Asteroid Belt: Not as Dense as Advertised

This is a scene that is repeated over and over again in movies, books, games and any other area where science fiction has a place. Our protagonists are in a ship, it's being pursued hotly by some alien doom vessel trying to destroy them, and their only chance at escape/survival is to dive into the asteroid belt and hope that the alien pilot can't keep up with the many collisions and flying rocks! Basically, flying through a scene that looks very much like this:


This scene has one very large mistake in it: space is very, very big. There are two consequences of this; the first is that it is unlikely that one will find an entire asteroid belt that is full enough of rocks to have this scene at all, but there will be more on this later. The second consequence is that most space flight "chases" are going to be taking place with the ships light seconds apart, with the chasing ship firing, and then waiting to see if the shot hit or not. There is a small subset of people who might enjoy that type of scene, and this is the type of person who likes submarine thrillers; who waits on pins and needles to see if the shot fired hits and if the ship was detected soon enough for the enemy to get their own firing solution. But for most people, having 20 minutes of movie waiting to detect an explosion five light minutes away would be pretty boring.

The truth of the matter is, although the asteroid belt is a comparatively densely packed part of space, there just aren't that many rocks in there. The entire asteroid belt of our solar system is only 4% the mass of the Earth's moon! Even more interesting, more than half of the total mass is contained in the four largest asteroids. What this means is that a spacecraft is not very likely to find an asteroid, let alone have to dodge around one. According to Alan Stern of Space Daily, there is a less than 1 in 1,000,000,000 (billion) chance that a ballistic trajectory satellite would hit even one of them when passing through the asteroid belt. To give some perspective on the amount of rock this is, if one were to smash up all the rocky planets in the solar system and place them in the asteroid belt, there would be 10,000 times as much rock as is in the belt right now. This would only bring a ship up to a 1 in 100,000, chance of hitting something when passing through the asteroid belts, assuming that the size distribution was similar to what it is now, and that the ship doesn't dodge. So, the odds of hitting a rock in the asteroid belt with a ballistic ship are similar to the odds of throwing a rock in the ocean and randomly hitting a whale. This would seem to be an unreasonable amount of rocky material to have in a single system. Real asteroid belts are hard to tell apart from the rest of the system from the inside.

So, the moral here is that if a chase scene of this type is needed, have it be near a planet. Maybe a moon broke up, maybe they've been dragging rocks nearby for mining purposes, maybe the planet just has unusually thick rings. But having an entire asteroid belt this dense is over the top.

Dragon*Con Photos

Here are all our Dragon*Con photos and these are from our Roomate. If you got to this site because I gave you a card, try to find yourself, and have a look at my site! Science Advising will continue later this month.

Dragon*Con Awesomeness

Hello to everyone who found this site because you got a random business card at Dragon*Con. If you don't need any science advising, please feel free to check out the site and see if anything amuses you. If you do, feel free to follow the email link and contact me. Also, I am going to be posting all the pictures I took at Dragon*Con for all to look at, so if you want to see yourself in your awesome costume, come and check it out!

Awesomeness Quotient

This is sort of general advice for anybody making anything science fiction. The degree to which you can get away with something that is scientifically unsound is proportional to how much more awesome it is than what real science would allow. In other words, if you have a plot device which requires bad science to exist, take a look at what real science would allow. If your device is much, much cooler than the real science, and isn't too unreasonable, you're probably good.

This can be represented by a simple formula:

Allowability = (Plot Device Awesome - Real Science Aweseome)/ Badness of the science

What this boils down to is, if your plot device is very awesome, and your science isn't too bad go for it. If, on the other hand, your plot device is kinda underwhelming, and/or the amount of bad science required to realize it is very high, then probably come up with a different plot device.

I'll give an example of each so you can see what I'm talking about. Let's start out with the bad science that doesn't in any way contribute to the story. What we are going to use is one of the worst science movies of all time, Mission to Mars. The scene which is the most guilty of this is the scene where the astronauts are transferring from their damaged space craft to an orbiting supply ship. Tim Robbins' character overshot the supply ship and was drifting off into space. His wife sets up her suit to use half of its fuel to try to thrust out to him and save him. Right there we have our problem. If you use half your fuel to thrust away from something in space, it takes the other half to stop. What they did was allow her to thrust away from the ship and then magically stop in space for her to be able to turn around and live! Let's try running this through our equation.

(Bad plot device - Both of them die ending the movie sooner!)/Terrible Scene = Shouldn't have been used.

Now, to help us feel better, let's give an example of a really good scene. The new Star Trek movie, love it or hate it, this movie had good science. Now, if you've seen this movie, you're probably wondering what I found to pick on. I admit, I didn't find this, it was pointed out to me by the most excellent Phil Plait. There was a scene where the Enterprise was coming up out of Titan's atmosphere to to ambush the Romulans. I know what you are thinking, this scene had some great science, Titan's atmosphere was the correct color, the Saturn images looked straight out of Cassini, what's the problem? Answer, Titan's orbit is in the same plane as the rings, you wouldn't be able to see them from Titan. However, let's just run that through the equation for this scene:

(Awesome view of Saturn's rings - Not seeing Saturn's rings)/Awesome Dramatic Scene = Must include in movie.

So, as you can see, even if the science is a little bad, you can use it in movies. Just try not to make the science types out there cringe.

Iron Giants Want Science Too (Spoilers)

The other day I was watching The Iron Giant. Now, this is basically a family movie about a giant robot from space that lands on earth and is damaged so it can't remember its purpose. This movie is overall a fantasy, and it doesn't worry me too much when it does odd things like have the robot eat metal. There was one thing that was bad enough to throw me a bit, and that was when the Robot heroically saves the town from the nuclear weapon at the end. Overall, I quite liked this scene, it showed the basic insanity of what was going on, and the self sacrifice was a nice touch, and I tend to think they did a very good job with it. It does bring to light one slight misunderstanding people have about how nuclear bombs work. Unlike conventional explosives, nuclear bombs won't be set off by an impact event as was shown in the movie.

In general, there are two types of fission warheads. The first type of warhead is what's called a gun-type warhead; basically you have two slugs without enough mass to go critical, but when brought together go supercritical and you get a large explosion. This type of nuclear bomb would, in fact, detonate just as was depicted in the movie. The other type of nuclear warhead is what is called an implosion type nuclear warhead. It uses much less fissile material, and instead has a series of explosive lenses which, when detonated very precisely, cause the fissile material to compress and go supercritical producing a nuclear blast. By 1957 the United States had switched to using almost entirely compression style nuclear warheads due to the fact that they use less fissile material, and are much safer to operate. Further, I was unable to find a single instance of the United States using a gun type warhead in a nuclear missile, they were only put into gravity bombs. Crashing into the side of one would almost certainly destroy the explosive lenses and prevent a supercritical explosion.

So, what does this mean for The Iron Giant and other movies of its type? The giant might have been blown apart when it destroyed the warhead due to the small explosions of the lenses inside the warhead, but there would not have been a nuclear blast as depicted. This is, admittedly, a very minor nitpick, but it was severe enough to pull me out of the story when it happened, so I thought it was worth mentioning. The Iron Giant was an excellent movie though, and I recommend you watch it if you haven't.

Speed Racer can really really go! (Oh Spoilers!)

I recently watched the film Speed Racer by the Wachowski brothers. Imagine my surprise that I really enjoyed the film! Overall, I think that the stunning visuals and bright colors, coupled with good to excellent acting force me to give this movie a bit of a pass as far as physics goes. But there was one scene that made me wonder if, even given the magical properties of car and driver, would be possible.

The scene in question takes place during a cross country race, which Speed has engaged in so that he might help the government with some investigations. At one point during the race, Speed's car is forced off the track! Not one to be stopped by a little setback like being forced down a cliff, he drives his car back up a nearly sheer cliff face! The question is, could even the Mach 5 have been able to achieve such a feat?

The answer should be no, probably not, but that would be boring. To find this answer though, we need to know two things. One, what is the primary force driving the car, and the second, what is the maximum force output that it's capable of. The answer to both questions can be found in how the car drives around normal turns.

In the movie, they state that the speed of the vehicles driving around the track is "800 km/h." We'll assume that this is a high end as we use this number to allow us to approximate the speed at which he goes around the turns. I'll guess he's going about half his maximum speed when taking the tight hairpin turns. If we assume that the Mach 5 can take a 10 meter radius turn at about 400 km/h, which is reasonable given what we see, then what would the acceleration be to keep him in the turn? Using the equation V^2/r, you find that the centripetal acceleration would be on the order of 200g. Notwithstanding that no human could survive that level of acceleration, this would at least be possible given a car made out of unobtainium and some magical drive system. It does tell us one important thing though: the primary motive system for the car is not the motors driving the wheels, but the thruster at the back of the car. To see why this is you need only look at how tires function. Tires rely on frictional forces between themselves and the road to provide the force on the car. The equation that describes this force is mu*normal force * gravity, where the normal force is the weight of the car and mu is what is known as the coefficient of friction. To provide the 200g's required, mu would have to be equal to 200, since the highest coefficient of friction that I could find was gecko feet, at 8, we can safely assume that this number is ridiculous. Now that we have all this, we can discuss the mountain climb.

We can see clearly in this scene that the mountain is not a sheer cliff, so there would be some small force holding his wheels to the ice. Combined with the spikes on his tires, this might be enough grip to allow him to control his ascent. Now, given that the nominal acceleration of the Mach 5 is 200g, minus 1g of gravity, he can not only drive up the cliff, but drive up it at 199g. Although the overall physics of this movie is silly with respect to the car, if you give them the Mach 5, the rest is surprisingly consistent. Well done, Wachowski's.

Death Race (Standard Spoiler Warning)

The movie Death Race has some great scenes of cars driving around a track on a prison island, firing weapons at each other, and generally doing awesome things. Many of the events in this movie are rather difficult to critique, as no details were given for most of the cars. This was a good thing as it allows audiences to enjoy the movie without the pickier people getting upset. Though, there were two particular scenes that would make even the most casual of science conscious persons cringe.

Both scenes are caused by the same plot device, which is a modification to the main character's, Frankenstein's, car. Frankenstein's car is a Ford Mustang fastback which has been heavily modified. The car is armored on all sides, and has both offensive and defensive weaponry. Although we have to speculate about some of the modifications and the performance specs, the car would mass in at about 4577 kg. The bulk of the extra weight comes from a defensive shield installed on the back of the car called the Tombstone. Using images from the movie it appears to be made of 4 plates of steel, getting wider as they reach the car. Each plate is about 2 inches thick, with the narrowest plate being 27 inches wide and 40 inches tall, and each plate closer to the car being 12 inches wider than the preceding plate. This gives the shield a maximum thickness of 8 inches at the center and a mass of 1855 kg using 7.85 g/cm^3 as the density. In the movie the stated thickness of the Tombstone was 6 inches, but with the varying thickness, we'll assume they meant that as an average thickness. The suspension of the car would have to be designed to handle this kind of weight, so we can assume that the spring constant for the rear suspension must be on the order of 1250 lbs per inch. The car in this configuration performs such that all the cars on the track have approximately the same handling and acceleration profiles.

At two points in the movie, the Mustang has to drop the Tombstone off of the back of the car for various plot related reasons. In and of itself this seems like a very good idea. 1855kg of steel flying back at the car behind you would certainly cramp his style, plus your car is now lighter, but in the movie there was no measurable difference in the performance of the car from before the Tombstone was dropped to after.

There are two major effects that would happen from dropping this large of a mass off of a car. The first is that the rear suspension would be heavily unloaded. Since the suspension was balanced for having an extra 1855 kg hanging off the back end, removing that would cause it to very quickly unload. If we assume that the car was designed with about 4 inches of droop on the rear suspension, then dropping the rear plate would cause that to decrease to less than one inch, and it would be almost impossible for the suspension to work in turns or over dips in the road. This would first cause some bouncing when you first unloaded it, potentially causing a loss of control, and would then cause your rear end to hop around the turns. It's possible that Frank 1 and 2 were both good enough drivers to compensate for the hop, but there should have at least been the initial bounce.

The second is that the car would now be lighter. Much much lighter. If you use the number that we assumed for the car's mass, dropping the Tombstone off of the back would decrease the mass from 4577 kg to a mere 2722kg! This is a 45% decrease in the total mass of the car. As we know, Force = Mass * Acceleration. Since the engine is putting out the same amount of force, if you could still put the power to the ground you would expect a 45% increase in acceleration. To put this into perspective, if we make the reasonable assumption that the car went from zero to sixty in 6 seconds as set up before dropping the Tombstone, the new zero to sixty speed would be 3.57 seconds! Even if we assume that he wouldn't be able to put the power to the ground via the wheels quite as efficiently, he should still have a marked improvement in acceleration over the other cars on the track which haven't dropped 1855kg off the mass of their car, but they pretty clearly keep up with Frank despite his last ditch emergency efforts.

The movie was fun, but they could have easily shown these effects on the car without changing the story in any way, and there would have been a much lower cringe factor for the car conscious in the audience. After all, they are the most likely to watch this kind of movie.