 47.02″ E in Fengbin Township, Hualien county.

Yup.

[geckzilla]

You mentioned precession of the Earth's axis. Could precession have anything to do with climate change?

Yes, a 26,000 year cycle. http://en.wikipedia.org/wiki/Milankovitch_cycles
So it's easy to conclude that the rate of change in the climate we are seeing now must be caused by something other than axial precession since it is happening over hundreds of years rather than tens of thousands of years.

[Case]

Mexico. Carretera 83 (Vía Corta) Zaragoza-Victoria, Km 27+800. In all crossings of the Tropic of Cancer with Mexican federal highways, this is the only place where the latitude is marked with absolute precision and where the annual drift between 2005 and 2010 can be appreciated.

---

Tropic of Cancer - 2. Geography
The Tropic of Cancer lies [approximately 23.45 degrees] north of the Equator. Its position is not fixed, but varies in a complicated manner over time. It is presently drifting south at the rate of almost half a second (0.47″) of latitude per year.

http://hpiers.obspm.fr/eop-pc/models/constants.html
Obliquity of the ecliptic for the epoch J2000.0: 23°26'21".4119 = 23.4392810833 (Definition constant (IAU 1976))

PHP Science Labs (as referenced in the Wiki page) has a page calculating the Obliquity of the Ecliptic and Nutation in Obliquity. Using the Solar Noon (China Standard Time (UTC+8), no DST) for the location of the monument, you get the following obliquity numbers:

Code: Select all

 YYYY MMM DD     Solar Noon*    True obliquity of the ecliptic (using IAU 2000B nutation series) 
 1980 Jun 21 Sat at 11:55:41    23.4396512848 = 23° 26' 22.745"
 1981 Jun 21 Sun at 11:55:38    23.4401367188 = 23° 26' 24.492"
 1982 Jun 21 Mon at 11:55:35    23.4407822990 = 23° 26' 26.816"
 1983 Jun 21 Tue at 11:55:32    23.4415493946 = 23° 26' 29.578"
 1984 Jun 21 Thu at 11:55:42    23.4422620062 = 23° 26' 32.143"
 1985 Jun 21 Fri at 11:55:39    23.4427842073 = 23° 26' 34.023"
 1986 Jun 21 Sat at 11:55:36    23.4431300768 = 23° 26' 35.268"
 1987 Jun 21 Sun at 11:55:33    23.4432879896 = 23° 26' 35.837"
 1988 Jun 21 Tue at 11:55:43    23.4431416553 = 23° 26' 35.310"
 1989 Jun 21 Wed at 11:55:40    23.4426614950 = 23° 26' 33.581"
 1990 Jun 21 Thu at 11:55:37    23.4419705414 = 23° 26' 31.094"
 1991 Jun 21 Fri at 11:55:34    23.4411500321 = 23° 26' 28.140"
 1992 Jun 21 Sun at 11:55:44    23.4401907484 = 23° 26' 24.687"
 1993 Jun 21 Mon at 11:55:41    23.4391671599 = 23° 26' 21.002"
 1994 Jun 21 Tue at 11:55:38    23.4382645828 = 23° 26' 17.752"
 1995 Jun 21 Wed at 11:55:35    23.4375737633 = 23° 26' 15.266"
 1996 Jun 21 Fri at 11:55:45    23.4370917342 = 23° 26' 13.530"
 1997 Jun 21 Sat at 11:55:42    23.4368721495 = 23° 26' 12.740"
 1998 Jun 21 Sun at 11:55:39    23.4370003485 = 23° 26' 13.201"
 1999 Jun 21 Mon at 11:55:36    23.4374070762 = 23° 26' 14.665"
 2000 Jun 21 Wed at 11:55:46    23.4379675453 = 23° 26' 16.683"
 2001 Jun 21 Thu at 11:55:43    23.4386430162 = 23° 26' 19.115"
 2002 Jun 21 Fri at 11:55:40    23.4394043299 = 23° 26' 21.856"
 2003 Jun 21 Sat at 11:55:37    23.4400807100 = 23° 26' 24.291"
 2004 Jun 21 Mon at 11:55:47    23.4405395434 = 23° 26' 25.942"
 2005 Jun 21 Tue at 11:55:44    23.4407850644 = 23° 26' 26.826"
 2006 Jun 21 Wed at 11:55:41    23.4408342093 = 23° 26' 27.003"
 2007 Jun 21 Thu at 11:55:38    23.4405840604 = 23° 26' 26.103"
 2008 Jun 21 Sat at 11:55:48    23.4400118820 = 23° 26' 24.043"
 2009 Jun 21 Sun at 11:55:45    23.4392347140 = 23° 26' 21.245"
 2010 Jun 21 Mon at 11:55:42    23.4383589121 = 23° 26' 18.092"
 2011 Jun 21 Tue at 11:55:39    23.4373851113 = 23° 26' 14.586"
 2012 Jun 21 Thu at 11:55:49    23.4363872038 = 23° 26' 10.994"
 2013 Jun 21 Fri at 11:55:46    23.4355382923 = 23° 26' 07.938"

In the last 34 years the number wasn't really close to 23.451352°.
In 2013, the latitude was about 1 mile off. The monument is located too far north, so I think the sun is never exactly in zenith.

It is only a little off, so it makes a small impact on shadow length. If my calculations are correct, an imaginary vertical pole of 20 meters (~66 ft) height, located 1 mile north of the Tropic of Cancer, would cast a shadow with a length of 0,54 mm (~0,016 inch).

[Chris Peterson]

That looks to be a different monument from the one in the APOD?

Yes. I found three different Tropic of Cancer monuments in Taiwan. Only one was on the road between Hualian and Taidong.

Edit: Oops, now I see Geckzilla's post. So that makes four monuments. The bloody island is overflowing with them. I guess every village along the line has built their own tourist trap.

[Beyond]

Tis the modern thing to do, now-a-days.

[neufer]

Click to play embedded YouTube video.

I found three different Tropic of Cancer monuments in Taiwan. Only one was on the road between Hualian and Taidong.

Edit: Oops, now I see Geckzilla's post. So that makes four monuments.

The bloody island is overflowing with them. I guess every village along the line has built their own tourist trap.

<<Metastasis (from μετά, meta, "next", and στάσις, stasis, "placement") is the spread of Tropic of Cancer monuments from one village to another.>>

[Sam]

JERRY: This you're not goin' to believe. The NYPL says that I took out Tropic of Cancer in 1971 and never returned it.

KRAMER: Do you know how much that comes to? That's a nickel a day for 20 years. It's going to be $50,000

Ya' sure it wasn't Tropic of Capricorn?

[Rogelio]

There's several Tropic of Cancer markers in Taiwan. The one at 23.46546, 121.35789 coordinates is not the one in the APOD. The one in the APOD is by the East Coast, next to the road (hwy 11).

Cheers,
Rogelio

[Rogelio]

Ok, I too just read all the other posts clarifying, sorry

[Guest]

So, the "Cancer" is spreading?

[Anthony Barreiro]

Mexico. Carretera 83 (Vía Corta) Zaragoza-Victoria, Km 27+800. In all crossings of the Tropic of Cancer with Mexican federal highways, this is the only place where the latitude is marked with absolute precision and where the annual drift between 2005 and 2010 can be appreciated.

---

Tropic of Cancer - 2. Geography
The Tropic of Cancer lies [approximately 23.45 degrees] north of the Equator. Its position is not fixed, but varies in a complicated manner over time. It is presently drifting south at the rate of almost half a second (0.47″) of latitude per year.

...
In the last 34 years the number wasn't really close to 23.451352°.
In 2013, the latitude was about 1 mile off. The monument is located too far north, so I think the sun is never exactly in zenith.

It is only a little off, so it makes a small impact on shadow length. If my calculations are correct, an imaginary vertical pole of 20 meters (~66 ft) height, located 1 mile north of the Tropic of Cancer, would cast a shadow with a length of 0,54 mm (~0,016 inch).

Thanks Case. The picture of the Mexican Burma Shave signs is worth a thousand words, or one long equation! It would be even more vivid if there were a person doing something goofy by one of the signs.

I've been thinking about the location of this monument since first seeing the picture on Friday (how far has the tropic of Cancer drifted since Friday?), and more generally about the question of approximation.

When I'm teaching people how to understand what they see in the sky, one of the first things I tell them is that the North Star is the only star that is always in the same place in the sky, because it is directly overhead from Earth's north pole, and that all the other stars follow circular paths around the North Star as the Earth rotates. For beginners, this is useful information. I don't tell a beginner that the North Star is actually 45 arcseconds away from the North Celestial Pole, so it too is following a tiny circular path in the sky. I don't tell them about precession, so the NCP will close in on the North Star for the next 100 years and then start moving away for the next 13,000 years. I don't tell them about Polaris' proper motion as Polaris and our solar system fly through the galaxy. I'm sure there are even finer subtleties in the relationship between Polaris and the NCP that I'm not aware of. For a beginner, "the North Star is always in the same place in the sky" is an important foundation. The few people who are interested will learn about declination, arcseconds, precession, and proper motion as they delve deeper into astronomy.

Similarly, I think this monument to the Tropic of Cancer is a wonderful thing for people who can stand there on the Summer Solstice and see that the monument's shadow, and their own shadows, are perfectly vertical. Nobody will notice that their shadow is actually pointing a fraction of a millimeter to the north. Perhaps there should be a small sign somewhere on the grounds pointing people to the current tropic.