Why Do We Have Nightmares?

It’s evening, and my wife and I are tucking my son into bed. As he snuggles down into his pile of stuffed animals – he has a bunch, and all of them share his bed with him – he looks up at us. “why do we have nightmares?”

“Because your brain’s active,” my wife tells him, kissing him goodnight.

“Well, they shouldn’t give us nightmares!” he declares.

Can’t argue with that.

Nope, not really. I mean, I don’t remember my dreams with any frequency. Heck, I’m not positive I do dream most nights, although I have a vague recollection of learning that people go crazy if they don’t. But the nightmares stay with me. Even the ridiculous one where zombies flooded my condo, but they couldn’t find me because I’d climbed up on the back of my couch. Which, now that I think about it, wasn’t a nightmare precisely. I woke up more bemused than anything.

Why do we dream?

I’ve always thought that, if you described it to an alien, “sleeping” and “dreaming” would be two of the most ridiculous things you could possibly imagine. I mean, we spend about a third of our lives immobile and paralyzed, unaware of our surroundings, and hallucinating. It sounds like utter madness. And yet, we do it. Why?

Back in February 2015, Psychology Today said that “dreaming is:

  • A component and form of memory processing, aiding in the consolidation of learning and short-term memory to long-term memory storage.
  • An extension of waking consciousness, reflecting the experiences of waking life.
  • A means by which the mind works through difficult, complicated, unsettling thoughts, emotions, and experiences, to achieve psychological and emotional balance.
  • The brain responding to biochemical changes and electrical impulses that occur during sleep.
  • A form of consciousness that unites past, present and future in processing information from the first two, and preparing for the third.
  • A protective act by the brain to prepare itself to face threats, dangers and challenges.

Which of these theories is correct? Well, the answer right now seems to be “most, if not all, of them”. Our brains are complicated things, after all, and we don’t understand how and why they work anywhere as well as we’d like. As the article says, “There is not likely ever to be a simple answer, or a single theory that explains the full role of dreaming to human life. Biological, cognitive, psychological—it’s very likely that dreaming may serve important functions in each of these realms.”

So, why do we have nightmares?

It’s complicated.

All right, all right, I’ll see what I can find.

To start with, there’s The threat simulation theory of the evolutionary function of dreaming: Evidence from dreams of traumatized children, a sadly paywalled article that looks like it might give one possible explanation. Here’s what the abstract says:

The threat simulation theory of dreaming (TST) () states that dream consciousness is essentially an ancient biological defence mechanism, evolutionarily selected for its capacity to repeatedly simulate threatening events. Threat simulation during dreaming rehearses the cognitive mechanisms required for efficient threat perception and threat avoidance, leading to increased probability of reproductive success during human evolution. One hypothesis drawn from TST is that real threatening events encountered by the individual during wakefulness should lead to an increased activation of the system, a threat simulation response, and therefore, to an increased frequency and severity of threatening events in dreams. Consequently, children who live in an environment in which their physical and psychological well-being is constantly threatened should have a highly activated dream production and threat simulation system, whereas children living in a safe environment that is relatively free of such threat cues should have a weakly activated system. We tested this hypothesis by analysing the content of dream reports from severely traumatized and less traumatized Kurdish children and ordinary, non-traumatized Finnish children. Our results give support for most of the predictions drawn from TST. The severely traumatized children reported a significantly greater number of dreams and their dreams included a higher number of threatening dream events. The dream threats of traumatized children were also more severe in nature than the threats of less traumatized or non-traumatized children.

Now, I’m not a psychologist or a neuroscientist, but “threatening dream event” sounds like a technical term for “nightmare”. So, speculating entirely from the abstract and wishing I could read (and try to make sense of) the article, it seems entirely reasonable that nightmares are – among other things – a threat response rehearsal. And I’d be curious to know if the “threatening dream events” of the traumatized children strongly related to the events that caused the trauma.

Both Psychology Today and LiveScience seem to agree, at least in broad strokes. “Most nightmares are a normal reaction to stress, and some clinicians believe they help people work through traumatic events,” reports Psychology Today, while LiveScience quotes Doctor Deirdre Barrett as saying that “Nightmares probably evolved to help make us anxious about potential dangers. Even post-traumatic nightmares, which just re-traumatize us, may have been useful in ancestral times when a wild animal that had attacked you, or a rival tribe that had invaded might well be likely to come back.”

So why am I dreaming about zombies?

Clearly, zombies aren’t a genuine potential danger, no matter how scary George Romero made them seem. Doctor Barrett, however, gave us some more information to consider: “However, some nightmares may be calling to your attention something you might do well to worry about or something that, once you are more conscious of the concern, you can convince your unconscious to stop wasting time on.”

So, I’m going to speculate here. Clearly, zombies aren’t real. Heck, for most of us, being eaten by a lion isn’t a real threat either. But your brain isn’t going to to generate a block of text in your dreams, telling you to be concerned about your spending habits and the amount of debt you’re carrying. No, it’s going to respond to your current stress in the office by trying to stage a dry run threat response drill. By making you practice running from popsicle-men wielding pinking shears for three virtual days. Because, your brain assumes, you’re obviously needing to run from something.

Do we go crazy if we don’t dream?

Well, the (fictional) Russian Sleep Experiment notwithstanding, the answer is pretty much “no”. At least, according to Harvard University. Mostly, when you don’t sleep, you get tired. Obvious, right? Well, that lack of sleep causes you to make poor decisions. Increased accidents are common, as are lack of focus and higher-level cognitive functioning – that’s concentration, memory, and the ability to do math and even reason logically.

But that’s sleeping. What about dreaming? Well, according to the Encyclopedia Britannica online, animal experimentation has revealed heightened levels of sexuality and aggressiveness after REM-sleep deprivation. Beyond that, there isn’t a whole lot of impact. In fact, there appears to be some value to REM sleep deprivation as a treatment for depression. So, no. You won’t go crazy. Just horny and aggressive and too tired to act on it.

Advertisements

Why Don’t We All Get A Balloon, And Then We Can Fly Into The Sky?

A couple of weeks ago, I was at a birthday party for one of my son’s friends. It was a great day, at a little park a half hour drive north and east of where I live, situated on a tributary of the Ohio River. The kids all had squirt guns and the like, and got each other soaked down while the adults sat back and watched and took pictures and were grateful that they brought extra clothes and towels. There were balloons as well, because there were kids.

One child was super excited about the balloons. They were your ordinary latex kind, that you blow up with your own lungs, but he was bouncing them around and laughing. “Why don’t we all get a balloon?” he asked excitedly. “And then we can fly into the sky!”

So, yeah. It wasn’t my son that asked it. But it’s the kind of question he could have asked, so I’ll answer it.

How does a balloon float?

The same way a boat does.

Care to elaborate?

Of course.

It’s tempting to say that things float because they’re light, but that’s not quite accurate. For example, an oil tanker floats but it is not light – they can carry anywhere from 1,500 to 550,000 deadweight tons, depending on size. No. Floating has everything to do with the mass of the object, and the fluid that surrounds it. See, all objects placed into a fluid displace some of the fluid (put a rock in a cup of water to see for yourself). If the mass of the fluid you displace is greater than your mass, you float. And air, for these purposes, can be considered a fluid.

But let’s look at some math, since the University of Chicago was kind enough to put together a document (Lighter Than Air: Why Do Balloons Float?) that explains all of this in some detail. There are two forces in play, the downward force (which is the pull of gravity) and the upward force (which is how much the fluid resists the downward force). The downward force (Fg) is the mass of the object (M) x gravitational strength (g), which is also how you calculate “weight” in physics. Weight, after all, is mass times gravity (which is why you weigh less on the moon, even though you retain the same mass). Upward force (Fb) is the mass of the fluid displaced (m) x gravitational strength (g).

Once you have Fg and Fb, you can calculate life=t. All that is is Fb – Fg. If the result is positive (meaning Fb is larger than Fg), you are sinking. If the result is negative (meaning Fb is larger than Fg), you are rising. And if the result is 0 (meaning the two forces are equal), you are floating immobile in midfluid.

Uhm. Okay.

Let’s do an actual example, shall we?

Yeah. Lets.

After consulting Google, I found an estimate that the average-sized party balloon masses 1.7 grams, and several notes that they can weigh more depending on the actual size, thickness, etc, etc. This will be important, momentarily.

Now, the density of air at sea level is about 0.0012 grams per cubic centimeter. So, if you inflate your hypothetical average-sized party balloon to a diameter of 1 foot (0.3048 meters, which means 30.48 centimeters), you get a sphere (for the sake of not making me crazy) containing 14,826.7 cubic centimeters of air. The inflated balloon weighs a total of (14,826.7 x 0.0012) + 1.7 = roughly 19.5 grams, and displaces 17.8 grams of air. So, it sinks. If you inflate the balloon to 2 feet in diameter (60.96 centimeters), you get a balloon containing 116,613 cubic centimeters of air. It weighs 141.6 grams, and displaces 139.9 grams of air.

Clearly, both balloons sink. And, in a vacuum, both would sink at the same rate because they have the same lift (-1.7).

But they don’t fall at the same speed. Not the ones I’ve played with, anyway.

Nope. Because we live in an atmosphere. And atmospheres create air resistance. I won’t go into the math there, because it made my head hurt a little, but it works like this: an object produces drag (a resistance to acceleration) based on the cross-section of the object perpendicular to the direction of movement. As the cross-section gets larger, the power needed to overcome the drag increases. How much? Well, it’s based on the cube of the cross-section. If you double it, you need 8 times as much power. If you triple it, you need 27 times as much power. And so on.

For the balloon, acceleration is down towards the ground and the cross-section is the diameter of the balloon. Doubling the diameter of the balloon means you would need 8 times the power to make it fall at the same speed as the smaller balloon. Since gravity (roughly) stays the same, that means you would expect to see it fall 8 times as slowly.

So, getting back to the wish to “fly into the sky”…

Sure. See, to make a balloon fly, you need something less dense than room-temperature air. That’s why hydrogen and helium are so popular. They’re gaseous at “room temperature”, and they weigh far, far less. Hydrogen weighs 0.000089 grams per cubic centimeter, and helium weighs 0.00018 grams per cubic centimeter. So, looking at the two balloons from the earlier example, we get the following information:

  • The 1 foot balloon weighs 3 grams if you fill it with hydrogen, and 4.4 grams if you fill it with helium. It displaces 17.8 grams of air.
  • The 2 foot balloon weighs 12 grams if you fill it with hydrogen, and 23 grams if you fill it with helium. It displaces 139.9 grams of air.

Regardless of which gas you fill the balloon with, it weighs less than the gas it displaces. So it has positive lift and it goes up. In fact, it could even lift additional weight – the 2 foot balloon filled with hydrogen would have neutral buoyancy with a 127.9 gram weight attached to it, so you could attach two Hershey’s chocolate bars (1.55 oz, or 44 grams each) to the balloon and still watch it go skyward.

Heating the air will also work, as gasses become less dense with heat. Sadly, I don’t have a good equation (that I understand) to show how much you’d have to heat the air to make it lift.

How many balloons would I need to fly to the sky, then?

Well, that’s more or less easy. How much do you weigh, and what gas are you using? I’ll illustrate with my son. He weighs around 60 pounds right now. That’s 27.2155 kilograms, or 27,215.5 grams. Looking at the two foot balloons, the lift for the hydrogen balloon is 127.9 grams per balloon and the lift for the helium balloon is 116.9 grams. So, it would take 27,215.5/127.9 = 213 2 foot hydrogen balloons to give him neutral buoyancy. 233 2 foot helium balloons would be required to achieve the same effect. You’d need another 18 hydrogen (20 helium) balloons to offset the weight of his clothes (maybe more if he’s planning on flying high). And I have no idea how many balloons would be required to offset the weight of the lines he’s holding on to or the harnesses to keep the balloons attached to him. And, of course, he’d need more to actually go up.

By contrast, I weight 316 pounds. So I’d need 1,121 hydrogen balloons or 1,227 helium balloons to achieve the same effect. That’s 37,553.5 cubic feet of hydrogen balloons, or a sphere roughly 42 feet in diameter. Oh, and it could explode.

Don’t do this at home.

No kidding.

You’d think so, but at least one person did.  Larry Waters used 45 8-foot weather balloons filled with helium to lift himself, his lawn chair, his parachute, his pellet gun (so he could pop balloons and descend), his CB radio, his camera, and sandwiches and beer to a height of 16,000 feet.  He flew for 45 minutes, and got fined $1,500 by the FAA after an appeal.  But, because he was a trained pilot and lucky, he didn’t die.

What Are Cataracts?

This question came up because my son’s babysitter is fostering a blind dog – an adorable little black poodle with milky white eyes named Rosie.

Seriously. How cute is that?

My son and his babysitter’s two children love her and spoil her and carry her around, and they describe her as having “moon eyes” because they sort of look like full moons. The Peppermint Pig Animal Rescue was going to get her eyes operated on to remove the cataracts, but it turns out she also has detached retinas. So the surgery wouldn’t really change anything for her.

We were talking about the dog, and the news, and my son asked “what are cataracts?” Because we’d used the word and he didn’t know it.

“It’s what makes Rosie’s eyes white,” my wife replied.

“But what are they?” he replied.

“It’s…” My wife thought for a second. ‘It’s like a film on her eyes, that she can’t see through.”

“But why are they called that?” my son persisted.

So. What are cataracts?

This. This is a cataract.

I’ll be honest, here. I don’t actually know. My wife’s explanation seemed as good as any, and I think I always sort of assumed that they were something like scar tissue. But, like with so many other things, I’ve never really stopped to ask what they were or what causes them. So, since my son asked, it’s time to change that.

Definition

Merriam-Webster, my go to for dictionaries thanks to a handy app, gives two definitions for “cataract“:

  1. [Middle English, from Medieval French or Medieval Latin; Medieval French catharacte, from Medieval Latin cataracta, from Latin, portcullis] : a clouding of the lens of the eye or of its surrounding transparent membrane that obstructs the passage of light
  2. a obsolete : waterspout
    b : waterfall; especially : a large one over a precipice
    c : steep rapids in a river the cataracts of the Nile
    d : downpour, flood cataracts of rain cataracts of information

I’m guessing that the medical term is used explicitly because of the “portcullis” meaning in Latin, since cataracts more or less block light from entering the eye. The Online Etymology Dictionary seems to agree, so that makes me feel better.

The medical condition

Multiple online sources (the Mayo Clinic and the American Academy of Ophthalmology to name just two) agree with the Merriam-Webster definition. Cataracts are a clouding of the lens of the eye. This can result in blurry vision, seeing double, light sensitivity, having trouble seeing well at night, needing more light when reading, seeing “halos” around lights, and seeing bright colors as faded or yellowed. They are the most common form of vision loss in people over the age of 40, and the single most common cause of blindness in the world (in the US alone, more than 22 million people have cataracts).

Aging is the most common cause of cataracts, because the proteins in the lens of your eye will denature over time. This is not a good thing, because your lens is made of living cells and denatured proteins disrupt the cells and can even kill them. Diabetes and high blood pressure can accelerate the process, as can ultraviolet light (UVB, specifically) and other radiation and blunt trauma to the eye. There is a genetic component to the development of cataracts as well, particularly if someone develops them in childhood or as young adults. These aren’t the only causes, of course. Just the most common.

The most common forms of cataracts are subcapsular, nuclear, and cortical. Subcapsular cataracts start at the back of the lens, and are most common in diabetics and people taking medical steroids. Nuclear cataracts start in the center of the lens, and are most commonly associated with aging. Cortical cataracts start at the edge of the lens and work inwards ina “spoke-like fashion”. There are also congenital cataracts, which you are born with or develop during childhood – usually due to your genes or some form of infection or trauma.

Treatment

Ultimately, the only treatment for cataracts is to remove the existing lens and replace it with an artificial lens called an intraocular lens that matches the prescription (if any) that you need for your glasses. The intraocular lenses come in a wide variety of different types, and if you need one you should consult with your ophthalmologist to see which ones make the most sense for you.

Surgery is generally considered a last resort, though. As long as the cataract symptoms aren’t bothering you, and the problems with your vision can be corrected with glasses, there generally no need to undergo surgery. Cataract surgery is considered pretty routine, but the only really risk-free surgery is one that you don’t have.

Hang on, hang on. This is all about people. Didn’t this start with a dog?

Yep. But cataracts aren’t limited to humans. It’s a condition caused by disruption and damage to the lens of the eye, so any animal with an eye with lenses can develop cataracts. There’s a lot of information on the internet about dog cataracts, and mentions of cats. One veterinarian stated that they are “the most common cause of blindness in dogs, and can also affect people or any species of animal”. Like humans, animal cataracts can develop from age, diabetes, trauma, genetics, or something called Progressive Retinal Atrophy – the name for a cluster of generic disorders that cause the retina to degenerate. Animal cataracts can be treated in the same way as human cataracts. Progressive Retinal Atrophy has no treatment, though.

Impaired vision and even blindness aren’t a death sentence for a house pet, though. Rosie gets around just fine, as long as you don’t move her food and water dishes and rearrange the furniture a whole lot. So if you live in the Cincinnati area and want to adopt an adorable little blind dog (or another animal), contact the Peppermint Pig Animal Rescue. They’ve got a lot of animals looking for a loving new home.

How Long Did It Take To Build That?

Over the weekend, we took my son and my 16-year-old (almost 17 years old, now) to visit the Hall of Justice.

All right, all right, I’m kidding.  Slightly. That building up there (which really was the inspiration for the Hall of Justice) is the Cincinnati Museum Center. It’s not quite as impressive as usual, because there’s a whole lot of internal and external renovations going on, but it’s still pretty cool.

“How long did it take to build that?” my niece asked.

“Two years!” my son declared.

“I don’t know,” I confess.

“Maybe forty years,” my niece suggests.

How long did it take?

Well, according to the Museum Center web site, construction started in August 1929 and was completed on March 31, 1933. So, about 3 and 1/2 years.

Well. That was short.

The construction time? Or the article?

Both.

Yeah, well, the building was built in the 20th century. As I pointed out to my niece when she guessed – half tongue-in-cheek – that it took 40 years, the building was originally designed to be a rail hub. They had ways to haul supplies and materials in, and things like cranes and bulldozers and the like. It wasn’t all teams of oxen dragging granite blocks and the like.

Rail hub?

The building that is now the Cincinnati Museum Center started out as Cincinnati Union Terminal. See, as Ohio History Central explains, Cincinnati was linked to “a number of other major cities through its rail lines, but the original system had not been well-coordinated. Trains ran through several different railroad stations around the city. In the early 1900s, railroad companies began developing plans for a single railroad terminal that would provide service for all passenger and freight lines entering the city. It was not until the late 1920s that construction actually began on the project, which became known as Union Terminal.”

The Union Terminal complex, at its height, took up 287 square miles acres and had 94 miles of track – some of which you can still see if you visit today. It was designed to handle a lot of traffic. See the way that the building rises up in a hemisphere in the center? That facade covers a half-dome that, when it was built, was the largest half-dome in the world (and is still the largest in the western hemisphere). The terminal could handle 108 arriving and 108 departing trains a day, and was designed to accommodate as many as 17,000 people (although it hit over 20,000 during World War II, when soldiers passed through on the way to their posts).

Union Terminal operated from 1931 to 1972, when it finally closed for business. The city of Cincinnati purchased the site in 1974. In 1979, the Joseph Skilken Organization converted it into a mall, which opened with 40 tenants on August 4, 1980. The mall failed and closed officially in 1984, although a single store (Loehmann’s) continued in operation there until 1985 and a weekend flea market operated on the site for several years.

In 1986, a Hamilton County bond levy was passed to fund renovation of the site and to convert it into a museum. Four years later, in November 1990, the terminal reopened as the Cincinnati Musuem Center. The next year, it also began serving as Union Terminal once more. Amtrak began thrice-weekly passenger train runs on July 29, 1991.

So, how long did it take?

It depends, ultimately, on what you’re looking at. It took three and a half years to build the original Union Terminal facility. Turning it into a mall took 23 months, and turning it into the Cincinnati Museum Center took four and a half years.

Are Emeralds Real?

“Dad?” my son said from the back seat of the car. “Are emeralds real?”

Mercifully, there is some context for that question. He’d been over at a friend’s house, and they’d been playing Minecraft. I don’t know much about the game, but apparently “emerald” is one of the construction materials in the game. Which led to the question.

“Yes,” I tell him. “They are.”

“Wow!” he says.

You knew this one, didn’t you?

Yes. Yes I did. But let’s have some fun with it anyway, because I don’t know as much about them as I’d like.

What is an emerald?

Every source I found (which includes mindat.org, minerals.net, and Wikipedia agree that emerald is a variety of beryl. Chemically it’s beryllium aluminum silicate (Be3Al2Si6O18), with a green color that derives from trace amounts of chromium (the mineral that gives us chrome) and (occasionally) vanadium (a silvery grey mineral). Both minerals oxidize in a variety of colors, which explains how a silvery mineral can turn the mineral green. It naturally forms into hexagonal crystals.

The full market value of an emerald is based on four factors: color, clarity, cut, and carat weight.

  • Color: To be an emerald, the mineral must have a medium to dark green color (light green stones are classified as “Green Beryl“, which is not considered as valuable), as measured on a scale from 0% (colorless) to 100% (opaque and black) – the finest emeralds rank about 75% on this scale.
  • Clarity: All crystals will have some level of flaws, mostly consisting of inclusions (other minerals trapped in the crystal) and cracks. Flawlessly emeralds are stones with no inclusions or fissures visible to the naked eye.
  • Cut: This is not a natural property of the stone, but the way it was cut after it was mined. Raw stones are less valuable for the same reason that a tree trunk sells for less per pound than a table of the same wood, but a bad cut can destroy the stone.
  • Carat weight. A carat is 0.2 grams (or 0.007055 oz). The value of stones of th same quality does not change in a linear fashion, because larger high-quality stones are rarer than smaller ones. Consulting Singhal Gems International, a good quality 1.0 carat emerald can range from $500 to $1,125, while a good quality 5.0 carat emerald can range from $7,500 to $15,000 in value.

Where are they found?

The largest emerald deposits can be found in Colombia, Brazil, and Zambia. They are mined elsewhere in the world, but those three nations produce most of them. Colombian emeralds are often considered to be the overall finest form of emerald, as they are primarily colored by chromium. Zambian and Brazilian emeralds are more frequently colored by vanadium, with Brazilian emeralds being darker and more heavily included and Zambian emeralds having a bluish-green or grayish-green color.

What is the biggest emerald ever found?

That’s… tricky. What, exactly, do you mean by that question?

The International Gem Society website breaks them down into three categories: named emeralds, unnamed emeralds, and “other large emeralds”. They state that the largest named emerald is the “Emerald Unguentarium”, a 2,860 carat emerald vase currently on display in the Imperial Treasury in Vienna.

The Daily Mail disagrees with this statement, as they report on a watermelon-sized emerald named Teodora, which came in at 57,500 carats. It should be noted, however, that gem experts were skeptical of this claim, and that the owner was arrested on multiple fraud charges. A gem expert who studied it found evidence that it was lower-quality emerald (possibly mixed with white beryl) that had been dyed to make it appear more valuable. Because of this, when it went up for auction, no bids were made.

The largest unnamed emerald is an uncut Colombian crystal in a private collection that weighs 7,052 carats.

“Other large emeralds” is dominated by the Bahia Emerald, which was an 840 pound stone from Bahia, Brazil. The stone “reportedly contains over 180,000 carats of emeralds”, one of which is a single stone that is apparently described as the size of a man’s thigh. There is an ongoing legal battle over ownership of this stone, which shouldn’t surprise anyone since it’s been valued at upwards of $400 million. This stone, unlike Teodora, appears to be genuine.

Genuine, and large.

How Long Would It Take To Get To The Moon?

“Dad?” my son asked while we were playing with his Legos. “How long would it take to get to the moon?”

“I think that depends on how fast you’re going,” I replied.

“No,” he says, sounding exasperated as only a 6-year-old can, “I mean, if you were going as fast as the Death Star!” Because that was entirely clear from the context, right?

“I don’t know,” I tell him. “I don’t know how fast the Death Star is.”

“It’s really fast,” he assures me.

Where to start?

There are a couple of things we need to know here, in order to answer the question. How far away is the moon? How fast do we have to go at minimum to make it? Oh, and how fast is the Death Star? So, let’s dig in.

How far is it to the moon?

The distance from the Earth to the Moon varies based on the time of the month, because the Moon orbits us in an ellipse – so it gets closer and then moves further away. At apogee (the farthest it gets from us), it’s 405,400 km away, while it gets as close as 362,600 km at perigee. So, clearly, how long it takes will really depend on how fast we’re going – just like any other trip we can take.

How fast do we need to go?

How fast you need to go to get to the moon will depend on the method you’re using to get there, and the amount of time you want to take. So, let’s start with the concept of escape velocity. This is the minimum speed required to “out-pull” gravity and leave an object behind. If you launch at that speed or greater, you fly away. If you don’t, you fall back to the surface. Eventually. Escape velocity varies with the gravity of the object and is approximately 11.2 km/s, or 40,320 kph on Earth. Assuming there is no friction, which is a popular physics assumption to keep equations simple. If you launch at that speed, you fly away from the earth – you slow down over time, as Earth’s gravity pulls on you, but you never actually stop moving. Ever.

There’s a down side to trying to get to the moon by launching at escape velocity (say, by using a variant of Project HARP’s big gun): Earth’s force of gravity is 9.807 m/s2, so you’re pulling around 1,142 gravities at the instant of launch. You would be a thin, wide smear on your pilot’s chair well before you reached the moon.

Clearly, we didn’t send a gelatinized melange of Neil Armstrong, Michael Collins and Edwin Aldrin to the moon on Apollo 11 – those three men made it to the moon and back with bones and organs intact, after all. So, how did they do it? Well, the important thing to remember is that escape velocity is only needed if you have an initial push and then add no additional thrust after that. This isn’t how the Saturn V – or any other rocket for that matter – works. They lift themselves at a slower pace, but apply a constant (or near-constant) thrust by carrying fuel. There’s a point of diminishing returns on this, because you have to lift your fuel as well as the ship (something described in the Tsiolkosky rocket equation, which I discussed when I tried to describe how to make a house fly).

The Saturn V was a multi-stage rocket, with the first stage burning for 2 minutes 41 seconds and pushing the rocket about 68 km into the air (hitting a velocity of 2,756 meters per second). Then it ditched the first stage and started the second stage burn. This pushed it another 107 km (for a total of 175 km) into the air over the course of 6 minutes, reaching a velocity of 6,995 meters per second). Stage 3 burned for about 2 minutes 30 seconds, reaching a velocity of 7,793 meters per second and putting it in orbit at an altitude of 191.1 km. Stage 4 burned for six minutes, pushing the ship to a velocity of 10,800 meters per second once it was time to head for the moon.

So, how long would it take?

How fast are you going?

Let’s say you just boosted off Earth with a canon, firing you straight up at escape velocity. Let’s also say you timed things so that you’d intersect with the moon at perigee. That’s 362,600 km, or 362,600,000 meters. At 11.2 meters per second, that’s 32,375,000 seconds to reach the moon. This translates into 8,993 days, or 24 years, 7 and one half months. Approximately. Your gelatanized corpse has a long trip ahead.

Apollo 11 was moving at 10.8 kilometers per second, which (mathematically) means you’d expect the trip to the moon to take 33,574.07 seconds. In theory, this means 9.326 hours. It actually took three days. Why? Well, there’s two reasons and they’re both gravity. See, the Apollo 11 wasn’t maintaining constant thrust. It had fuel that it used for course corrections and orbital insertions and the like, but it coasted most of the way. Earth’s gravity pulled on the ship the whole time, slowing it down. In addition, the ship didn’t fly in a straight line. It was in a long, figure-eight-shaped orbit with the Earth and the Moon – like so:

But what about the Death Star?

Ah, yes. That. Well, it still depends on the speed the ship can manage.

How fast is the Death star?

This is… questionable. According to the DS-1 Orbital Battle Station entry on Wookieepedia, the Death star had a speed of 10 megalight (MGLT).

So, what’s a megalight? Well, also according to Wookeepedia, a megalight “was a standard unit of distance in space”. Which is entirely unhelpful, although it does indicate that when it was used in the Star Wars: X-Wing Alliance instruction manual, it appeared to be a unit of distance and that when used as speed it should imply “megalights per hour”.

In all likelihood, “megalight” is a word that got made up because it sounded cool and had no actual meaning attached to it. But if we try to break it down, “mega” as a metric prefix means million. So, one megalight could be a million light seconds. However, this would mean that the Death star flies at 10 million light seconds per hour, or 2,777.7 times the speed of light – meaning that it could reach Alpha Centauri from earth in less than 14 hours of cruising on its “sublight” drives.  So I’m going to assume that this is not what was intended.

The Star Wars Technical Commentaries on TheForce.net speculate in “Standard Units” on what MGLT means in terms of real world [i]anything[/i]. The author of the article comes to the conclusion that 1 MGLT is “at least 400 m/s2” acceleration, which is roughly 40 gravities of acceleration.

One thing we also know about ships in Star Wars is that constant acceleration isn’t an issue – they have something close to the “massless, infinite fuel” I mentioned above. The Death Star isn’t fast, compared to the other ships in Star Wars, but it can accellerate at a constant 4 kilometers per second. Now Dummies.dom provides us with a simple formula for determining the distance (s) covered for a given time (t) at a particular acceleration (a), and that formula is s = 0.5at2. Which means we can reverse engineer, because all we need is the time. The equation looks like this:

362,600 = 0.5(4)t2
362,600 = 2t2
181,300 = t2
t = square root of 181,300 = 425.7933771208754 seconds

So, assuming that the Death Star didn’t engage it’s hyperdrive, it would take a little over 7 minutes to reach the Moon at a velocity of approximately 1,703.17 kilometers per second. And it would keep going, because it can only slow down at 4 kilometers per second. So, if the Death Star wanted to stop at the Moon, it would need to slow down about halfway there (yes, I know that orbital mechanics are a little more complex than this, but we’re talking about a 160 kilometer diameter ship that can accelerate at 4 kilometers per second. So cut me some slack, would you?). That it would have to accelerate to halfway to the moon, and then decelerate the rest of the way. So, that would look something like this:

2(181,300 = 0.5(4)t2)
2(181,300 = 2t2)
2(90,650 = t2)
2(t = square root of 90,650 = 301.0813843464919)
t = 602.1627686929838 seconds, or slightly over 10 minutes.

“All your tides are belong to us, now.”