Saturday, July 23, 2011

How Michigan managed to empty its penitentiaries while lowering its crime rate.
When parolees are less likely to reoffend, more prisoners can be let go without jeopardizing public safety. Going hand in hand with Michigan’s improved recidivism rates, therefore, has been a correspondent increase in parole approvals. Over 3,000 more prisoners were paroled in 2009 than were paroled in 2006; approvals for violent offenders have gone up by more than half (from 35 to 55 percent), while approvals for sex offenders have more than quadrupled (from 10 to 50 percent). As a result, during the past three years, the number of state inmates in Michigan has shrunk by 12 percent, reversing a sixteen-year trend of steady prison population growth. The turnaround enabled Governor Jennifer Granholm to shut down ten prisons last year, and an additional eight are slated to be closed by the end of 2010.

Wednesday, July 20, 2011

Sunday, July 17, 2011

Why don't things in orbit fall?

This has been explained in plenty of places, probably a lot better than I'll do, but I enjoy explaining things, and it is a good way to solidify my own understanding of them.

If you asked random people why things in orbit don't fall I'd expect you'd get an answer about lack of gravity in space.  While strictly speaking there is so little gravity in the majority of space as to be considered none, this is not true of near Earth orbit.  Things like the space shuttle and the International Space Station orbit at about 200 miles above the surface of the Earth. 

Orbital mechanics can be pretty complex. There are strange results like it taking more energy to send a probe closer to the sun than farther away from it. However, the basics are easy enough to understand. To begin, we can look at the the formula for finding the force of gravity, which is pretty easy.  $$$F=G\frac{m_1 m_2}{r^2}$$$ Using this formula we can find the force that an object should have at orbital height.
$$F=G\frac{m_1 m_2}{r^2}$$
F is force of gravity
G is the gravitational constant, 6.67384 × 10-11N m2 kg-2
m1 is mass one (Earth 5.9742 × 1024 kg)
m2 is mass two (object)
r is the distance between the masses

Before we move on, it is important to discuss r. You may be tempted to think the distance between the Earth and an object sitting on Earth's surface is 0 (or very close). Indeed, in common usage it is. However, when dealing with gravity all distances are measured from centers of gravity. As far as these formulas are concerned everything is infinitely small with all the mass in a point (which would make everything a blackhole [which leads to an interesting consequence that blackholes behave the same as any other object at a distance beyond their event horizon]). This means that we must add the radius of Earth (6,378,100 m) to whatever height above Earth the object is at.

Is there no gravity in orbit?
Let's begin with a 100 kg object on Earth's surface:
$$F=6.67384 × 10^{-11} \mathrm{N\,m^2\,kg^{-2}}\frac{5.9742 × 10^{24}\,\mathrm{kg} \cdot 100\,\mathrm{kg}}{(6,378,100\,\mathrm{m}) ^2}$$
$$F=980\, \mathrm{N}$$

Newtons (N) is the SI unit of force, analogous to pounds.  An apple has a weight of about one newton.  It doesn't matter if you have a intuitive feel for what that force is. You just need to be able to compare it to the force in orbit, which is:
$$F=6.67384 × 10^{-11} \mathrm{N\,m^2\,kg^{-2}}\frac{5.9742 × 10^{24}\,\mathrm{kg} \cdot 100\,\mathrm{kg}}{(6,731,100\,\mathrm{m}) ^2}$$
$$F=880\, \mathrm{N}$$

Note the only difference is the increase of r from 6,378,100 m to 6,731,100 m, or a 5.5% increase. That is significant, but not overwhelming. The force on Earth's surface is 980 N while the force at ISS orbit is 880 N. This force is weight. Thus, an object in ISS orbit weighs 90% what it does on Earth's surface.

Why don't things in orbit fall then?
Now that we know there is only a small decrease in the force of gravity a few hundred miles up in orbit, the next question is why don't the things fall then? The answer is that they do. This isn't some silly trick answer either. Objects in orbit are falling towards Earth at all times. Indeed, orbit is accurately called free fall.

Why don't they hit the Earth then?
This question leads to the key aspect of orbit. It isn't the height; it's the speed. When we put something in orbit, the bulk of the fuel is used not to get the object high, but to get it moving very fast. I calculate that it takes about 9 times the energy to get an object to orbital velocity as to get it to orbital height. To understand why this is important, let's look at the picture from above again:

Now I have no idea which direction the astronaut is moving, but let's assume it's from left to right. Notice the curvature of the Earth below him. It's slight, but it's there. The Earth is nearly a perfect sphere, thus the curve is constant. If you travel in a straight line on the Earth the surface will slightly curve down and away from you. This drop off is very slow, and thus not noticed. We can figure out how fast the drop off occurs, and the answer is 7.98 inches per mile. To be clear, this means when you travel one mile on the Earth's surface you drop about 8 inches (relative to a flat plane parallel to your first step).

How long would it take to fall 8 inches?  Since acceleration due to gravity is constant we can use the kinematic equations to find the answer.
$$d= v_i t + \frac{1}{2}a t^2$$
d is distance traveled (7.98 inches = 0.202692 meters)
vi is the initial velocity (0 in this case so this term drops out)
t is time, what we are looking for
a is acceleration, which in this case = g = 9.80665 m/s2

Doing some shuffling we find:
Solving for t, we find t=0.2033 seconds.

Thus, it would take about 0.2 seconds to fall 8 inches. Here's an interesting question: What would happen if you traveled a mile in the 0.2 seconds it took you to fall 8 inches? You would fall 8 inches closer to the Earth, but the surface of the Earth would also drop away about 8 inches. In the end you would be no closer or farther from the surface of the Earth. This is precisely what orbit is.

A mile in 0.2 seconds works out to about 18,000 mph. We tend to think that very fast speeds are unstable, but this is only because of atmosphere, which creates drag and slows things down. If there was no atmosphere then things would continue at whatever speed they are at indefinitely. It should now be clear why things must be lifted to be put into orbit. It is not to get them a little bit higher above Earth's center of gravity. It is to get them out of the atmosphere so that the incredible speeds required for orbit can be achieved.

Orbits tend to be ellipses, and rather complicated. But, for our purposes, we can treat them as perfect circles. Here is the formula for circular orbits:
$$v=\sqrt{\frac{m_2^2 G}{(m_1 + m_2) r}}$$
v is orbital velocity
m2 is the mass of object being orbited (Earth)
G is the gravitational constant
m1 is the mass of the object orbiting
r is the distance between (the center of masses of) the two objects

Notice that if m1 is insignificant compared to m2 that the bottom term becomes m2 * r. Since the top is (m22 * G), a $$$\frac{m_2}{m_2}$$$ can drop out to 1, leaving:
$$v=\sqrt{\frac{m_2 G}{r}}$$
Since the mass of Earth is constant, the only thing that matters is height above Earth. You should already be thinking that this height won't have much effect at normal orbital heights since it is only a 5.5% increase in r. We can use Google calculator to do this math for us very easily.
At Earth's surface, v=17,685 mph
At ISS orbit, v=17,215 mph
Which comes very close to Wiki's figure of 17,239.2 mph. To put these numbers in some context, a 747's cruising speed is about 570 mph. The fastest known plane was the SR-71 with a top speed around mach 3.3 or 2200 mph.

Tuesday, July 12, 2011

What I Saw in North Korea and Why it Matters

A good talk by a guy with first hand knowledge of both North Korea (from visits) and nuclear weapons (from working at Los Alamos).

Sunday, July 10, 2011

Web Comics

I have a folder called web comics with 15 or so links in it that I check every day.  Often, it's the first thing I do in the morning* before eating or peeing or breathing.  I've decided to share the list of these web comics with the rest of the world.  Many of these will not be much of a surprise if you are familiar with web comics.  In addition, the humor of most could be described as nerdy, eccentric, and absurd.  Actually, that more or less describes my life.
*"morning" may actually be late afternoon

Here's the list.  They are vaguely in order of how much I like them:
xkcd - Probably the most popular nerdy web comic out there.
Saturday Morning Breakfast Cereal - The same description for xkcd could be used here, although they do differ quite a bit.  Probably my favorite web comic.
Married To The Sea - I used to think he found old drawings and gave them absurd captions.  However, some of the drawings are too ridiculous to be real.  Updated 365 days a year.
Toothpaste For Dinner - Ran by same guy as MTTS.  Pretty much just awful drawings with funny text.
Cyanide & Happiness - I suppose this may be the most popular web comic, or at least the one I most often see copied and pasted to random sites.  Humor could probably be summarized as 'offensive'.
Buttersafe - Would probably rank higher if it updated more than twice a week.  Humor could probably be summarized as 'absurd'.
Amazing Super Powers - Hard to pin down the humor on this one.  Perhaps, 'people who would be poor role models'.
Three Word Phase - There's a 1% chance you will love it.  There's a 99% chance you will say "okay?".
Surviving the World - A unique execution.  The author draws the comic on a chalkboard and then takes a picture of it.  I suppose they are supposed to take the form of life lessons.
Abstruse Goose - Good, rather heavy on the nerdiness.
Something of that Ilk - A recent addition to my list.
Doghouse Diaries - I'm running out of descriptions that aren't covered by my general one.
channelATE - Why am I writing description when you should just be looking at the actual web comic?
Cowbirds in Love - Could probably be summarized as 'inoffensive'.
Basic Instructions - Taking the form of instructions on handling life's problems, it is a bit heavy on text, but good.
Questionable Content - I think this could be summarized beautifully as 'hipster soap opera'.  I'm not sure how I started reading it, or why I continue, but I am sure that reading it is probably the gayest thing I do.

Honorable Mentions:
Perry Bible Fellowship - A comic that isn't really updated anymore.  However, it would probably be at the top of the list if it were.  I think it was published in a newspaper, whatever the hell that is.
The Oatmeal - Not really a web comic.  More of a guy ruthlessly tearing people apart with drawings.

Thursday, July 7, 2011

Overwhelmingly Large Telescope

People are talking about the debate to stop funding the James Web Space Telescope.  In this discussion some one brought up the OLT, which is a ground based telescope that would cost $2.2 billion (newest JWST estimate is $6.6 billion) and have much greater resolution than even the JWST.
While the original 100-m design would not exceed the angular resolving power of interferometric telescopes, it would have exceptional light-gathering and imaging capacity which would greatly increase the depth to which humankind could explore the universe. The OWL could be expected to regularly see astronomical objects with an apparent magnitude of 38; or 1,500 times fainter than the faintest object which has been detected by the Hubble Space Telescope.

Q&A: Bill Gates on the World’s Energy Crisis
Chris Anderson: How has Fukushima changed your perspective on nuclear power?
Bill Gates: What happened in Japan is terrible, and there are many reasons it should have been avoided. It’s a 1960s plant design, generation two, put into service in the early 1970s. Emergency planning and execution were quite weak. The environmental and human damage is clearly very negative, but if you compare that to the number of people that coal or natural gas have killed per kilowatt-hour generated, it’s way, way less. The nuclear industry has this amazing record, even equipment from generations one and two. But nuclear mishaps tend to come in these big events—Chernobyl, Three Mile Island, and now Fukushima—so it’s more visible. Coal and natural gas have much lower capital costs, and they tend to kill only a few at a time, which is highly preferred by politicians.