Never Tell Me The Odds

One of the best getaway scenes in movie history is in The Empire Strikes Back, when Han Solo navigates the Millennium Falcon through an asteroid field, with TIE Fighters in hot pursuit.

The famous chase scene. Start at 1:44

The scene starts with the Falcon getting hit by two asteroids. The asteroid field appears to have thousands of asteroids all flying around as far as the eye can see. The asteroids range in diameter from small rocks to the size of a small city. Han successfully navigates the asteroids while the Imperial fighters get pulverized by the rocks.

Star Wars’ portrayal of the asteroid field propagates a common misconception about the likelihood of colliding with, or even encountering, an asteroid.

As a bonus, I figure out how much kinetic energy the space rocks would carry in our solar system and the equivalent force in TNT.

What are the odds?

NASA’s Dawn Mission FAQ estimates the the volume of the Asteroid Belt is 16 cubic AU. An AU is the distance from Earth to the Sun. NASA estimates that there are 2 million asteroids greater than a mile in diameter within the asteroid belt. If the asteroids were distributed evenly, the distance between the asteroids would be about 1.9 million miles. This is 760 times the distance from NYC to Los Angeles.

A spacecraft has almost no chance of getting hit by an asteroid. In fact, it would be hard for someone sitting in a spaceship to see an asteroid with their naked eye. If the spacecraft was NYC, the nearest asteroid could be hundreds of Los Angeles(es) away.

What is the damage?

An asteroid does not have to be a mile long to inflict catastrophic damage to a spaceship. Imagine a space probe in our own solar system (miraculously) collides with an asteroid similar in size to the asteroids that hit the Falcon. Let’s calculate the kinetic energy of one of these tiny asteroids, and the equivalent force in kilotonnes of TNT.

What do we need to know for this calculation (we will use mks units):

  • Asteroid Shape: The asteroid definitely looks like a potato, but for math’s sake, I am going to pretend the asteroid is a perfect sphere.
  • Asteroid Diameter: The Millennium Falcon is about 35 meters in length. Since the asteroids were a bit smaller, we will use a diameter of 30 meters, and a radius of 15 meters.
  • Orbital Distance: Many asteroids orbit at 2.4 AU. This is 3.9E11 meters.
  • Asteroid Density: Average of 2g/cm^3 is 2000 kg/m^3

Now we do the math (on a separate sheet of paper):

Circumference of Orbit =  \pi 2r = 2.26 \, E12 \, \, m
Orbital Period =  \sqrt{a^{3}} = 3.72 \, \, y = 1.28 \, E8 \, \, s
Avg Orbital Speed =  \frac{dist}{time} = 3000 \, \, \frac{m}{s}
Asteroid Volume =  \frac{4}{3} \pi r^{3} = 14000 \, \, m^{3}
Asteroid Mass =  \rho V = 2.8 \, E7 \, \, kg
Kinetic Energy =  \frac{1}{2} m V^{2} = 2.8 \, E15 \, \, \frac{kg \, \, m^{2}}{s^{2}}

We got an answer! A spherical asteroid travelling at 3000 m/s should carry a kinetic energy of 2.8 quadrillion joules. This is equivalent to 2800 terajoules (a standard for nuclear weapon yields). For comparison, the Ivy King was the largest pure-fission bomb tested by the US, and yielded about 2100 terajoules.

Conclusion

Asteroids are incredibly deadly, even the extremely tiny ones. But, the odds of getting hit by one is astronomically low. You could fall asleep in an asteroid field expect to never get hit. Try not to dream about nuclear space rocks.

Sources:

Reducing Sky Glow

Stargazing is awesome! But sometimes, the night sky is not visible due to light pollution. In cities like Nashville, a common type of light pollution is “sky glow”.
Sky glow is the brightening of the entire night sky, especially in populated areas. The light pollution around Nashville inhibits our view of zodiacal light, airglow, and many of the Messier objects.

Bortle Dark-Sky Scale by Skyglowproject

How can we reduce sky glow? One method for cities to reduce skyglow is to reduce uplighting and excess / wasteful light through shielding or cutoff lights. For other tips, check out this blog by Mara Bermudez.

Shielded Lights

Light fixtures prevent light from immediately scattering in the atmosphere. Many fixtures also aim the light towards the ground, reducing glare and providing better ground visibility. Light shielding also reduces unwanted lighting on other people’s property, called light trespass.

Cutoff Lights

The Main Types of Cutoff Lights. by The Nguyen Manh, slide 26.

Cutoff lights focus light towards the ground similarly to shielding fixtures. The amount of cutoff determines how much light gets distributed at or above the horizontal. Cutoff lights have many benefits, including focused light for better surface visibility, and less uplighting, which is wasteful and the excess light scatters in the atmosphere.

In Nashville

Broadway night life in downtown Nashville. by John Russell/Vanderbilt University

Many of the street lights at Vanderbilt University are non-cutoff, as shown in this picture on the Vanderbilt admissions page of downtown Nashville. This type of light pollution contributes to the skyglow around Nashville.

Sources

Gravity and Sun Size


Comparison of the current-day Sun and the Sun as a red giant in the future. by
Oona Räisänen. 2007.

Gravity as the Driving Force

The Sun has a mass of 2 * 10^30 kg. Gravity exerts a compression force on the Sun proportional to this immense mass. So why doesn’t the sun collapse under the weight of its gravity?

The pressure of the center of the Sun is about 340 billion times the air pressure on Earth at sea level. Temperatures at the Sun’s core reach 15 million Kelvin. The conditions at the Sun’s core allow nuclear reactions to occur.

We will leave the exact reactions for a different time. Nevertheless, the basic reaction for stars the size of our Sun is called the proton-proton chain:

 4{_{1}^{1}\textrm{H}}\rightarrow{^{1}\textrm{He}^{2-}}+2e^{+}+2v_{e}

The nuclear reactions inside the core result in energy and an outward pressure that combats the inward pressure of gravity. Gravity is the driving force behind the nuclear reactions that power the Sun, which in turn determines its size.

Hydrostatic Equilibrium

While the core of the Sun is able to fuse hydrogen into helium, the size of the Sun will be relatively stable. The outward pressure of the reaction matches the inward force of gravity exerted on a star proportional to its mass.

During this period, the Sun is in “Hydrostatic Equilibrium” along the main sequence. Eventually, the Sun’s core will run out of hydrogen to fuse. The core will begin to contract and core temperatures will increase.

Red Giants

Once the core of the Sun runs out of hydrogen material to fuse, the core will begin to collapse. The extreme temperature and pressure caused by the core collapsing allows layers of hydrogen just outside the core (which previously had no role in nuclear fusion) to begin reactions. This outer layer contains more volume. Additionally, the star uses a different fusion reaction that results in the star producing much greater net energy.

The Sun will expand and become a Red Giant due to the greater outward pressure exerted as a response to the force of gravity collapsing the star.

Post-Red Giant

Our Red Giant Sun will eventually lose much of its mass and its emitted material will become a planetary nebula. It will become a white dwarf and slowly cool.

Gravity initiates the process that forms nebulae and stars, influences the formation and size of the star, and determines the life cycle and death of the star. In this way, gravity is the catalyst for change, and the driving force, in the life of our Sun.

Sources

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

Copernicus in Context

Nicolaus Copernicus

A statue of Copernicus.
Copernicus Monument in Toruń, Poland. Uploaded to Pixabay by BadziolTV.

Nicolaus Copernicus was born February 19, 1473 and died May 24, 1543. Copernicus‘ most important contribution to astronomy is his heliocentric model of the solar system that placed the Sun at a fixed point in the center, and depicted the planets orbiting the Sun. In this model, Earth was just another planet. The model explains apparent retrograde motion by comparing the relative orbits of Earth and other planets.

Copernicus’ heliocentric model inspired astronomers such as Galileo, Kepler and Newton to develop similar theories and models about planetary orbits and the solar system. Moreover, the posthumous publication of Copernicus’ De Revolutionibus is typically regarded as the beginning of the Scientific Revolution.


Heliocentric Model with circular orbits.
Copernican Heliocentrism in De Revolutionibus. Derivative work by Professor Marginalia. uploaded to Wikipedia Commons. 2010.

What else was going on in the world while Copernicus was developing his heliocentric model of the solar system?


The Spanish Inquisition

Monty Python surprises unsuspecting heretics with the Spanish Inquisition.
Nobody Expects the Spanish Inquisition. Added by LexsJB to the Monty Python Wiki.

On November 1, 1478, Ferdinand II of Aragon and Isabella I of Castile established the Tribunal of the Holy Office of the Inquisition to promote hegemonic Catholicism throughout Spain. The Inquisition prosecuted heretical Jewish conversos and Islamic converts to Catholicism. In 1492, Ferdinand and Isabella issued the Alhambra Decree, which expelled Jews to reduce their influence on conversos. The Inquisition’s rise and fall reflects the growing fears of religious diversity, increased secularism, Christian reformations, and religious warfare. The Spanish Inquisition disbanded in 1834.


The Ninety-Five Theses

On October 31, 1517, Martin Luther nailed the Ninety-Five Theses to the doors of Wittenberg Churches, beginning the Catholic Reformation. Martin Luther, a monk-turned-priest-turned-scholar-turned-professor of theology, wrote the Theses in response to what he perceived as sinful practices by the Catholic Church. Luther admonishes the practice of buying and selling indulgences, which the clergy claimed could allow a remission of sin. In addition, Martin Luther dismisses the concept of Papal Supremacy, especially in regards to penance and to souls in Purgatory.

A drawn mural of Martin Luther. The words "Luther war hier" appears to the side.
Facade of Martin Luther. Uploaded to Pixabay by Hansbenn.

The Theses sparked great debate within the Catholic Church. Luther’s simple writing and the reproduction of his works via the printing press facilitated the growth of Catholic Reformation movements. The Ninety-Five Theses set the stage for long-lasting religious, social, and political changes in Europe.


Hernán Cortés

Cortés was born in 1485 and died on December 2, 1527. Cortés was a Spanish Conquistador. He was famous for exploring the New World and defeating the Aztec Empire.  In 1519, and against the orders of his commanding officer, Velázquez, Cortés commanded an expedition to colonize the Mayan and Aztec territory of Mexico. Cortés convinced native peoples to ally against Moctezuma II, leader of the Aztecs. To prevent his men from escaping to Cuba, Cortés reportedly scuttled his own ships. With reinforcements, thousands of native allies, and a long siege on Tenochtitlan in 1521, Cortés destroyed the Aztec capital and declared victory for Spain. Cortés’ expeditions reflect the successes of colonialism and the establishment of new European trade routes in the New World. The fall of the Aztec Empire illustrates the destructive capacities and lasting impact European colonialism has on native peoples, landscapes and cultures. As for Cortés, all he wanted was a fancy title, land holdings, and treasure.

A picture of the impressive Templo Mayor at the Aztec Site.
Templo Mayor at the site of Tenochtitlán, Mexico. Uploaded to Pixabay by
EntretenimientoIV.

Learning in Context: a reflection

In many textbooks, we learn about the history of topics with a similar theme. For instance, we might take a class on philosophy and science and learn about the Enlightenment. A class on colonialism might teach the Age of Exploration. We might take a class on the Scientific Revolution, or the Catholic Reformation. In each of those classes, we would learn about different historical figures and events.

But the ages listed above all happened at the same time. Michelangelo, da Vinci, and Shakespeare. Nostradamus, Galileo, and Copernicus. Bacon, Machiavelli, and Hobbes. Luther, Xavier, and Calvin. Nobunaga, Ivan the Terrible, and Charles V. Every single person on this list lived in the 16th century and helped shaped the ideas and history of the time.

We often learn about history in these isolated themes. We should remember that the history of astronomy, for instance, cannot be severed from the history of art, religion, politics. All these histories are interwoven.


sources

  • History.com Editors. “Inquisition”. 2018. HISTORY. A&E Television Networks. Last updated 21 August 2018.
  • Hillerbrand, Hans J. 7 December 2018. “Martin Luther”. Encyclopædia Britannica. Encyclopedia Britannica, inc.
  • Innes, Ralph Hammond. 1 January 2019. “Hernán Cortés”. Encyclopædia Britannica. Encyclopedia Britannica, inc.
  • Luther, Martin. “The 95 Theses”. 1517. Translated and published in 1997. KDG Wittenberg.
  • Westman, Robert S. 20 May 2018. “Nicolaus Copernicus”. Encyclopædia Britannica. Encyclopedia Britannica, inc.
  • Wikipedia Contributors. 2019. “Copernican Heliocentrism”. Wikipedia, The Free Encyclopedia. Last revised 28 January 2019.
  • Wikipedia Contributors. 2019. “Hernán Cortés”. Wikipedia, The Free Encyclopedia. Last revised 4 January 2019.
  • Wikipedia Contributors. 2019. “Nicolaus Copernicus“. Wikipedia, The Free Encyclopedia. Last revised 29 January 2019.

How Much Does Light Weigh?

Light is made of photons. And photons are massless particles, which means they have no invariant/resting mass. Therefore, light has no mass and no weight. End of story, right?

The Force of Light

Did you know that light exerts pressure on objects? This force can even increase an objects weight, albeit to a small degree. For instance, Vsauce explains how much a landmass might weigh covered in sunlight (for the city of Chicago, sunlight only adds 300 lbs).

Michael Stevens from Vsauce describes the weight of light. Octover 7, 2012. Youtube. For the section we discuss, please watch up to 0:56.

Although insignificant on a small scale, scientists must account for this force – called radiation pressure or solar radiation pressure – in planing space missions.

Solar radiation pressure plays a role in the formation of galaxies, stars and clusters, and solar/planetary systems. Additionally, solar radiation shapes the tails of comets.

A Common Misconception

Light carries energy and momentum. We know that energy, momentum and mass are related. Can we assume that light also has mass?

E = mc^{2}

This misconception stems from Einstein’s mass-energy equivalence formula. Einstein proposed that an object with energy has an equivalent amount of mass. Einstein’s formula only applies to objects with invariant/resting mass. Since photons have no resting mass, we have to use a different formula:

E = pc

where p is the momentum of the particle. Therefore, we can observe momentum and energy for massless particles.

tl;dr Light does not have weight or mass. Light can push an object or increase its weight, to a minimal degree.

We Weigh Less in the Dark, technically

Do we actually weigh more in sunlight? Functionally, no. But, we can still estimate an upper bound.

First, solar radiation pressure is applied to objects in the direction of sunlight. For this problem, let us pretend that we are shaped like rectangular solar panels.

Second, we learned from Vsauce that light exerts a force of pressure on the surface of Earth of about 1e-9 lbs per square inch. Considering the average human has a surface area of 1.9 meters squared, we can calculate the following:


  \frac{1.0*10^{-9} lbs}{in^{2}}  * \frac{1550 in^{2}}{m^{2}}\  * 1.9m^{2}

 = 3.0 * 10^{-6}lbs

So the next time you weigh yourself, turn off the lights. You might not notice a difference, but you just shaved a couple millionths of a pound.

Sources:

My First Post

A tree branch, weighed down by snow, blocks a walkway.
A tree branch, weighed down by snow, blocks a walkway outside North House at Vanderbilt University. 21st Avenue, Nashville, TN. 2016. Photo by JSpin.

A particularly brutal winter, especially because Nashville’s idea of dealing with snow is throwing salt everywhere and call it a day.

When I was a freshman, I would come to this spot outside North House to study and enjoy nature.

I said, “Excuse Me” to the tree as I walked past on my way to the Commons Center.