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The “Unfairness” of the Electoral College Didn’t Swing the 2016 Election


2016 election results via google’s election map.

In the wake of the election, there have been renewed complaints about the Electoral College, specifically, how it unfairly rewards small states with disproportionate voting power. The supposed implication is that Donald Trump won the election, despite losing the national popular vote, because small states vote Republican. Well, I did a little number crunching.

If the Electoral College’s 538 votes were redistributed proportionally to their populations (i.e., removing the “bonus” small states receive from their senators) but kept the winner-take-all format, Trump would have won about 56 percent of the electoral votesIn real life, he won about 57 percent of the electoral votes (assuming he wins Michigan, Clinton wins New Hampshire, and Maine goes 3-1 for Clinton). If anyone’s been worried about the Electoral College favoring small states, it didn’t affect this election. The determining feature of the Electoral College this time around was its winner-take-all format, at least, outside of Maine and Nebraska.

Here are my calculations based on US Census estimates from 2015.


A friend of mine, a Democrat, also made the following observation:

Lastly, clearly the Electoral College favors the Republicans right now given that Trump won the election and Hillary won the popular vote, but it’s not because “less populous states are red” or any variant of that argument. The [less-populus] red states are just bigger and in the middle, so they’re easier to see.

Of the smallest 12 states (all the states with <= 4 electoral votes), 6 went red (Wyoming, Alaska, ND, SD, Montana, Idaho) and 6 went blue (Hawaii, NH, Maine, RI, Delaware, VT). In fact, the Dems also won DC, so the dems are more helped by the electoral college on the low end.

On the high end, the top 4 split 2-2 (CA, NY vs FL, TX). It’s the next 8 that had a big effect on this election, Hillary only won 3 (IL, NJ, VA), while Trump won 5 (PA, OH, GA, NC, MI).

He later added fittingly, based on the analysis of the smallest states, “New Hampshire is the swing state to see if small states favor Republicans or Democrats.”

Why We Have Gun Safety Rules


There are three cardinal rules of gun safety. One negligent Florida police officer outrageously violated all three at the same time and accidentally killed a woman.

Mary Knowlton arrived at the Punta Gorda, Fla., police station Tuesday night to learn how to be a community steward.

The 73-year-old was there as a student in the citizens police academy, a two-hour course intended to give an intimate look at what makes the department in the quaint Florida town work. On this night, the group of 35 would tour the station and talk with officers, an essential part of academy curriculum that has gained popularity across the country amid a heated national debate about police violence.

When it came time to get involved, Knowlton volunteered.

The hosting officers chose two students to role-play a lethal force simulation, a scenario intended to demonstrate how and when officers decide to pull the trigger. Knowlton played the victim, Charlotte Sun photographer Sue Paquin told the newspaper, and a Punta Gorda police officer played a “bad guy.” These scenarios are usually safe, acted out with either fake or empty weapons.

But when the officer’s gun was fired, Knowlton — a mother, wife and career librarian — was hit with a live round.

She was rushed to a local hospital and was pronounced dead.

Her husband of 55 years witnessed the shooting and is “devastated,” her son, Steve Knowlton, told the Associated Press. …

At a news conference Wednesday afternoon, Lewis shared few details about how the tragedy unfolded but said his department was unaware that live ammunition “was available to the officer” during the class.

Lewis has asked the Florida Department of Law Enforcement to conduct an independent investigation which, the chief said, will determine how the ammunition ended up in the handgun without anyone noticing.

That same weapon has been used in previous simulation classes, which the department holds annually, Lewis said.

This is precisely the reason these rules were developed as best practices and must be followed universally. In no particular order:

  1. Always check the chamber when you pick up a gun to make sure it is unloaded. Even when you’re sure it is unloaded, take all precautions as if it were loaded. Someday you will be wrong.
  2. Always point a gun in a safe direction, never at a person, even if you’re sure it’s unloaded. Someday you will be wrong.
  3. Never touch the trigger until you are pointing at the target you intend to shoot. Never pull the trigger idly just because you’re sure it’s unloaded. Someday you will be wrong.

No exceptions for training, make-believe, or “just this once.”

There are several photos and videos available at the Facebook page of local reporter Corey Lazar, including one which purports to show the officer who fired. It’s not clear who or what he’s pointing at, but it looks like his finger is curled right around the trigger of a loaded gun.


I can’t imagine why a real gun was required for this exercise. Surely they’ll modify that practice now.

Share Your Expertise: Some Things You Should Know About Orbital Mechanics


The Ricochet staff solicited our expertise. Your friendly neighborhood aerospace engineer is here to deliver it from my desk on the corner of Karman Vortex Street and Tomcat Alley. (You may have seen my previous writing on the NAVSTAR GPS.) In this article we’ll cover a few common misconceptions about orbital mechanics and then ‘splain some fundamentals for the layman. There’s always some overlap between topics, and this article touches on reentry aerodynamics as well, but without further ado here is the orbital mechanics edition.

There is gravity in space


With sufficient speed a free-fall trajectory never intersects the Earth.

Some people imagine that if you just fly high enough you’ll reach space, escape Earth’s gravity, and start floating around. But at 300 miles altitude where the the International Space Station orbits, Earth’s gravity is still 90% as strong as it is on the ground. What makes the astronauts feel weightless is that they and the ISS are mutually in free-fall. It’s like they are perpetually on the downhill leg of a giant roller coaster, falling toward the ground at about 0.9 g and giving them that floaty feeling in their stomachs.

But the ISS and the astronauts inside it are also moving laterally at tremendous speed — faster than other free-falling objects like golf balls, bullets, artillery shells, and even ICBMs. Their path of free-fall is so far ahead of them it doesn’t even intersect the Earth. That’s called orbit.

So to get up in space and stay there, it’s not enough just to fly up to a high altitude outside the atmosphere. You have to achieve enough lateral speed that when you inevitably fall back toward the Earth, you miss.

Orbiting is all about speed

It takes much, much more energy (i.e. fuel) to reach orbital speed than merely to reach a space altitude. That’s why orbital rockets are so much bigger than suborbital space planes. Compare the X-15 at the left side of the figure with similarly sized X-37B at the right (the little gray vehicle inside the nose fairing at the top). The X-15 reached space altitudes but even at Mach 6 was far to slow to stay in orbit. The enormous Atlas V/Centaur rocket system is required to give the similarly-sized X-37B enough speed to stay in orbit. Almost all of that extra size is fuel.

The world's space planes. (Credit: By Kelvin Case at English Wikipedia - Transferred from en.wikipedia to Commons by The Bushranger using CommonsHelper.(Original text : Primarily a personal artistic creation, created by myself, Kelvin Case. Additional derivative work was from these following U.S. government and Wikipedia images. (Furthermore, for a summary of additional visual arts reference images reviewed, see Licensing below.)File:Atlas EELV family.pngFile:Boeing X-37B inside payload fairing before launch.jpgFile:Centaur upper stage of Atlas V rocket.jpgFile:Flag of the Soviet Union.svgFile:Roundel of the USAF.svgFile:Size Comparison.pngFile:X-15.jpgFile:X-15 three view diagram .pngSpaceShipOne image posted at NASA web site,, CC BY-SA 2.5,

The world’s space planes. (Credit: By Kelvin Case at English Wikipedia. CC BY-SA 2.5,

The speed required to stay in orbit depends on the strength of the gravity field (i.e. the mass of the planet or star you are orbiting) and the altitude of the orbit. But perhaps counter-intuitively, the required speed does not depend on the mass of the orbiting object* — a pebble and a school bus at the same altitude will orbit at the same speed. This is directly related to the principle that all objects fall at equal speeds under gravity regardless of their mass. (* However, the size of the rocket required to achieve a given speed is highly dependent on the mass of the object.)

Imagine swinging a ball on a string in a circle around you. Without any force on it the ball would naturally move in a straight line, but the tension in the string provides a centripetal force (a force “toward the center”) and the result is a circular motion. We have an equation for the unique amount of centripetal force required for circular motion at any given speed and radius. If you change the speed or the length of the string the force changes. If you let go of the string, the ball flies off in a straight line.


The vector “v” represents the velocity, and the vector “a” represents the centripetal acceleration due to gravity. Since the acceleration is perpendicular to the velocity, the object changes direction but not speed. Not to scale.

In the same way, gravity provides the centripetal force to keep an object in orbit. At any given altitude the force of gravity has a specific value, so there is one specific speed that results in a circular orbit at that altitude (Other speeds give different orbit shapes. More on that later.). Gravity is stronger at lower altitudes and gets weaker as you go up, so higher orbits have lower speeds. In principle you could orbit a planet at any altitude, but there is a practical lower limit because at some point atmospheric drag causes objects to slow down and fall back to Earth. There is also a practical upper limit where the gravity from other celestial objects becomes comparable in strength to the gravity from the Earth and affects the motion.

Now you might think back to the ball analogy and realize a heavier ball requires more force from the string. That’s true for orbiting objects too. But gravity by its very nature pulls harder on heavier objects precisely proportional to their mass, so it perfectly evens out.

Orbits come in many shapes and sizes

Circular orbits are easy to conceptualize and understand. But in general, orbits are not perfectly circular. Most orbits take the shape of an ellipse. Some ellipses are nearly circular, and some are so elongated (eccentric) they appear to be a long thin sliver. There are even orbits so eccentric that the ellipse never closes at the other end. More on that later.

CC BY-SA 2.0 at,

An elliptical orbit has the gravitating body at one focus and nothing at the other. (Credit: CC BY-SA 2.0 at,

In an elliptical orbit, the gravitating body is not at the center, but rather tucked down in one end at a focus of the ellipse (plural: foci; every ellipse has two). This is Kepler’s First Law of orbital motion. The other focus is an imaginary point symmetrically placed on the other side of the ellipse. 

Although the motion is more complex than a circular orbit, it obeys the same type of relationship between speed and distance. At the near end of the ellipse, the orbital speed is very fast, and at the far end the speed is very slow. The relationship between speed and distance is mathematically complex but geometrically very simple: the orbiting object sweeps out equal areas in equal time. This is Kepler’s Second Law of orbital motion.

This video shows wedges of blue and gray which each have exactly the same area. The planet takes exactly the same amount of time to sweep across the base of each wedge. 

One of the most famous examples of a highly eccentric elliptical orbit is Halley’s Comet, which takes 76 years to complete one revolution. The speed of Halley’s Comet varies by more than a factor of 60 between its closest approach to the Sun (perihelion) and its farthest reach (aphelion). At the near end to the Sun it spends about 2.5 years inside the orbit of Jupiter. At the far end, it takes over 30 years to cover the same distance. Other comets even have orbits that are much more extreme.


A two-dimensional view of the orbit of Halley’s Comet. Its progress is indicated by year, showing the great variation in speed throughout its course. (Credit: Steven Dutch, University of Wisconsin-Green Bay)

You don’t have to achieve escape velocity to reach orbit

Escape velocity is the speed of an orbit that will reach infinite altitude. That’s not an exaggeration ­– an object which has achieved escape velocity will never stop and fall back down. Given enough time it will pass any arbitrarily large altitude you can think of. The escape velocity depends only on the mass of the gravitating body and your altitude from it — it is higher for larger planets and at lower altitudes.

Any object travelling slower than escape velocity will either fall to the ground or curl around and orbit the Earth in an ellipse. An object moving faster than escape velocity is on an escape orbit, which is not an ellipse, but a hyperbola*. A hyperbolic orbit is an arc that passes near the planet but never curls back around at the other end. Instead it extends to infinity as it asymptotically approaches a straight line. The following video demonstrates the different orbit shapes very clearly. (* The rare object traveling at exactly escape velocity follows the closely-related parabola.)

The conic sections.

The conic sections. (Credit: By Drini (Own work) [GFDL ( or CC BY-SA 4.0-3.0-2.5-2.0-1.0 (], via Wikimedia Commons)

 All of these shapes are called the conic sections: the shapes you get when you slice a cone at different angles.

In a sense, an object in a hyperbolic escape orbit is traveling so fast it is outspeeding gravity’s ability to restrain it. It is slowed by gravity just like any other object, but as it speeds away from the planet gravity gets weaker. Its very high speed causes it to enter ever weaker regions of the gravity field such that there is never enough gravity to slow down and start descending. You can usually calculate the time at which an object under the force of gravity would lose all its speed and start to fall. For an object at escape velocity, that time is infinite.

Satellites launched into Earth orbit never reach escape velocity, they settle into nice circular or elliptical orbits. Spacecraft launched to the Moon or other planets, or into deep space like Voyager and New Horizons, leave the Earth above escape velocity. They will never return to Earth barring a drastic maneuver imparted by either a rocket or the gravity of some other object.


A circumlunar free-return trajectory. The translunar injection in the lower left put the Apollo capsule on an escape trajectory. Another burn was required on the return leg to slow down below escape velocity and re-enter. Not to scale.

The Apollo spacecraft returned using both of those methods. The first several Apollo missions were launched into Earth-escape orbits that happened to intersect the Moon’s orbit in a special way. They used the Moon’s gravity to interrupt the escape trajectory and turn their orbit around to create a “free-return trajectory”. However, the vehicle would now be travelling back toward Earth above escape velocity, so a rocket burn and aero-braking were required to slow down and keep from flying right past Earth and into deep space again.

Which brings up my final point about escape velocity. The weirdest thing about escape velocity is that it works in any direction, up, down, or sideways, so long as you don’t crash into the planet. That is, if you had a tunnel through the Earth with no air in it, you could launch a rocket directly downward into the tunnel at escape velocity and it would be just as effective as launching it straight up.

The Lagrange points bring balance to the cosmos

I’ve written about the Lagrange points before, but they are so great I couldn’t resist repeating it here.

So far we have only talked about orbits in the simplest possible two-body scenario, in which the body in orbit is so minuscule compared to the primary body — like a planet and a spacecraft — that the effects of the smaller body’s gravity field on the primary are negligible.

Another interesting configuration is the restricted three-body problem, which expands on the above by adding a second massive body which interacts with both the primary and the minuscule object — like a star, a planet, and a spacecraft. In general, any system of orbiting bodies has a set of Lagrange points, and a restricted three-body system has five such points labeled L1 through L5.


The five Lagrange points of the Earth-Sun system. Not to scale.

Using the Earth-Sun system as an example, think of our Lagrange points as balancing points where the Sun’s and Earth’s gravitational pulls combine to provide precisely the required centripetal force for a circular orbit about the Sun which passes through that point. An object placed there will not fall toward the Earth or Sun, nor will it pass ahead or behind the Earth. Its orbital angular speed around the sun will match the Earth’s even though it’s at a different orbital altitude from the sun, and it will seem to be suspended in place relative to the Sun and Earth.

The L1 point is the equilibrium point that lies about one million miles on a direct line from the Earth toward the Sun. From the Earth’s perspective, an object at L1 always remains directly in front of the Sun. L1 is a useful place to put a Sun-observing spacecraft because it will have an unobstructed view of the Sun, or an Earth-observing spacecraft because it will always see the fully illuminated daylight side of the Earth.

The L2 point is another useful place for spacecraft because it is in perpetual midnight, so light from the Sun and Earthshine never enters the field of view and it provides a dark place from which to observe the sky. 


A representation of the asteroid belt (white) and the Trojan asteroids of Jupiter (green). The latter are congregated around the gravitational equilibrium points called L4 and L5 of the Jupiter-Sun system.

The L4 and L5 points are historically interesting. They are 60° ahead and behind a planet in its orbit, forming two equilateral triangles. In 1772 Pierre Lagrange was analyzing the restricted three-body problem, probably with a quill and paper, and upon calculating the combined gravitational field, he hypothesized that asteroids should have accumulated over time at equilibrium points we now call L4 and L5 of the Sun-Jupiter system (because Jupiter has by far the strongest gravity field after the Sun). But no telescopes were powerful enough at the time to see them. Finally in 1906, astronomers spotted the first of Jupiter’s “Trojan asteroids“, shown in green in the figure at right. I am not aware of a scientific experiment that had a longer time gap between hypothesis and observation.

Here’s an animation that removes the “normal” white asteroids from the image and shows only the interesting asteroid motions involving the Jupiter-Sun Lagrange points. (The magenta asteroids are another interesting class called the Hildas.)


Bonus Topic: Reentering spacecraft don’t heat up because of friction

Now to bring things back down to Earth. You often hear about fast traveling objects heating up “due to friction” with the air. In fact, the heat is generated not primarily by friction but by the process of compressing the air in front of the craft. If you’ve ever emptied a can of pressurized air to clean your computer, you probably noticed how cold the can gets when the pressure drops. The opposite effect also applies. If you could jam a bunch of air back into the can, it would get very warm. Take this to the extreme.


Shadowgraph images of various re-entry vehicles at supersonic speeds in a wind tunnel. The shockwaves and other air density variations cast shadows which are captured by the camera.

When an object travels at supersonic or hypersonic speed, it travels faster than the air molecules can get out of its way (in a sense). This results in a sort of “pile-up” of air molecules on the front of the craft, in which the energy of motion of the craft is transferred to the air molecules as it collides with them. This creates a zone of very high air pressure and usually one or more shock waves on the front side of the craft. A shock wave can be thought of as the leading front of an air molecule pile-up. The temperature, pressure, and density of the air just behind a shockwave are many multiples higher than the air just a few millimeters away on the other side of the shock wave. Imagine a runaway train barreling down the tracks and piling up other train cars and debris on its front bumper. Just a few car lengths ahead of the train everything is normal, but then suddenly it’s just a compressed pile of hot steel. 

The kinetic energy of the spacecraft’s motion is transferred to the air molecules through the compression process, converting it into thermal energy and heating up the air. The compressed air is very hot and it transfers this thermal energy back to the skin of the spacecraft through direct contact with the outer surfaces. So there is actually a two-way exchange of energy that heats up the spacecraft.

I hope you find this informative and interesting. Post any questions in the comments and I’ll do my best to answer them.  There are no dumb questions!

The Global Positioning System Is Just a Bunch of Fancy Clocks

Artist's rendition of a GPS III-A satellite (US Air Force)

Artist’s rendition of a GPS III-A satellite (U.S. Air Force)

The Global Positioning System provides a simple and invaluable service to any Earthling who chooses to access it. It solves an ancient problem with ultramodern technology, answering a challenge that spelled doom for so many of our ancestors. With some irony it answers the profoundly local and timeless question — “Where am I?” — using atomically synchronized radio transmitters orbiting thousands of miles up in space.

The knowledge of one’s precise location is now so mundane it almost seems strange to ask the question. It’s a problem we no longer think about, taking for granted that knowing where we are is just a matter of looking down at our smartphones. But how does a smartphone know where it is? Some people would be happy with “by using satellites and computers.” I find it hard to phrase the question in such a way that inspires curiosity. But it is actually an interesting and challenging technical problem with an impressive solution.

First I’ll mention a few things GPS does not do. It doesn’t know any addresses, plan routes, or give turn-by-turn directions. And it doesn’t track anybody. Those are all add-on systems that take advantage of GPS positioning technology, an explanation of which follows.

The United States Air Force operates the NAVSTAR Global Positioning System (as it’s officially called), providing a completely free-of-charge, continuous, worldwide, highly accurate position, velocity, and time (PVT) service, simultaneously to any user with a receiver. They even provide something of a user’s manual for GPS developers. It’s light reading at only 226 pages of orbital mechanics, relativity, radio frequency equations, and encoding keys.

It was developed as a military system starting in the 1970s and ’80s, becoming fully operational in the ’90s. A person involved in the original development once told me that when they forecast all the ships, airplanes, tanks, helicopters, and soldiers who would use the system, they estimated there would be a maximum of 40,000 users worldwide. Now there are tens of millions of new civilian GPS receivers manufactured every month and billions of users. While it is a government-developed infrastructure so to speak, this is a testament to the power of the free civilian market to find new, productive, and unimagined ways to exploit resources.

A modern, fully functional GPS receiver. (Photo credit: AIN Online)

A modern, fully functional GPS receiver. (Photo credit: AIN Online)

Two soldiers test early models of GPS manpack receivers in 1978. (U.S. Air Force)

The GPS constellation contains about 32 satellites carrying synchronized atomic clocks and radio transmitters. They are distributed around the world in six sets of nearly circular 12-hour orbits at 20,000 km altitude, a little more than half the altitude of geostationary satellites. The satellites travel in their orbits at almost 4 km/s and their paths are angled 55 degrees to the equator. A user anywhere on the globe has a clear view of about 6 to 12 satellites in the sky at any time.


A visualization of a 24 satellite GPS constellation showing which satellites are visible (red) to a user in Colorado. Credit: By Paulsava – Own work, CC BY-SA 4.0,

Given the thousands of different uses for GPS in commerce, agriculture, transportation, surveying, and scientific research, many people wonder: how do the satellites know where you are, and how can they handle tracking billions of worldwide users?

The answer is they don’t, and they don’t need to.

The GPS satellites are broadcast-only, receiving no data from the users and performing no position calculations onboard. The satellites never know where you are or even that you exist. All position calculations are performed by the receivers, so the number of users is unlimited just like FM radio. The only way somebody can track you using GPS is if your receiver actively rebroadcasts your position.

The data messages broadcast by the satellites contain a lot of detailed information about their operational status and orbital parameters. But this data is also available for free on the internet, which is how most smartphones get it nowadays. So really the only unique information the satellites are broadcasting is the time. Each satellite broadcasts a precise timing signal at precise intervals interspersed with its data messages. All GPS satellites broadcast these timing signals simultaneously using atomic clocks onboard which are maintained in very tight synchronicity by the ground controllers.

When a GPS receiver receives the regularly scheduled timing signal from each satellite, it records the time of receipt based on its own internal clock and subtracts the time it was sent to find the signal travel time. It multiplies the travel time by the speed of light (and compensates for a few second-order effects like relativity and ionospheric refraction) to find its range from each satellite. Then it uses the orbital parameters to calculate the satellite’s position at the precise time that it sent the signal.

Now, knowing where the satellites were and having a range measurement to each, it’s simple for the receiver to calculate the its position using a process called trilateration (not to be confused with triangulation, which uses angle measurements). In simple terms, it is finding the intersection of multiple spheres. Each measurement tells you that you are somewhere on the surface of a sphere centered on one of the satellites. Let’s call these range spheres. You are therefore located at the intersection of the the range spheres.GPS-3D-trilateration

Intuitively it seems like three satellite range measurements are all you need to calculate your position in three dimensions. But three’s not enough. There is an inherent, common uncertainty in the range measurements, and therefore the sizes of all the spheres. This is because the receipt time provided by the internal clock of your GPS receiver is not accurate. Remember, receipt time is used to calculate the range to each satellite. For a signal traveling at the speed of light, every nanosecond of offset in the receipt time due to receiver clock error is a foot of range error. A millisecond of receiver clock error is a million feet of error in the size of all the spheres! If you only use three satellites, there is no way to get an accurate position calculation with a reasonably affordable clock.

Adding a fourth satellite locks in the receiver clock error. There is only one unique value of receiver time that gives compatible sizes of all four range spheres to place you at a single point of intersection. By using four range measurements, the receiver simultaneously fixes its own clock error and determines your position accurately.

With the full NAVSTAR constellation now operational it’s rarely a problem to find four or more satellites. More than four satellites usually gives a more accurate position by allowing the receiver to partially account for other more subtle errors in the range measurements like the effects humidity in the lower atmosphere.

We have only scratched the surface of GPS here. There is so much that could be written about the brilliant signal encoding that allows all the satellites to broadcast on the same frequency simultaneously, the magic of pulling a very faint signal out of a cacophony of background noise, and the other signals and techniques that can be used to greatly increase the accuracy. Every time I sit and think about it, I am in awe of the system and how it works so intricately and precisely. Calling it “just a bunch of fancy clocks” is not a sleight, but a testament to its elegance. I would not be alone in saying GPS is one of mankind’s greatest technological achievements, right on par with the Apollo moon landings.

How to Improve the NFL’s Goofy Point-After-Touchdown


The 25-yard point-after-touchdown kick is a bad rule change. It introduces uncertainty, but at the cost of reduced heroics, which is the lifeblood of any spectator sport, and greater disappointment and heartbreak, which only sells tickets in certain unusual markets.

danmowrey_display_imageOne of the most exciting, dramatic, and satisfying aspects of football is the fourth-quarter comeback. The trailing team gets the ball deep in their own territory with the clock breathing down their necks. But they hit a couple of key passes, step out of bounds at the right times, and make efficient use of their timeouts. As the seconds wind down, they put the ball in the end zone for the game-tying touchdown!

akersbad…except the game’s not tied, they just lost in the most anti-climactic way, a missed PAT from 25 yards out. A PAT missed by a professional placekicker, whose only job is to kick the ball off the ground and through uprights. He’s the most specialized player on a team of hyperspecialists. Even the punter usually has a second job, to hold the ball for the placekicker.

A miss from that distance is uncommon enough that it’s considered an automatic make. Then the gut-wrenching critical miss happens. It’s an awful way to lose; no colossal hit forcing a fumble, a leaping interception, or herculean fourth down defensive stand that puts a decisive end to the game. It’s a kick that drifts wide of the goalposts because, in the strangest formation in the game, one guy sets the ball on the ground so another guy can kick it and the laces were turned the wrong way.

67854379_186deab7f5Winning on a missed PAT is even worse than winning on a missed field goal. It leaves the trailing team stunned, forced to hide their frustration and console the hapless placekicker, and the winning team with a victory they didn’t quite earn. It’s bizarre to watch players jump and cheer and high-five each other after winning on a missed placekick. Their defense failed to hold, allowing the other team to move down the field into kick range or score a touchdown — they just got lucky that the other team failed in execution. Nine times out of 10 the missed kick had nothing to do with the special teams coverage, but an error by the kicker, holder, or long snapper.

imagesThe 25-yard PAT is bad for the game because it reduces heroics by negating a higher number of potentially game-tying touchdowns, while concomitantly creating more goats. And what’s the upside? More unusual scores like 22-16? More two-score games that remain two-score games after a missed PAT?

If the goal is to make the PAT less of a sure thing, but avoid neutering tying-touchdown heroes and increasing the placekicker’s already high goat potential, I propose the following: The PAT should not be kicked from the 15, but rather from the 2, but it has to be kicked by the player who scored the touchdown.

This way, hotshot players who score a touchdown still have an incentive to focus on the next play. They won’t be able to do a ridiculous dance and strut off the field, leaving the finishing work to the lowly placekicker. They’ll have to develop a secondary skill and finish the job themselves.

In baseball, there are players who can field but not hit, and players who can hit but not field. Players who can do both well are at a premium. Imagine how the market for football players will change when some players’ touchdowns are worth more, on average, than others’ because of their secondary kicking skills.

“The Martian” Is Thrilling, Surprisingly Funny, and Scientifically Accurate


The_Martian_film_posterThe Martian features Matt Damon as NASA astronaut Mark Watney, who with a six-member crew including commanding officer Jessica Chastain, is on a month-long science mission on the beautifully desolate surface of Mars. Of course, one month is only the planned duration of their stay on the surface; the deep space transit to and from Mars takes several hundred days each way, which becomes important later in the film.

We enter the story partway into the surface mission. The crew is collecting Martian soil samples when NASA sends them an urgent message about an impending storm. The storm is apparently so severe that the rocket which is supposed to lift the crew back into space at the end of their mission won’t survive the harsh winds on the ground. So the crew is forced to abort their surface mission and perform a hasty emergency launch. In the rush and confusion, Watney is left behind, presumed dead. All of this introductory material is completed in a very breezy few minutes, plunging us right into the survival story.

Damon is charming, self-deprecating, full of creativity, and despite the all the rational reasons to believe himself doomed, he remains confident in his training and problem-solving abilities. He shows well-earned pride of accomplishment and just the kind of cockiness you’d expect from a flyboy as he conquers the litany of challenges thrown at him by the deserted red planet, including lack of breathing air, food shortages, transportation, weather, and communication. However, the film seems to gloss over his coming-to-grips with his extremely perilous situation. Instead, it jumps ahead several weeks, thereby depriving us of the opportunity to watch Damon experience the full range of emotions you’d expect from a marooned spaceman, including grief, denial, anger, resentment, loneliness, despair, and hopelessness — especially in light of the events that stranded him there. We see a lot of footage of Damon entertaining himself by making smart remarks into a camera, and he is often hilarious. But there is little sense that he feels alone or lonely at all (in contrast with, say, Sam Rockwell’s performance in Moon), which reduces the euphoria we should feel when he finally re-establishes communication with NASA. Perhaps it is this unworldly optimism that helped keep him alive.

The Martian has a lot in common with Apollo 13, the film that set the standard in the genre. The story alternates between scenes of the stranded Damon, the rest of his crew in long transit back to Earth, the NASA leadership (featuring a strong tension between the political appointee Jeff Daniels and the canny flight director Sean Bean, with some comic relief from PR head Kristen Wiig), and the crack teams of mostly faceless Jet Propulsion Lab engineers on the ground, pulling out all the stops to keep their man alive and put together a rescue plan, while sending up improvised plans and instructions to Watney so he can stretch his equipment far beyond its design limits.

I wish we could see more of Bean with his more sentimental approach to the problem, and his personal concern for the crew’s autonomy and right to be informed. After a while, Daniels’ executive style of snap decision-making seems just a way to move the plot forward.

Benedict Wong plays the JPL lead engineer, quite effectively portraying the burden every leader feels as he commits his team to meet the unrealistically short production schedule without compromising technical performance of a resupply craft — this time with an elevated purpose, because Watney’s life is on the line. He gives the sense that he is honored to accept the challenge before him, making him one of my favorite characters.

In contrast with Apollo 13, the focus is almost exclusively on the aforementioned people who are working the problem, and we see only a few short glimpses of anyone’s families. This doesn’t detract from the character development or the audience’s attachment to them, though, because there are several endearing scenes portraying the crew-as-family. Michael Peña in particular has a youthful optimism that somehow induces you to cheer for him as an underdog despite his being an extremely skilled astronaut and spacecraft pilot. And in fact, the “family of the crew” is used as part of a very satisfying plot twist.

There are two particularly relatable and inspiring characters. Mackenzie Davis portrays Mindy Park, a young female engineer whose job is to analyze Martian surface imagery for the planning of future missions. After making a discovery that confounds her superiors, she doesn’t let their alpha-male personalities steamroll her. She overcomes their skepticism by walking them through her data, after which she earns their respect and becomes an important member of the recovery team.

The second is the scatterbrained young aerospace engineer Rich Purnell, played by Donald Glover. True to the stereotype, he has below-average communication skills and easily gets lost in his work. He has a bolt of inspiration and works out, all on his own, an unorthodox plan to execute a rescue mission that just might fit within their ever-shrinking window of opportunity. Oblivious to protocol or rank, he barges into the office of a higher-up whom he’s never met, demands that he hang up the phone, and explains his plan. Then he stages a goofy and highly entertaining demonstration in a conference room, using Daniels and Wiig as human props to illustrate his proposed orbital maneuvers with a flying stapler. Purnell later receives a high compliment that will put a smile on the face of anyone familiar with the (link contains minor spoiler) hotshot jargon of the Apollo era.

From start to finish, the science and engineering of the movie is of a very high quality. It has just the right balance of technical jargon and explanatory dialogue, so it’s neither inaccessible nor tedious. The crew convincingly discusses astronautical concepts like orbital rendezvous, gravity assist, and delta-V, while Damon demonstrates some impressive agronomy, inorganic chemistry, and electro-mechanical know-how down on the surface. There were a few times when my engineer’s ears perked up upon hearing a quantity expressed in the wrong units, for example, but it wasn’t enough to ruin my typically fragile suspension of disbelief.

In terms of the plot, it’s a straightforward survival-and-rescue movie, although heavy on engineering rather than backwoods techniques, with only a few unexpected twists and turns. The launch sequences and space rendezvous scenes are gripping and sometimes breathtaking.  One of the twists, in my opinion, is poorly executed because it’s too telegraphed, but you can be the judge.

The space scenes seem to have used true zero-gravity filming techniques such as the Vomit Comet, with nifty transitions to 1-g as the astronauts “descend” the ladders out to the rim of the spinning section of their interplanetary craft.  At the very beginning of the movie there seems to have been an effort to portray the lower Martian gravity (1/3 of Earth’s) in the way Damon walks in his spacesuit, but after a while you stop noticing, or they stopped trying to portray it. Either way it’s just a nit.

The Martian runs a fast 141 minutes, with no lulls or slow sequences that I can remember. It’s a fantastic aerospace showcase that couldn’t have had better timing with its release to theaters, given real-world events.

Update: See also anonymous’s review of the original book from last year.

The Dark Side Is Weak With This One


NASA’s Deep Space Climate Observatory (DSCOVR) has captured a series of unusual images showing the astronomical phenomenon known as the transit of the Moon across the Earth. They are unusual because out of the handful spacecraft are beyond the orbit of the Moon, very few are close enough to perceive the Earth and Moon as larger than a speck. The video below is not a computer simulation; it is a series of actual photographs taken on July 16, 2015.

As the Moon passes in front of the Earth, the visible portion of the Moon is what we Earthlings refer to as the far side, not the “dark side” as reported in many news outlets. Since the Moon is tidally locked with the Earth — meaning it rotates at exactly the same angular rate that it orbits — it always presents us the same face. In other words, the Moon has a permanent far side that cannot be seen from Earth. The far side has an entire set of craters and other surface features that were completely unfamiliar to us until the Space Age.

But, as any child can observe, the portion of the Moon that is illuminated by the sun goes through phases, meaning that different parts of the Moon are illuminated at different times. So the “dark side” is not a fixed feature but rather a cyclical phenomenon exactly like night and day on Earth.  The far side of the Moon sees just as much sunlight as the near side, only on the opposite schedule. lagrangepoints

DSCOVR is positioned at a unique point in space called the Sun-Earth L1 Lagrange Point, or L1 for short.  In general, any system of orbiting bodies has a set of Lagrange points, and a two-body system has five such points.  Think of our Lagrange points as the balancing points between the Sun’s and Earth’s gravitational pulls and the orbital centrifugal force.  An object placed there will not fall toward the Earth or Sun, nor will it pass ahead or behind.  Its orbital angular speed will match the Earth’s, and it will seem to be suspended in place relative to the sun and Earth.

The L1 point is the equilibrium point that lies about one million miles on a direct line from the Earth toward the Sun. From the Earth’s perspective, an object at L1 always remains directly in front of the sun.  If the Moon passes between the Earth and L1, the far side of the Moon is visible from the L1-orbiting spacecraft, fully and brightly illuminated by the sun. It’s disheartening the way so many news outlets are reporting this exactly wrong. Viewed from L1 the Moon is full, so the only part of the Moon not visible in the images is the dark side, which, incidentally, is coterminous the Moon’s near side at that time.

Now, since you are a Ricochet member — and I know you love to do so — you can go around correcting people for the rest of the day.

America Facts


shutterstock_131461559Here are some facts about this great nation:

  • Longest continuous string of US Presidents born here
  • Most Star Wars movies produced of any country
  • Tied for most Space Shuttles invented
  • Longer Canadian border than any other country
  • Largest Hawaiian Island of any country
  • 238 consecutive years of being the USA, the longest active streak
  • Highest quality of Chuck Norris facts produced by any country

If you know any other facts, write them in the comments.

Missile Defense: Fourth Time’s the Charm (Updated With Video)


A GMD interceptor launching from its siloUpdate: See comments 18 and 19 for video. After failing in three consecutive flight tests (two in 2010 and one in 2013), the Ground-based Midcourse Defense system finally intercepted a mock nuclear warhead launched on an IRBM from the Marshall Islands in a test flight designated FTG-06b. 

For this exercise, a threat-representative, intermediate-range ballistic missile target was launched from the Reagan Test Site. The U.S. Navy destroyer USS Hopper (DDG 70), with its Aegis Weapon System, detected and tracked the target using its onboard AN/SPY-1 radar, which provided data to the GMD fire control system via the Command, Control, Battle Management and Communication (C2BMC) system. The Sea-Based X-Band radar also tracked the target, and relayed information to the GMD fire control system to assist in the target engagement and collect test data. About six minutes after target launch, the Ground-Based Interceptor was launched from Vandenberg Air Force Base. A three-stage booster rocket system propelled the interceptor’s Capability Enhancement II EKV into the target missile’s projected trajectory in space. The kill vehicle maneuvered to the target, performed discrimination, and intercepted the threat warhead with “hit to kill” technology, using only the force of the direct collision between the interceptor and the target to destroy the target warhead. This was the first intercept using the second- generation Exoatmospheric Kill Vehicle.

The system was thwarted in previous tests by a series of technical problems, which critics quite credibly argue are the result of a too-hasty deployment by the Bush Administration. Both sides like to lump all four missile defense weapon systems together (GMD, Aegis, THAAD, Patriot) and argue in generalities — somewhat understandably, because many of the details required to form specific arguments are classified. Critics use GMD’s failures to criticize the entire project, while supporters cite the aggregate test record (65 out of 81), which is buoyed by the success of the other elements, to divert attention from GMD’s spotty record (9 out of 17, including 1 out of the last 4). But as President Obama loves to remind us, this is not a political football. Americans all over the political landscape should be glad that we are making progress toward the goal of creating a defensive shield against the most terrible weapons ever devised.

Pacific Ocean map showing test areaIn case you haven’t glanced at a map of the Pacific Ocean recently, the approximate area involved in this test, stretching from the Reagan Test Site in the Marshall Islands to Vandenberg Air Force Base on the California coast, is enormous. The tests require these vast test ranges in order to create realistic trajectories for the incoming targets, with threat-representative flight times and closing velocities. It also gives the system the opportunity to practice data handover between systems that detect enemy launches over the horizon and provide a targeting solution to the home defenders. These tests are expensive in large part because of the geographic challenges. But the speeds and distances involved will only go up from here as the system takes on more challenging scenarios.

(One other cool fact. The target IRBM was launched from the Marshall Islands on the other side of the International Date Line, 19 hours ahead of Pacific Daylight Time, on Monday morning, June 23rd.  The interceptor was launched in California on Sunday afternoon, June 22nd, and successfully destroyed the target a few minutes later on  Sunday. We can intercept threats from the future.)

Mark Wilson

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