Why Do Tornadoes Suck Things Up?

My six-year-old nephew spent the weekend at my house, which delighted my son to no end. The end result was the sort of excited chaos you might expect – lots of six-year-old bickering, and toys strewn everywhere, and strange non sequitur laced conversations. At one point, tornadoes came up. I don’t know why, because I wasn’t paying attention to the start of that conversation. But my nephew declared that he’d seen a tornado, and that his mom had made them get in the closet. And my son responded that you didn’t get in the closet, you got in the tub, because we’d had a tornado warning once and our front bathroom is the safest place in our condo for that sort of thing. So they argue the merits of bathroom versus closet for a few minutes, and then my son looks at me. I smile, preparing my “it depends on the house” explanation for the question I’m sure is coming.

“Dad?” my son asks. “Why do tornadoes suck things up?”

All right. So that isn’t the question I expected.

What is a tornado?

The National Oceanic and Atmospheric Administration has a page titled The Online Tornado FAQ, and I’ll be referencing it a lot over the course of this question. To begin with, I’ll just quote their answer to the question:

According to the Glossary of Meteorology (AMS 2000), a tornado is “a violently rotating column of air, pendant from a cumuliform cloud or underneath a cumuliform cloud, and often (but not always) visible as a funnel cloud.” Literally, in order for a vortex to be classified as a tornado, it must be in contact with the ground and the cloud base. Weather scientists haven’t found it so simple in practice, however, to classify and define tornadoes (per this essay by Doswell). For example, the difference is unclear between an strong mesocyclone (parent thunderstorm circulation) on the ground, and a large, weak tornado. There is also disagreement as to whether separate ground contacts of the same funnel constitute separate tornadoes. Meteorologists also can disagree on precisely defining large, intense, messy multivortex circulations, such as the El Reno tornado of 2013, compared to the parent mesocyclone and surrounding winds of damaging intensity. It is well-known that a tornado may not have a visible funnel. Mobile radars also have showed that tornadoes often extend outside an existing, visible funnel. At what wind speed of the cloud-to-ground vortex does a tornado begin? How close must two or more different tornadic circulations become to qualify as a one multiple-vortex tornado, instead of separate tornadoes? There are no firm answers.

In other words, a tornado is a vortex, very much like an atmospheric whirlpool. In an oversimplified fashion they form under basically the same conditions – our atmosphere is described by the same fluid dynamics that describes the behavior of water, after all. Moving air hits a barrier – in this case, denser colder air – and twists back on itself. The air is still moving into the barrier, however, so the air that is deflected back picks up speed thanks to the conservation of angular momentum, creating a vortex.

But, like I said, that’s the oversimplified explanation. Here’s what NOAA says on the subject:

The truth is that we don’t fully understand. The most destructive and deadly tornadoes occur from supercells–which are rotating thunderstorms with a well-defined radar circulation called a mesocyclone. [Supercells can also produce damaging hail, severe non-tornadic winds, unusually frequent lightning, and flash floods.] Tornado formation is believed to be dictated mainly by things which happen on the storm scale, in and around the mesocyclone. Recent theories and results from the VORTEX programs suggest that once a mesocyclone is underway, tornado development is related to temperature changes across the edge of downdraft air wrapping around the mesocyclone (the occlusion downdraft). Mathematical modeling studies of tornado formation also indicate that it can happen without such temperature patterns; and in fact, very little temperature variation was observed near some of the most destructive tornadoes in history on 3 May 1999. The details behind these theories are given in several of the Scientific References accompanying this FAQ

What this means is that they’re vortices, and they form just like any other vortex. But, like most things in nature, they’re super complicated and we don’t really quite understand what makes them start.

So how do these tornados suck things up?

The famous “sucking tornados” are “multiple vortex tornados“, and they create what is called a “suction vortex“. Interestingly, the suction vortex has little to do with air pressure, and everything to do with wind speed. That is, the lower air pressure within the vortex isn’t low enough to “suck” things up. Tornadoes aren’t straws. Instead, the speed of the winds traveling up the vortex funnel create the “suction” effect.

Here’s what happens. The secondary vortices of a multiple-vortex tornado orbit the axis of the primary vortex, increasing the wind speed around the primary vortex. When the wind from and around the secondary vortices “turns the corner” – that is, enters the primary vortex and suddenly changes from horizontal to vertical flow – angular conservation causes the wind to pick up an enormous amount of speed. It is this wind speed that lifts objects – cows, trucks, people, roofs, whatever – and hurls them into the air. Note that all tornadoes have this “turn the corner” effect, but it takes the secondary vortices to really get the wind moving fast enough to lift really heavy objects.

Waterspouts and fire tornadoes

My son had heard of waterspouts, and guessed that they were water tornadoes. He was right. A waterspout is literally just a tornado that forms over water and that sucks up water.

Fire tornadoes are a little different. They are similar to actual tornadoes in appearance – except, you know, for the fire – but are formed by rising surface winds (usually generated by the heat from the fire) that meet turbulent winds to form a spiral of rising flame. They aren’t formed by supercell thunderstorms and aren’t tornadoes. Doesn’t make them safe, mind.

 

Can They Hear Me In China?

“BOO!” my son yells, leaping out from a shrub.  And then he dissolves into a fit of laughter.

This is a game he likes to play, whenever he gets the chance.  As soon as we’d parked and he got out of the car, he ran up the sidewalk towards the front door of our condo.  And then he ducked back behind the hedge, lurking.  The game, now, is for me to walk towards the door.  Then he’ll jump out and shout “boo” and try to make me jump.

“Did you know I was there, daddy?” he asks.

Of course I did, I think.  You hide in the same place every time.  “Kind of,” I tell him.  “I guessed where you were.”

He blows that off.  “I was loud, wasn’t I?”

“Yes, you were,” I answer, unlocking the door.

“Was I loud enough for them to hear me in China?”

How Do We Hear?

Obviously, we hear with our ears.

howdowehear

Sound waves, which are really just pressure waves in the atmosphere, strike the outer ear and are channeled into the ear canal.  These pressure waves vibrate the eardrum, which in turn vibrates the bones of the inner ear (the malleus, the incus, and the stapes), amplifying the vibrations and transmitting them into the inner ear (or cochlea).  Hairs in the cochlea are stimulated by these vibrations, creating an electrical signal that transmits along the auditory nerve to the brain.

Yes, this is terribly simplified.

How Loud Are You?

Strictly speaking, “loud” is a matter of perception – the same pressure wave can result in different experiences of “loudness”.  However, this perception is tied to the intensity of the pressure wave, just as the perceived pitch of a sound is tied to the frequency of the wave.

wavy33b

A wave

Using the above image of a wave, the intensity is how high the peaks and how low the valley is – the higher the peak, the more intense the wave.  Another way to think of intensity is how much energy the wave carries – the taller the wave, the more energy (just like how bigger ocean waves hit harder than small ones).  Frequency, on the other hand, is how fast the wave moves – the closer together the peaks, the faster the wave moves and the higher the frequency.  Generally speaking, we perceive intensity as loudness (because the pressure wave hits the ear harder) and we perceive frequency as pitch (because the pressure wave stimulates the bones in the ear faster).

“Loudness” is measured in decibels (dB), because one decibel is the “just noticeable difference” in sound intensity for the human ear – assuming the pressure wave generated is in the 1,000 Hertz (Hz) to 5,000 Hz range we are best at hearing.  Every 10 dB represents multiplying the intensity of the pressure wave by 10 – that is, a 10 dB sound is 10 times more intense than a 0 dB sound, a 40 dB sound is 10,000 times more intense than a 0 dB sound, and a 100 dB sound is 10,000,000,000 times more intense than a 0 dB sound.

We generally can’t hear anything below 0 dB, and normally speak in the 60 to 65 dB range.  A jackhammer 50 feet away is about 95 dB, a power mower 3 feet away is around 107 dB, and loudness causes pain starting around 125 dB.  Sounds at 140 dB and greater can cause permanent damage with even short exposure.

How Far Away Can We Hear?

This gets tricky, because the answer is “no further than when the perceived volume falls to 0 dB”.  Tricky, because sound obeys the inverse square law which states that for any source power P generated at the center of a sphere, the intensity of at the surface of that sphere is P/4πr2 (although a good approximation is P/r2, since the math gets easier).  According to Hyperphysics, r is pretty much always measured in meters for these purposes (because sound intensity is actually measured in watts per meter squared, so it keeps the units the same).

Since sound intensity can be transformed into decibels, it’s really not a stretch to directly apply the inverse square law to decibel measurements.  So, a 60 decibel conversation would be perceived as 60 decibels at 1 meter away, 60/(2*2) = 15 decibels at 2 meters, 60/(3*3) = 6.6 decibels at 3 meters, 60/(4-4) = 3.75 decibels at 4 meters, less than 1 decibel at 8 meters, and so on.  Realistically, at this point, it’s probably safe to call it “inaudible” (even though you could technically detect it).

How Loud Would You Have To Be For Someone To Hear You In China?

All right, here’s where the math gets… entertaining.  I live in Cincinnati, Ohio, which is (according to Google) 10,969 kilometers from Beijing.  Measuring along the curved surface of the Earth, that is.  But, to keep things simple, we’ll ignore that.  So, 10,909 kilometers is 10,909,000 meters.  To be heard in Beijing, we’d have to generate enough decibels to result in a greater than 0 dB sound 10,909,000 meters away.

For laughs, let’s aim for a 60 dB sound.  That way, our sound can be clearly understood.  The radius is 10,969,000.  So, the equation looks like this:  x/10,969,0002 = 60.  Solving for x gives us x = 60(10,969,0002), or x = 7,219,137,660,000,000 dB.  This is a nonsensical level of perceived volume, and would render you deaf in ludicrously tiny fractions of a second.

What could generate that?  Well, we’d have to reverse engineer the decibels into watts of power, which converts to 721913765999988 watts per meter, or about 721.9 terawatts of power.  Now, you can roughly convert watts to Joules per second, so that’s roughly the explosion of a 200 kiloton nuclear weapon.

Assuming I did my math correctly, which I’m not guaranteeing.  What I can guarantee is that there is no way you’d want to be standing anywhere near something loud enough in Cincinnati that you can hear it in China.

Why Does Oil Make A Rainbow?

It’s summer, and it’s just finished raining, and we’re walking across a parking lot on our way back to the car from running an errand. My son is, as five-year-olds are wont to do, taking the opportunity to jump in puddles and laugh as they splash. Suddenly, he stops. “Look!” he cries, pointing at the ground. “There’s a rainbow!”

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I go and look. Sure enough, there’s a small puddle with a thin film of oil slicking the top. I nod at him, and looks at it again. “Why is there a rainbow on the ground?” he asks.

“There’s oil on the puddle.”

He looks at it for a moment, then looks up at me. “How does oil make a rainbow?”

Yeah. You’ve just stumped me son.

So, what’s up?

science

Specifically, PHYSICS!

Could you… elaborate? Just a little?

It all starts with the nature of light, which as we all know is simultaneously a particle and a wave. Here’s how Professor Emeritis Dinesh O. Shah explains it in Scientific American:

Light reflects upward both from the top of the oil film and from the underlying interface between the oil and the water; the path length (the distance from the reflection to your eye) is slightly different depending on whether the returned light comes from the top or from the bottom of the oil film. If the difference in path length is an integral multiple of the wavelength of the light, rays reflected from the two locations will reinforce each other, a process called constructive interference. If, however, the rays reach your eye out of step, they will cancel each other out due to destructive interference.

oil_interfere_e

Sunlight contains all the colors of the rainbow–the famous ROYGBIV (red, orange, yellow, green, blue, indigo, violet). Each color of light has a different wavelength. Hence, a given disparity in the path length will cause constructive interference of certain colors, whereas other colors will not be observed because of destructive interference. Because the oil film gradually thins from its center to its periphery, different bands of the oil slick produce different colors.

Constructive and destructive interference?

Think of the classic sine curve you had to draw (we all had to draw them) when you took algebra or pre-calculus in high school. The wavy line that looks kind of like a snake. That thing. It’s the most common way to represent a wave of any sort, with the height of the “hills” of the wave representing amplitude (how intense the wave is – brightness for light, loudness for sound, and so on) and how close together the “hills” are representing frequency of the wave (how energetic it is).

Now, think hard about that math class. Do you remember what happens if you add two sine waves together? It changes the nature of the wave. Two identical waves will end up dobuling the amplitude (making it brighter or louder), while two utterly opposite waves will flatten the wave into a line. Check out the image below, if that isn’t clear.

interference

The amplitude of the light is how bright it is, so the areas of the puddle where the reflected light interferes constructively you can see it clearly while you can barely see it when the light interferes destructively. The colors shift because the frequency of the reflected light (which determines the color) vary with the thickness of the oil on the water and the angle at which the light hits your eye.

SCIENCE!

How Does Air Conditioning Work?

“The car is cold!” my son declares as he climbs in. “Good!”

It’s a hot day out, although not as hot as it’s been recently. Stil, the car’s pleasantly cool because I’d just parked it a few minutes ago so I could pick him up from Kindergarten, and the air conditioning had been running. “You’re right,” I agree.

“Why is it cold?” he asks.

“I had the air conditioning running,” I answer.

“Does it run all the time?” he asks, fastening his seatbelt.

“No,” I answer. “Only when I turn it on. You wouldn’t want it running in the winter, after all. When it’s cold out, you don’t want to make it colder.”

He nods at that, agreeing with the idea. “How does it make it cold?”

Uhm. “I… don’t know,” I answer, although I’ve got a vague idea in my head of how I think it works. Something to do with freon and fans, clearly. “I’ll have to find out.”

How do air conditioners work?

Air conditioners work, it turns out, for reasons very similar to the water cycle we all learned about as children. They have a liquid in them (the refrigerant) which absorbs heat from the environment (your house or car), evaporating into a gas in the process. This gas is warmer than it was as a liquid, but it’s still not hot. It gets hotter, though as it’s circulated into a compressor, a device designed to pressurize the gas back into a liquid. A side effect of this pressurization is heat (to see this yourself, try squeezing a rubber ball – the pressure generates heat).

The hot liquid is then passed into a condensor, where it goes through a radiator that allows the heat to dissipate. This works because, even if it’s really hot outside, the pressurized refridgerant is hotter. The cooler pressurized liquid is then passed through a narrow hole into the evaporator, where the pressure drops and the temperature drops along with it. Once it enters the evaporator, the whole cycle has started over.

FAQ_air-conditioner-ope-phase

This is an extremely simplified version of the process, of course. You can read a far more detailed explanation of air conditioning here.

Why does changing pressure make things hotter or colder?

According to Hyperphysics, heat is “energy in transit from a high temperature object to a lower temperature object. An object does not possess ‘heat’; the appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object – this is properly called heating.”

Internal energy is “defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale.”

Now, let’s turn to the first law of thermodynamics, which states that “the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.” Based on this, it makes sense that increasing pressure increases internal energy and decreasing pressure decreases internal energy. Why? Because when you increase pressure you’re adding energy (because work is being done to the system), and when you decrease pressure you’re removing energy (because the system is working at pushing outwards). The added energy when you increase the pressure increases the internal energy that can be transferred to other systems, increasing the heat. Likewise, the decreased energy when you reduce the pressure reduces the internal energy that can be transferred to other systems.

What’s a system? The thing in question. The refrigerant in the air conditioner, for example, is a system for this purpose. So is the air in your home, or your car.

So, why does an air conditioner work? Thermodynamics, and clever engineering.

Is It Medicine?

Recently, we were at our local “natural and health foods” store. While my wife shopped for a specific supplement she was advised to use, I got to ride herd on my energetic five year old as he roamed around the store looking at everything. He loved the posters over by the pet food section, one of which showed a lion with a lamb curled up against it. He thought that was amazing and cute. Nearby was an entire wall of homeopathic products, including an entire array of products for pets. My son stopped and looked at the boxes, then turned and looked at me.

“Is this all medicine?” he asked.

I didn’t really feel like tackling that subject right there in the store. Not in any detail, anyway. “No,” I said.

“Okay,” he answered, and then he was off to look at the selection of vegan, glutin free baked goods.

What is homeopathy?

According to the American Institute of Homeopathy:

Homeopathy, or Homeopathic Medicine, is the practice of medicine that embraces a holistic, natural approach to the treatment of the sick. Homeopathy is holistic because it treats the person as a whole, rather than focusing on a diseased part or a labeled sickness. Homeopathy is natural because its remedies are produced according to the U.S. FDA-recognized Homeopathic Pharmacopoeia of the United States from natural sources, whether vegetable, mineral, or animal in nature.

The website goes on to explain that there are three guiding principles of homeopathy:

  1. “Like cures like”. A principal that a symptom can be treated with a substance that causes a similar symptom.
  2. The minimum dose. From the AIH website, “Homeopathic medicines are prepared through a series of dilutions, at each step of which there is a vigorous agitation of the solution called succussion, until there is no detectible chemical substance left. As paradoxical as it may seem, the higher the dilution, when prepared in this dynamized way, the more potent the homeopathic remedy. Thereby is achieved the minimum dose which, none the less, has the maximum therapeutic effect with the fewest side effects.”
  3. The single remedy. Again, from the AIG website, “Most homeopathic practitioners prescribe one remedy at a time. The homeopathic remedy has been proved by itself, producing its own unique drug picture. That remedy is matched (prescribed) to the sick person having a similar picture. The results are observed, uncluttered by the confusion of effects that might be produced if more than one medicine were given at the same time.”

Is homeopathy medicine?

Merriam-Webster defines medicine as:

1 a: a substance or preparation used in treating disease
b: something that affects well-being

2 a: the science and art dealing with the maintenance of health and the prevention, alleviation, or cure of disease
b: the branch of medicine concerned with the nonsurgical treatment of disease

3: a substance (as a drug or potion) used to treat something other than disease

So. By some definitions of medicine it qualifies. Homeopaths are certainly involved in “the science and art dealing with the maintenance of health and the prevention, alleviation, or cure of disease” and homeopathic medicines are certainly “a substance or preparation used in treating disease”.

Does homeopathy work?

No.

Uhm… could you elaborate on that?

There’s no way it could work. Let’s take another look at that second principle of homeopathy, the minimum dose. The AIH states that “Homeopathic medicines are prepared through a series of dilutions, at each step of which there is a vigorous agitation of the solution called succussion, until there is no detectible chemical substance left.”

Here’s how the dilutions work, as explained by a FAQ from Boiron (described as a “world leader in homeopathic medicines”):

What does the “C” listed after the active ingredient stand for?

The most common type of dilutions is “C” dilutions (centesimal dilutions). The 1C is obtained by mixing 1 part of the Mother Tincture with 9 parts of ethanol in a new vial and then vigorously shaking the solution (succussion). The result is a 1/100 dilution of the plant (the Mother Tincture being a 1/10 dilution of the plant itself). The 2C is obtained by mixing 1 part of the 1C with 99 parts of ethanol in a new vial and succussing. Recurrently, the 3C is obtained by mixing 1 part of the 2C with 99 parts of ethanol in a new vial and succussing.

What does the “X” listed after the active ingredient stand for?
X dilutions are decimal dilutions prepared similarly to C dilutions, but the factor of dilution is only 1/10 from one dilution to the next.

What does the “K” listed after the active ingredient stand for?
The K refers to a method of manufacturing known as the Korsakovian method. The Korsakovian method dilutes the homeopathic preparation of the substance at the rate of 1 part of the previous dilution with 99 parts of solvent.

What does the “CK” listed after the active ingredient stand for?
Korsakovian dilutions are manufactured using a device specially designed to ensure that the dilution process is reproducible from one dilution to the next. Only one vial is used for the entire process. Using ultra-purified water as the solvent, the machine removes 99% of the Mother Tincture and replaces it with the same volume of solvent. The vial is succussed for 10.5 seconds. The result is called 1CK. The 2CK is prepared identically from the 1CK. The automatic process using only 1 vial allows higher dilutions to be reached. The most common Korsakovian dilutions are 200CK, 1,000CK (also called 1M), 10,000CK (10M), 50,000 CK (50M) and 100,000CK (100M or CM).

What does “200CK” mean?
200CK means that the substance has been homeopathically diluted 200 times at the rate of 1 to 100.

The dilutions on the medicines I looked at (I didn’t look at all of them) appear to range between 3C and 12C, counting by threes (3C, 6C, 9C, 12C), with one hitting 30C. Here’s what that looks like:

  • 3C: 1 part active ingredient to 9,999 parts solvent (100 parts per million, or PPM).
  • 6C: 1 part active ingredient to 9,999,999 parts solvent (0.1 PPM).
  • 9C: 1 part active ingredient to 9,999,999,999 parts solvent (0.0001 PPM).
  • 12C: 1 part active ingredient to 9,999,999,999,999 parts solvent (0.0000001 PPM).
  • 30C: 1 part active ingredient to 9,999,999,999,999,999,999,999,999,999,999 parts solvent (0.0000000000000000000000001 PPM)

For comparison, let’s talk about the US Environmental Protection Agency’s Maximum Containment Level Goals (MCLG), Maximum Contaminant Levels (MCL), and Maximum Residual Disinfectant Level Goals (MRDLG):

  • Maximum Contaminant Level Goal (MCLG) – The level of a contaminant in drinking water below which there is no known or expected risk to health. MCLGs allow for a margin of safety and are non-enforceable public health goals.
  • Maximum Contaminant Level (MCL) – The highest level of a contaminant that is allowed in drinking water. MCLs are set as close to MCLGs as feasible using the best available treatment technology and taking cost into consideration. MCLs are enforceable standards.
  • Maximum Residual Disinfectant Level Goal (MRDLG) – The level of a drinking water disinfectant below which there is no known or expected risk to health. MRDLGs do not reflect the benefits of the use of disinfectants to control microbial contaminants.

With that in mind, let’s have a look at the EPA Table of Regulated Drinking Water Contaminants. If you go and look at it yourself, bear in mind that the units are in milligrams per liter (mg/L), which is equivalent to PPM:

  • Chlorine has a MCL of 4 PPM (effectively 4 5C dilutions).
  • Arsenic has a MCL of 0.01 PPM (meaning a 7C dilution)
  • Cyanide has a MCL of 0.2 PPM (two doses of a 6C dilution).
  • Lead has a MCL of 0.015 PPM (one and a half doses of a 7C dilution).
  • Mercury has a MCL of 0.002 PPM (two doses of an 8C dilution).

By sheer logic, if the “like cures like” principal was correct and the minimum dose worked, then we’d be immune to eye/nose irritation and stomach discomfort (caused by chlorine), circulatory system problems (arsenic), nerve damage and thyroid problems (cyanide), developmental development issues and kidney problems (lead), and kidney damage (mercury).

Moles and atoms and molecules

Let’s put it a different way, and talk about moles.

mole6

No, not these guys

A mole is the SI unit of that measures the amount of a chemical substance that contains as many elementary entities (atoms, molecules, whatever) as there are atoms in 12 grams of carbon-12. This odd calculation is used because the number of atoms in 12 grams of carbon-12 happens to be the same as the Avogadro constant: 602,214,085,774,000,000,000,000.

Why is this important? Watch, and see.

A homeopathic “mother tincture” is 10% ingredient and 90% solvent, by weight. So a mother tincture of peppermint would be, say, 1 gram of peppermint oil and 9 grams of water. The active ingredient of peppermint oil is menthol (C10H20O), and water is H2O. Consulting the Lenntech molecular weight calculator, menthol has a weight of 156.26 grams per mole and water weighs 18.02 grams per mole. So one gram of menthol has 3,853,923,497,849,737,616,792 molecules of menthol, and one gram of water has 33,419,205,647,835,738,068,812 molecules of water. So the mother tincture has a total of 304,626,774,328,371,380,236,100 molecules, and is only 1.2% menthol by quantity of atoms (despite being 10% menthol by weight).

A 1C dilution takes 1 gram of the mother solution and mixes that with 99 grams of water, giving us 100 grams of dilution with a total of 3,338,964,036,568,570,000,000,000 molecules, of which 385,392,349,784,973,000,000 are menthol.  That makes it 0.0115% menthol at this point.  Each dilution after that reduces the number of menthol atoms by a factor of 100, until at a 12C dilution you get 3.85 atoms (let’s be optimistic and call it 4).  So, at a 13C dilution, you quite literally have nothing but water.

Homeopathic-Dilutions_thumb18-621x210

Bear in mind that this is the case with a relatively simple molecule like menthol.  Most of the “active ingredients” in homeopathic dilutions are far more complex – according to Chemical composition, olfactory evaluation and antioxidant effects of essential oil from Mentha x piperita, for example, the components of peppermint essential oils were “menthol (40.7%) and menthone (23.4%). Further components were (+/-)-menthyl acetate, 1,8-cineole, limonene, beta-pinene and beta-caryophyllene”.  This reduces the number of atoms per gram of each ingredient, causing the atoms of each chemical that make up the ingredient to go away faster (although in the case of the peppermint essential oils, menthone’s molecular weight is 154.25 grams per mole, so you’d end up with about 2 atoms each of menthol and menthone at a 12C dilution).

So, is homeopathy medicine?  Only in a strict and narrow definition, because it is used to treat illnesses.  After all, the definition we looked at above doesn’t say the medicine has to work.  And it really doesn’t work.

What if the Sun turned into a Black Hole?

This week, I’ve been writing about the sun. I blame the summer solstice for this, because the news that Monday was the longest day of the year fired my son’s imagination and got him asking question after question about the sun, and about the stars, and about related astronomical phenomena. So far, I’ve answered his questions about whether or not the sun can melt (it can’t) and what the hottest star is (H1504+65). Now it’s time to move on to his next question, one which demonstrates that he’s learned some interesting things.

“What if the sun turned into a black hole?” he asked, as we walked up the stairs to the front door of our condominium building. “Would it swallow the earth and all the planets?”

That one took me off guard, because I’m pretty sure that when I was five I didn’t even know what a black hole was. But then, I also realized that the first black hole was discovered the year I was born, so it’s not surprising the term wasn’t in common usage when I was five.

It’s a chilling thought, isn’t it? “Nothing escapes a black hole,” science fiction tells us. “Not even light.” Black holes are the great white sharks of space – remorseless predators consuming everything in their path. And we’d never see them coming. But they have one other thing in common with sharks.

black-holes-opener-615

They have an exaggerated reputation.

Newton’s Laws of Motion and Universal Gravitation

Although aspects of his laws have been superceeded by Einstein and his General and Special Theories, Newton’s laws remain an excellent (if ever so slightly inaccurate) model of motion. In brief, his three laws of motion state:

  1. If no forces act upon it, a body in motion will remain in motion and a body at rest will remain at rest, and velocity will remain constant in either case.
  2. If force is applied to an object, there will be a change in velocity proportional to the magnitude to which the force is applied.
  3. If body A exerts force on body B, then body B will exert a force of equal strength but in opposite direction on body A. This is also stated as “for every action there is an equal and opposite reaction”.

In addition, Newton put forth a law of universal gravitation. This law states that “two particles having masses m1 and m2 and separated by a distance r are attracted to each other with equal and opposite forces directed along the line joining the particles. The common magnitude F of the two forces is

eq4-02

where G is an universal constant, called the constant of gravitation, and has the value 6.67259×10^-11 N-m^2/kg^2.”

Yeah? What does this have to do with black holes?

I’ll get to that. But first, let’s cover what a black hole actually is.

Fine. What’s a black hole?

Does it surprise you to know that NASA has some good resources about black holes? It really shouldn’t.

A black hole is a region in space where the pulling force of gravity is so strong that light is not able to escape. The strong gravity occurs because matter has been pressed into a tiny space. This compression can take place at the end of a star’s life. Some black holes are a result of dying stars.

Because no light can escape, black holes are invisible. However, space telescopes with special instruments can help find black holes. They can observe the behavior of material and stars that are very close to black holes.

Black holes come in four size categories, representing both their mass and their physixal size. There are:

  1. Micro black holes. These can run all the way up to about 7.342 x 10-8 M (the mass of our Moon), and can get as big as 0.1 millimeters. Yes, it would suck if one hit you.
  2. Stellar black holes. These range up to 10 M in mass, and can be up to about 30 kilometers in diameter (0.5 x 10-4 R).
  3. Intermediate-mass black holes, which can get up to 1,000 M and up to about the mass of the Earth itself.
  4. Supermassive black holes. These are the monsters that lurk at the center of most galaxies, massing up to 1010 M and up to 400 astronomical units in size.

Wow. So, why do you say they have an exaggerated rep?

It’s true that the escape velocity of a black hole exceeds the speed of light, which is what it means to say that “no light can escape”. However, no black hole will be larger or more massive than the sum of all of the mass that went into making the black hole in the first place. So, outside the event horizon (the point at which gravity becomes too powerful to escape), the black hole has the same effect as any other object of the same mass. With that in mind, Newton’s law of universal gravitation tells us that – if the sun were to be instantly replaced with a 1 M black hole – there would no impact on our solar system. the r2 figure in the equation is measured from center of m1 to center of m2, so nothing changes.

Nothing?

Well, all right. That’s not true. Black holes have no luminosity – no energy would be generated and nothing would reach the Earth. So, to quote Randall Munroe’s Sunless Earth article, “We would all freeze and die.”