Celestial Navigation

Sekstant
Using a Sextant

Celestial navigation is the practice of navigating from one place to another using celestial bodies as a guide. Prior to the invention of GPS, people would use the position of the stars in relation to themselves as a method of orienting oneself to their destination. The process is simple in concept – the navigator uses the angle created between the chosen celestial body (or bodies) and the visible horizon to narrow down the amount of possible places on Earth they could be. In modern times, this process is completed using a sextant, which is a tool to looked into by the navigator that can help measure the angle between the celestial body and the horizon. For each celestial body viewed at a certain time, the possible positions of the observer can be narrowed down into a large circle on Earth. This process works because every celestial body is directly above exactly one spot on Earth. To view that celestial body from directly below (90 degrees), you would have to be in exactly one spot. But to view that celestial body from a slight angle (perhaps 85 degrees), the observer would have to move a specific distance away from the 90 degree spot in ANY direction. This is what creates the circles used in the positional calculation! In order to improve accuracy, celestial navigators often consider multiple celestial bodies, each projecting their own large “possibility” circle onto Earth. Where multiple of these circles meet corresponds to the position of the observer! To be sufficiently accurate, most navigators use three to five celestial bodies, as using just one would only deduce the large circle, and using two would create multiple intersections between the circles.

Video on Celestial Navigation Math

Wikipedia article on Celestial Navigation

 

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Transgressing the Boundaries: A Look at the Sokal Affair

1996sokal_lead
Photo Credit: The Museum of Hoaxes

I’ve been lucky to be able to study across very different academic fields in my undergraduate curriculum. This breadth of academic focus has made apparent to me the differences between how scholars in certain fields practice their craft. These differences contribute to the not-so-friendly rivalry between the so-called ‘hard’ sciences (physics, chemistry, biology, mathematics, etc.) and ‘soft’ sciences (psychology, economics, sociology, political science, etc.). One startling product of this rivalry I’ve come across recently is the Sokal affair, also known as the Sokal hoax. Physics professor Alan Sokal submitted a bogus paper to a postmodern academic cultural studies journal, Social Text. The paper, “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity”, was accepted and published in the 1996 issue. Sokal later revealed that his paper was not genuine and outlined his intent to determine whether “a leading North American journal of cultural studies […] [would] publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors’ ideological preconceptions”.
I encourage you to read the paper and Sokal’s discussion for yourself. Sokal believes his “experiment” revealed a dangerous lack of intellectual rigor in academic humanities; do you agree? Do you think Sokal’s method (knowingly submitting phony work to an academic journal) was justified in this case? For further reading, take a look at the Bogdanov affair, sometimes referred to as a “reverse-Sokal hoax”.

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Retrograde Motion simplified.

the path of mars

The path of Mars, as viewed from the Earth.

         Retrograde motion is the apparent backward motion of a planet caused by its being lapped by another planet, or vice-versa.1  These two planets are usually on two different orbits, a larger one and a smaller one, and they move around the sun in the same direction (eastward). The planet on the smaller orbit moves faster than the planet on the larger orbit. When the two planets on different orbits do overlap, and align with the sun, either one of the planets sees the other planet as moving in the opposite direction. However, this is only an apparent motion, as the planets are truly moving in the same direction. This apparent motion is what we call “retrograde motion.” The period between two retrogradations is the synodic period of the object/planet.2 A practical example of retrograde motion is the motion that when you pass a car on the freeway. The car being passed appears to move backwards relative to you. Alternatively, you can experience this by standing side by side with a friend, and having them. walk forward slowly. Now walk forward at a faster speed and watching your friend, think about how they are moving relative to you. At first, they move away, then as you pass them, they appear to be moving backward relative to you – even though they are still walking forward. Ancient Greek astronomer Ptolemy in 150 AD believed that the Earth was the center of the Solar System and therefore used the terms retrograde and prograde to describe the movement of the planets in relation to the stars, and the names have remained since then.3

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Antipodal Tides

It makes sense that the tide comes in as the Moon approaches that side of the Earth. The gravitational pull attracts the water away from the Earth. It would seem them that logically a low tide would happen at a location farthest from the Moon. But that is not the case.

Tide_overview.svg

image link

In the Moon only scenario, the tides follow a 12 hour cycle and not a 24 hour cycle. The tide facing the Moon is called the sublunar tide, and the tide opposite the Moon is called the antipodal tide. But why does the antipodal exist?

An immediate explanation would be: “Oh, the Sun must be on the other side of the Moon pulling the waves in that direction!” But, in that consideration one fails to realize that the Moon is not always across from the Sun. A careful analysis of the location of the Moon during its different phases would make that clear.

So then how do we explain the antipodal tides? Turns out it’s kinda complicated and somewhat of a contentious topic. As seen in this stackexchange debate. What I find to be the simplest to understand is that as the Earth and the Moon pull on each other, there is an instantaneous force on each of them, and according to Newton’s Second Law, F=ma, there must an acceleration meaning that at any particular instant we can describe the Earth as moving towards the Moon. We know, obviously, that the Earth and Moon have constant mass, so according to Newton’s Law of Gravitation, F=(GMm)/r^2, the only variable is the distance between the the two masses. At the surface facing the Moon, the water is closer than the center of the Earth, so its acceleration will be greater meaning that any particular instant the surface facing the Moon is moving away from the Earth relatively. Likewise, the surface opposite the Moon has a force that is less than the center of the Earth, so its acceleration will be lower meaning that we can describe the Earth moving away from it or that it is moving away from the Earth relative to the Earth. This model of course becomes more complicated when the Sun gets involved, but for describing simply the phenomenon of antipodal tides I find it both useful and fascinating.

 

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Why is the Sky Blue?

Schematic animation of a continuous beam of light being dispersed by a prism. The white beam represents many wavelengths of visible light, of which 7 are shown, as they travel through a vacuum with equal speeds c. The prism causes the light to slow down, which bends its path by the process of refraction. This effect occurs more strongly in the shorter wavelengths (violet end) than in the longer wavelengths (red end), thereby dispersing the constituents. As exiting the prism, each component returns to the same original speed and is refracted again.
Light Dispersion Conceptual Waves by
Lucas V. Barbosa. 2007.

Some Background

In the image above, a beam of light passes through a medium. The medium slows down the light and causes it to refract. And the degree of refraction is dependent on the wavelength of light: shorter wavelength light will slow down more and therefore have a greater angle of refraction. See Cauchy’s equation below for the inverse relationship between refractive index and wavelength of light in a transparent medium.


  B + \frac{C}{\gamma^{2}}

Our Sun emits a continuous spectrum of light, called black body radiation, which is predictable by its temperature. For the purposes of clarity, we will assume that the Sun emits all the visible wavelengths of light and they reach Earth’s atmosphere.

Why does the sky appear blue?

The shorter wavelength blue light scatters in Earth’s atmosphere more than the longer wavelength red light. Thus, the sky appears blue. And when the Sun’s light travels a long distance to reach us, such as during a sunrise or a sunset, the sky will appear yellow, orange, or red. This phenomenon also explains why a lunar eclipse appears reddish in color, since red light scatters the least as Earth reflects light into space.

Since violet is the shortest wavelength, the sky should appear violet, right?

The sky does appear violet… but not to humans.

The human eye uses three different types of cones to view color. About 64% of these cones are sensitive to red light, about 32% are sensitive to green light, and about 2% are sensitive to blue light. The sensitivity of the cones tend to be similar, despite the disparity of blue cones.

Simplified human cone response curves. Curves show blue, green, and red sensitivities.
Simplified human cones response curve. based on Dicklyon, which is based on Stockman, MacLeon and Johnson. by Vanessaezekowitz. 2007

When the light from the atmosphere reaches our eyes, the blue-sensitive cones are stimulated the most, with a small amount of stimulation to the green- and red-sensitive cones. This mixed hue actually creates the same cone response as “pure” blue and white light.

In the same vein, animals have varied abilities to see color. Many animals only have two cones instead of three. And some animals can see wavelengths invisible to humans. For instance, the honeybee can see ultraviolet light and discerns UV patterns on flowers, which facilitates gathering nectar.

sources

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Archeoastronomy

Archeoastronomy is the study of how ancient civilizations understood astronomy. It examines past people’s cultures, religions, and lore and observes how it affected their art and architecture. There are many examples of this throughout history and through archeoastronomy, we can learn about the development of astronomical thought around the world. (Source)

Stonehenge at Sunset Google Images

Archeoastronomy was developed through the Stonehenge in the 1960s where scientists discovered that it was used to predict the suns and moons eclipses. (Source) Other examples or archeoastronomy include the pyramids of Giza and the Lascaux Cave in France. Theories about the pyramids include the alignment of the stars in the Big Dipper to show where north is and astronomical carvings on the pyramids. The caves in France indicate early star charts and are illuminated by the sunset on the winter solstice. (Source). All of these examples show how astronomy was studied thousands of years ago.

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Shaving for Science – the Principle of Occam’s Razor

One of the most crucial aspects of the Scientific Method is finding a model that fits observational data. However, what happens when multiple models fit our observations equally well? Which one do we choose?

tained-glass window showing William of Ockham
William of Ockham
Photo Credit: User Moscarlop via Wikimedia Commons

Here is where Occam’s Razor comes in. This principle states that we should generally choose the simplest model in such situations. Named after 13-14th century English friar, philosopher, and scholar William of Ockham (who did not invent this principle but nonetheless used it frequently), Occam’s Razor describes a “shaving away” of extraneous models. It prevents one from “saving” an unreasonable model by adding increasing numbers of details. Consider this everyday life example from the children’s story The Berenstain Bears and the Truth (by Stan and Jan Berenstain):

Brother and Sister Bear, home alone, play soccer in the house and the ball ends up hitting Mama Bear’s favorite lamp, breaking it. When the parents return, they of course ask what has happened, to which the cubs respond that a bird flew into the window, hit the lamp with enough force to knock it over, and then flew back out the window. Of course, this would require that the bird was massive enough to knock over the lamp, that it would collide directly with a stationary object, and that it wouldn’t leave any other trace of its presence. Each of these would necessitate further explanation, i.e. the bird was of a particularly large species, it was somehow disoriented (maybe it was intoxicated from eating fermented berries?), and that it left immediately without leaving behind any feathers. Furthermore, the cubs try to prove they are telling the truth by describing the unusual features of the bird, e.g. that it was purple with a red head, had strange feathers growing out of its head, and squawked and whistled. The parents, however, postulate instead that the lamp was broken by the cubs via the soccer ball that is sitting in the same room.

Both models (the bird and the soccer ball) perfectly fit the observation (the lamp was broken). However, the bird model is far more complex and requires an absurd amount of explanation to fill in the gaps, so by Occams’ Razor, we should choose the soccer ball model. Occam’s Razor thus helps us reject such ridiculous models that still technically match observations.

Speaking of the Berenstain Bears, many people (myself included) remember their name being spelled as Berenstein. This phenomenon is part of a wider set of mismatches between memories and reality, known as the Mandela Effect. It is named after Nelson Mandela, because the most prominent example is that people remember Mandela having died in prison long ago, when in fact he passed away only about five years ago. Some people attribute this mismatch to influence from alternate universes. For instance, Gaia.com describes the possibility of a “multiverse in which waves of events from a parallel universe have washed over into ours, creating subtle nuances in the time-space continuum.” Although this model would fit with what we are observing, Occam’s Razor states that we should prefer the much simpler explanation: that humans’ fallible brains are simply misremembering information, particularly information accrued during childhood.

Finally, an example from astronomy: Ancient astronomer Claudius Ptolemy proposed a geocentric model of the Solar System in which all the “planets” (including the Sun and Moon) orbit the Earth on circular orbits, which have smaller circles (epicycles) attached to them. This model fit observations at the time, but so did the newer Copernican model, introduced in the 16th century, which had the planets (including Earth) instead orbiting the Sun. Occam’s Razor states that when two models explain data equally well, the simpler one should be chosen, and in this case that is the Copernican model.

Do you have any interesting examples of Occam’s Razor from science or your daily life? And have you experienced the Mandela Effect at some point in your life? (Which of you still remember the Bereinstein Bears?) What do you think causes the Mandela Effect? I’d love to hear your thoughts!

Sources:

Bennett, Jeffrey O., et al. The Cosmic Perspective. Pearson, 2018.

Berenstain, Stan, and Jan Berenstain. The Berenstain Bears and the Truth. Paw Prints, 2009.

“False Memory.” Wikipedia, Wikimedia Foundation, 25 Jan. 2019. Web.

“Occam’s Razor.” Wikipedia, Wikimedia Foundation, 22 Jan. 2019. Web.

“Mandela Effect: Is a Parallel Universe Changing Our Reality?” Gaia. Web.  

Maxouris, Christina, and Brandon Griggs. “Birds in Minnesota Keep Crashing into Things and Police Think It’s Because They’re Drunk.” CNN, Cable News Network, 5 Oct. 2018. Web.

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Newton’s Law of Gravitation and General Relativity

Isaac Newton’s law of universal gravitation first appeared in the Philosophiæ Naturalis Principia Mathematica in July 1687. It describes why that apple fell on Newton’s head (as some stories would have it), why we stay rooted to the ground (without drifting off into space), and why the Earth is locked in orbit around the Sun (among other things). However, while Newton’s law continues to be used as an excellent approximation of the effects of gravity in most applications, it has since been superseded by Albert Einstein’s theory of general relativity.

General relativity uses Einstein’s equivalence principle whereby, on a local scale, it is impossible to distinguish between the physical effects due to gravity and those due to acceleration. Currently, gravity is treated as a consequence of the curvature of spacetime (caused by an uneven mass distribution) – and, the solution of the field equations that describe general relativity are able to explain physical situations such as planetary dynamics, stellar evolution, black holes, and the evolution of the universe.

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Yep, Physics Works. – Blog2

Physics is all around us in our daily lives, it’s the reason things…are the way they are. The reason we get from point A to point B and exist on this Earth the way we do. And yet some people don’t buy it, and it drives certain professors to use this demonstration:

If video doesn’t work, the link to the original source is here

While entertaining, it really is true. Ui+Ki=Uf+Kf…barring any external work being done. Conservation of energy at its finest…but it extends far beyond the scope of what we think about in our daily lives; conservation laws lie at the core of our existence. Why does the Earth orbit the sun in the way that it does? Conservation of angular momentum (or L=Iw…the mvr simplification in the book is only for a point mass).

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Blog #2: Special Relativity

Albert Einstein was one of the most influential thinkers regarding the fabric of the universe. Einstein’s major contribution to modern physics was his theory of relativity. The first part of this revolutionary idea was his special theory of relativity. Published in 1905, it established two major points: the laws of physics are the same in any inertial frame and the speed of light is always constant no matter the speed of the source or the observer. While the theory most directly dealt with physics on a microscopic scale, it still had many major implications. His first point dealt with the idea of relative motion and the fact that there was no ether, a nonmoving frame of reference, that all previous physics was based upon. The ether was an important idea in the belief that the universe was orderly and structured. The new idea of relativity where there was only relative motion rather than absolute motion unraveled this idea. There was nothing absolute. His second point about the consistency of the speed of light is a bit more difficult to understand; however, it constitutes the idea of a curved spacetime, something that was explained more elaborately in his general theory of relativity. The idea of time as a dimension that, along with space, could be warped showed that we did not live in a universe of the orderly Euclidean geometry but in a non-Euclidean universe. These concepts unraveled the prevailing idea that the universe was fundamentally structured and worked according to Newton’s orderly laws and vaulted scientific thought into a whole new era. 

Image of the Non-Newtonian Spacetime

Sources (from research I did in high school so I couldn’t hyperlink them):

“Relativity” World Book Encyclopedia. 1989.

Pearce Williams, L. “Ether.” Encyclopedia Americana.Scholastic Grolier Online,   ea.grolier.com/article?id=0147190-00. Accessed 15 Feb. 2017.

 Will, Clifford M. “Relativity.” Grolier Multimedia Encyclopedia.Scholastic Grolier Online,   gme.grolier.com/article?assetid=0244990-0. Accessed 16 Feb. 2017.•

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