by Anthony Barreiro » Mon Aug 05, 2013 8:55 pm
Case wrote:
Wikipedia wrote: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.
[quote="Case"][float=right][img3="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."]http://tiny.cc/n6m80w[/img3][/float]
[quote="Wikipedia"][url=https://en.wikipedia.org/wiki/Tropic_of_cancer]Tropic of Cancer[/url] - 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.[/quote]
...
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 [i]exactly[/i] 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).[/quote]
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.