[I’m approaching the Desktop Project endgame here; I’m almost out of pictures to post. I’ve done this every day for weeks, and my computer desktop is almost clean! Of course, more stuff keeps coming in, so I could do this forever. But that would be cheating. Sweet, sweet cheating.]
I’ve got something different for you today. Over the past few weeks I’ve posted an illustration, and a couple of dozen pictures, but no graphs! That’ll change now, and I think this particular set of plots is nifty.
Whenever a big satellite is about to re-enter Earth’s atmosphere — like UARS, or ROSAT, or Phobos-Grunt — the media freak out. You start seeing numbers being thrown about of the odds of getting hit by a chunk of flaming debris, and I get lots of panicked email and tweets. Then I have to point out to people that the Earth has a lot of real estate for a satellite to come down on, and of that, 3/4 is water. And most of that is Pacific Ocean. So really, the most likely scenario is a re-entry into the Pacific, or some other ocean, and that’s that.
But is that really true? After all, satellites can have different orbits, inclined with respect to the Earth’s equator. So the odds of getting dumped in the ocean might be different for a satellite that’s over the equator versus one in a polar orbit (that is, orbits almost completely in a north/south direction).
Happily, orbital debris specialist Mark Matney did the math! In a paper published in the Orbital Debris Quarterly Newsletter (bet you didn’t know that existed!) he calculated those odds. He created two graphs for the paper, and both are really cool if you’re a graph nerd like I am.
Here’s the first one:
That plot shows the fraction of the total area of the Earth covered by land versus latitude. It’s easy to read: at 0° latitude — the equator — the amount of land is 23%. In other words, if you flew a plane around the world at the equator, you’d be over land 23% of the time.
In what is becoming an annual January tradition celebrating my laziness, I’m reposting this article about why astronomers are no fun at New Year’s parties. Well, they can be, but only until you actually say "Happy New Year!" to them, whereupon they’ll corner and lecture you about how to measure orbital periods. It’s amazing any astronomers reproduce. Anyway, here’s the article, which was a lot of fun to originally write, and even more fun to cut and paste here.]
Yay! It’s a new year!
But what does that mean, exactly?
The year, of course, is the time it takes for the Earth to orbit the Sun, right? Well, not exactly. It depends on what you mean by "year", and how you measure it. This takes a wee bit of explaining, so while the antacid is dissolving in your stomach to remedy last night’s excesses, sit back and let me tell you the tale of the year.
First, I will ignore a few things. For example, time zones. These were invented by a sadistic watchmaker, who only wanted to keep people in thrall of his devious plans. So for now, let’s just ignore them, and assume that for these purposes you spend a whole year (whatever length of time that turns out to be) planted in one spot.
However, I will not ignore the rotation of the Earth. That turns (haha) out to be important.
Let’s take a look at the Earth from a distance. From our imaginary point in space, we look down and see the Earth and the Sun. The Earth is moving, orbiting the Sun. Of course it is, you think to yourself. But how do you measure that? For something to be moving, it has to be moving relative to something else. What can we use as a yardstick against which to measure the Earth’s motion?
Well, we might notice as we float in space that we are surrounded by zillions of pretty stars. We can use them! So we mark the position of the Earth and Sun using the stars as benchmarks, and then watch and wait. Some time later, the Earth has moved in a big circle and is back to where it started in reference to those stars. That’s called a "sidereal year" (sidus is the Latin word for star). How long did that take?
Let’s say we used a stopwatch to measure the elapsed time. We’ll see that it took the Earth 31,558,149 seconds (some people like to approximate that as pi x 10 million (31,415,926) seconds, which is an easy way to be pretty close). But how many days is that?
This is one of the coolest videos I’ve seen in a while: during a routine reboost of the International Space Station to a higher orbit, the astronauts on board show that the station tries to leave them behind!
What a fantastic example of Newtons’s First law: an object in motion tends to stay in motion unless acted upon by an outside force. As the ISS circles the Earth, all the forces on it are balanced. You can think of it this way: the force of gravity pulling it toward the Earth is balanced by the centrifugal force (or the centripetal acceleration, which is equivalent*) outward. Because there are no leftover forces on the ISS, it feels like it’s in free fall, what some people call weightlessness. No force means no acceleration which means no weight.
However, that’s not always the case. Even a few hundred kilometers up, there’s air. It’s thin, but over time it robs energy from the ISS, dropping it lower in its orbit. This is called drag, and it’s a very tiny force (too small to feel on board the ISS), but it adds up over time. To prevent the station from falling too far and burning up, every now and again low thrust rockets are used to push it up into a higher orbit.
But that applies a force that is not balanced! Read More
I almost missed this, but an email from astrophotographer Anthony Ayiomamitis (whose photo I feature below) reminded me: tonight’s full Moon occurs at apogee, the point in the Moon’s orbit where it is most distant from Earth. I actually wrote quite a bit about this last year, so I’ll repost the article below. Full Moon occurs officially tonight at 02:06 UTC (10:06 p.m. Eastern US time), so in a couple of hours as I write this. Apogee occurs about 9 hours later (October 12 at 11:44 UTC), when the Moon will be 406,176 km (252,286 miles) from the Earth. It was at perigee on September 28, when it was a mere 357,555 km (222,174 miles) from us… but make sure you read the footnote below!
And I’ll note: the difference in size between the Moon at closest and farthest approach isn’t something you’d probably never notice it by eye, especially since you can’t compare the two at the same time. The change is gradual, and the Moon is actually pretty small in the sky. But it’s still neat when you take a picture and compare them…
I’ve been posting a lot of extreme close-ups of the Moon, but sometimes you can learn something by taking a step back.
For example, I imagine if I went out in the street and asked people what shape the Moon’s orbit was, they’d say it was a circle (or, given recent poll results, they’d say it was Muslim). In fact, however, the Moon’s orbit is decidedly elliptical. When it’s closest to Earth — the point called perigee — it’s roughly 360,000 kilometers (223,000 miles) away*, and when it’s at its farthest point — apogee — it’s at a distance of about 405,000 km (251,000 miles).
That’s a difference of about 10% — not enough to tell by eye, but certainly enough to see in a picture… like this one, by the Greek amateur astronomer Anthony Ayiomamitis:
[Click to emperigeenate.]
Amazing, isn’t it? The Moon is noticeably different! He took those images at full Moon, but seven months apart, when the Moon was at perigee (last January) and apogee (just a few days ago as I write this). It’s part of a project he does every year, and it’s pretty cool. He was able to get these images within a few moments of the exact times of apogee and perigee.
You might wonder how the Moon can be at apogee when it’s full one time, and perigee at another time it’s full. Read More
Today is the Fourth of July, Independence Day for us American types.
It also happens to be aphelion*, the point in Earth’s ever-so-slightly elliptical orbit when it’s farthest from the Sun. Perihelion — closest approach — happens in early January, and aphelion six months later. The dates change a bit from year to year because there aren’t an even number of days in a year (that pesky extra 0.24 in the 365.24 days per year messes things up), and there are other minor factors as well.
Today though, aphelion occurs on or about 15:00 UT (11:00 Eastern US time), when the center of the Earth will be about 152,102,715 km (94,512,245 miles) from the center of the Sun — give or take a few hundred meters. If you’re curious, that’s about 1.67% farther from the Sun than on average. That in turn means the Sun appears about 1.67% smaller in diameter than usual, which isn’t noticeable to your eye — and I don’t recommend trying to find out — but is pretty obvious in photographs using telescopes and heavy filtering, like this one from astrophotographer Anthony Ayiomamitis:
Cool, huh? When we’re farther from the Sun we receive a bit less heat, so perhaps those of you suffering from the midwest heat wave can take consolation that it could be worse by a couple of degrees right now.
Later today, coincidentally, I’ll be at a picnic with lots of solar astronomers. What do I say to them? "Hap-helion Fourth of July"? Or, "Enjoy us being at a(1+e) [where a = 1 AU and e = 0.0167] from the Sun today"?
That seems awkward. The thing is, I’m pretty sure a lot of them would get it…
* I pronounce it app-HEEL-eeyun, if you care.
[Update: My apologies: due to a cut-and-paste error, I had mistakenly listed the perihelion distance as the average distance of the Earth to the Sun (147 versus 149 million km). To avoid confusion, I simply replaced the error with the correct value. The rest of the post is correct since this wasn’t a math error but a typographical one, and I used the right value when doing my calculations below.]
Since last July, the Earth has been falling ever closer to the Sun. Every moment since then, our planet has edged closer to the nearest star in the Universe, approaching it at over 1100 kilometers per hour, 27,500 km/day, 800,000 km every month.
But don’t panic! We do this every year. And that part of it ends today anyway.
The Earth’s orbit around the Sun is not a perfect circle. It’s actually an ellipse, so sometimes we’re closer to the Sun, and sometimes farther away. Various factors change the exact date and time every year — you can get the numbers at the Naval Observatory site — but aphelion (when we’re farthest from the Sun) happens in July, and perihelion (when we’re closest) in January.
And we’re at perihelion now! Today, January 3, 2011, around 19:00 GMT (2:00 p.m. Eastern US time), the Earth reaches perihelion. At that time, we’ll be about 147,099,587 kilometers (91,245,873 miles) from the Sun. To give you an idea of how far that is, a jet traveling at a cruising speed of 800 km/hr would take over 20 years to reach the Sun.
Of course, since today is when we’re closest to the Sun this year, every day for the next six months after we’ll be a bit farther away. That reaches its peak when we’re at aphelion this year on July 4th, when we’ll be 152,096,155 km (94,507,988 miles) from the Sun.
Not that you’d notice without a telescope, but that means the Sun is slightly bigger in the sky today than it is in July. The difference is only about 3%, which would take a telescope to notice. Frequent BA Blog astrophotograph contributor Anthony Ayiomamitis took these images of the Sun at perihelion and aphelion in 2005:
This may seem a bit odd if you’re not used to the physics of orbital motion, but you can think of the Earth as moving around the Sun with two velocities: one sideways as it sweeps around its orbit, the other (much smaller) toward and away from the Sun over the course of a year. The two add together to give us our elliptical orbit. The sideways (what astronomers call tangential) velocity is about 30 kilometers (18 miles) per second, which is incredibly fast. But then, we do travel an orbit that’s nearly a billion kilometers in circumference every year!