Mynd you, Møøn bites Kan be pretti nasti…

Today, NASA successfully put a new mission into lunar orbit: GRAIL, for Gravity Recovery and Interior Laboratory. Great acronym, weird name, right? What this mission will do is map the gravity field of the Moon, and use that to probe the interior composition. The basic idea isn’t all that complicated: fly a probe around the Moon. If it goes above a region where the density is higher, there will be a slightly stronger gravitational pull, and the spacecraft will accelerate a bit. By carefully measuring the spacecraft position and velocity, you can make the lunar gravity map.

In detail, that’s a bit tougher! What NASA has done is launch two probes, GRAIL-A and GRAIL-B, that will fly in the same orbit, one behind the other^*. They’ll stay in constant communication, sending radio pulses to each other. The timing of these pulses allows an extremely accurate determination of their separation: their distance will be known to an accuracy of about a micron: that’s a hundredth the width of a human hair, or the size of a red blood cell!

So how does that help? If one of the two probes speeds up or slows down, the radio signal timing will change, taking more or less time to get from one probe to the other. The amount of change is related to the force of gravity felt by the probe, and that in turn is related to the density of the material below. In practice, making a gravity map this way is extremely complex, but it’s been done before here at Earth using probes like GRACE and GOCE. It’s tried and true.

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What happens if you hold a slinky at the top end, let it extend, and then drop it? Here’s a video setting up the problem:

OK, so what do you think? Now watch this video to get the answer:

Were you correct? I’m proud to say I figured out what would happen, and even for the correct reasons. But then I’m used to problems like this; when you write a science blog you wind up thinking about how best to explain certain phenomena, and acceleration due to gravity is a common one. All parts of the slinky are accelerated by gravity equally, but the bottom of the slinky is being supported by the top. When the top is let go, it takes time for the bottom to find out, and in that time the slinky can collapse.

Here’s another question then: what if the slinky were looser, that is, less springy? Would the same thing happen?

I’ll leave that to you to figure out. But I’ll note that at the end of the second video, they post another question answered in a third video. I got that one right, too, and again for the right reason. Maybe there’s a future in science for me.

Tip o’ the Hooke’s constant to Jeri Ryan on Google+. Yup, that Jeri Ryan.

In late March of 2011, an extraordinary event occurred: a black hole in a distant galaxy tore apart and ate a whole star (I wrote about this twice at the time; here’s the original post, and a followup article including a Hubble image of the event).

Now, there’s more info: the black hole, lying at the center of a galaxy nearly 4 billion light years away, has about 8 million times the mass of the Sun. When it tore the star apart, about half the mass of the star swirled around the black hole, forming twin beams of matter and energy that blasted outward at a large fraction of the speed of light. The folks at NASA’s Goddard Space Flight Center made a great animation to show this:

The star was ripped apart by tides. The thing about black holes is, they’re small: this one was probably about 15 million kilometers across. A typical star is about a million km across (the Sun is 1.4 million kilometers in diameter, for comparison). This means the star could get really close to the black hole, and that’s why it was doomed. The force of gravity drops with distance, so as the star approached, the side of it facing the black hole felt a far greater force than the size facing away. That stretched the star, and the stretching increased as the star got closer. At some point, the force was so great it exceeded the star’s own gravity, and it could no longer hold on to its material. The black hole won — as they usually do.

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[UPDATE (April 5, 2011): It turns out some of the descriptions I used below to describe a geoid were not accurate. I refer you to this page at the University of Oklahoma for a good description. I've made some changes below to hopefully ease any confusion.]

Most people think of the Earth as being a sphere. For most purposes that’s close enough, but it’s actually a spheroid, something close to but not precisely a perfect sphere. It bulges in the middle (as so many of us do) due to its spin, the Moon’s gravity warps it, the continents and oceans distort the shape. And the surface gravity changes with all this too; it’s different on top of the highest mountain, for example, compared to its strength in Death Valley.

So if you could map out the average shape of the Earth’s gravity, a shape where the gravity is the same no matter where you stood on it, what would it look like?

So if you could map out the Earth’s gravity — essentially, a diagram showing you the direction of "down" — what would it look like?

It would look like this:

That is a (somewhat exaggerated for easy viewing) map of the Earth’s geoid, produced by the European Space Agency’s GOCE satellite. A good way to think of the geoid is the shape a global ocean would take if it were governed only by gravity, and not currents or tides or anything else. If the Earth’s gravity were a little stronger in one place, water would flow toward it, and if it were weaker water would flow away. In the end, the surface of this global ocean would feel the same gravity everywhere, shaping itself to the geoid. If the Earth’s surface were an actual geoid, then the direction of "down" would point perpendicularly toward the geoid surface (or, in the same vein, if you had a carpenter’s level, the level would be, um, level if it sat parallel to the geoid). It’s the ultimate "sea level".

This may seem esoteric, but this knowledge is actually important. (more…)

[UPDATE: I have posted an article with more info on the earthquake and where you can donate money toward the relief efforts.]

Japan suffered a massive earthquake last night, measuring nearly magnitude 9. This is one of the largest quakes in its history, causing widespread and severe damage. Before I say anything else, I’m greatly saddened by the loss of life in Japan, and I’ll be donating to disaster relief organizations to help them get in there and do what they can to give aid to those in need.

While there isn’t much I can do to directly help the situation in Japan, I do hope I can help mitigate the panic and worry that can happen due to people blaming this earthquake on the so-called "supermoon" — a date when the Moon is especially close to the Earth at the same time it’s full. So let me be extremely clear:

Despite what a lot of people are saying, there is no way this earthquake was caused by the Moon.

The idea of the Moon affecting us on Earth isn’t total nonsense, but it cannot be behind this earthquake, and almost certainly won’t have any actual, measurable effect on us on March 19, when the full Moon is at its closest.

So, how can I be so sure?

The gravity of the situation

Here’s the deal. The Moon orbits the Earth in an ellipse, so sometimes it’s closer to us and sometimes farther away. At perigee (closest point) it can be as close as 354,000 km (220,000 miles). At apogee, it can be as far as 410,000 km (254,000 miles). Since the Moon orbits the Earth every month or so, it goes between these two extremes every two weeks. So if, say, it’s at apogee on the first of the month, it’ll be at perigee in the middle of the month, two weeks later.

The strength of gravity depends on distance, so the gravitational effects of the Moon on the Earth are strongest at perigee.

However, the Moon is nowhere near perigee right now!

The Moon was at apogee on March 6, and will be at perigee on March 19. When the earthquake in Japan hit last night, the Moon was about 400,000 km (240,000 miles) away. So not only was it not at its closest point, it was actually farther away than it usually is on average.

So again, this earthquake in Japan had nothing to do with the Moon.

Time and tide

So why would people think this is due to the Moon?
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It might seem like a tautology — and that’s because it is — but sometimes the only word you can use to describe an image from the Cassini Saturn probe is otherwordly:

[Click to engasgiantize.]

This otherworldy picture was taken on March 24, 2010. The big moon is Rhea, seen from 1.2 million kilometers (750,000 miles) away, and the little one below it is Epimetheus, from 1.6 million km (990,000 miles) away. Perspective makes them look right next to each other, but in reality the distance between them is the same as the Moon from the Earth! Saturn and its rings provide the backdrop for this stunning alien portrait.
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This is totally cool: an animated simulator that lets you make model solar systems! It’s put together by the PhET Interactive Simulations group at — hey! — the University of Colorado at Boulder.

All you have to do is put in the masses, locations, and initial velocities of the objects (up to four) and then hit "go". What you’ll probably find is that for almost any parameters you use, you won’t get a stable system. You’ll fling off the tiny moon, or drop a planet into the star, or collide two planets (when you do, one survives after a brief comical flash). There are preset conditions that will put together a stable simulation, so I suggest you start there and then tweak the numbers. The most fun thing is to fiddle with the mass and see what happens.

You’ll note a slider that says Accurate vs. Fast. That has to do with bin size. Basically, a simulation like this calculates the force of gravity of each object on every other object using Newton’s law. But it needs a time interval to do this: where will all the objects be after some period of time? You can pick that time step, but the smaller the time step the more accurate it will be. That’s because gravity works continuously. If you take the Earth’s current position and velocity and ask where it will be a year from now by just adding a year to the program, it’ll extrapolate the Earth’s current velocity direction! The program will take that velocity (about 30 km/sec) and multiply it by one year, and get a distance of about a billion kilometers. It’ll then place the Earth there. But that’s not right, because the Earth orbits the Sun; the Sun’s gravity is continuously changing the direction of Earth’s motion. So the smaller the time step, the more accurate the program will be.

At least, I think that’s what’s going on here. I’ve fiddled with programs like this before, and that’s what I’ve found. Roundoff error can be bad too; because the program can’t do the calculations exactly — the decimal value has to cut off somewhere — every step has a little bit of error in it. That adds up, and after a few orbits things can go wonky. This one does a pretty good job of that, it looks like.

Anyway, go play god with your very own cosmic erector set. It’s fun, and before you know it a long time will have passed… but you might get a feel for orbital mechanics. It’s worth it.