Physics Today, the Flash and project Rosetta

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A random conflation of three separate items for this post:

Physics Today’s Facebook page just added a link to a Q&A session they did with me about my book.  The reviewed it in the last issue of the journal, and it got a very nice review from Edward Belbruno, a physicist I respect quite a lot.

The Flash can run on water!  At least, so says the episode last night.  According to his lab rat friends, he needs to run at 650 mph to do this – is this accurate?  I think the answer’s lower: more like 60-100 mph.  Still an impossibility, but not so impossible an impossible.  The issue is momentum transfer: every step he takes across the water transfers some fraction of his momentum to the water.  The rate of momentum transfer is the force he applies; Newton’s third law says that an equal force is pushing up on him.  A quick estimate says that the speed is about the square root of (g (the acceleration of gravity) times the stride length (maybe 2 meters?) times a fudge factor (which should be somewhere between 10 and 100, in lieu of difficult detailed models)).  Putting all this together, the needed speed is about 50 meters per second, or about 100 mph, maybe even lower.  Running up the side of a building is a different matter: if he tries to run up fast, he’ll just bounce off because of his high speed of approach.  Better he should run up a long ramp and launch himself into the air, except that landing after doing that is a problem…

Of course, the big news today is Philae, the lander for project Rosetta, landing on comet 67P/Churyumov-Gerasimenko.  It may have bounced once after harpoons failed to anchor it to the surface, which worried the scientists, for good cause. The escape velocity of a body like it depends on two things: its density and its mean radius.  Because it’s small and light (most comets are loosely-held conglomerations of dust and ice), the escape speed is going to be very low.  It’s about 4 km across, roughly 1,000 times smaller than Earth; if its density is 1/10 that of Earth, the escape speed will be about 3,000 times less than Earth’s (escape speed goes as size times square root of density.)  This might lower the escape speed to meters per second, making it very possible for it to drift away on a bad bounce.

xkcd, as usual, has an excellent comic covering the landing.

The first images look amazing.

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For the budding science fiction writer: More local color

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The third in our sequence of posts for those who are starting to write science fiction.

So now you’ve picked your world and the star it circles.  You’ve figured out how far away it should be.  What should the world look like?  How can you make it distinct?

There are limitless ways in which you can pursue this.  Exotic fauna is one way: make the animals different from those on Earth.  We’ll explore this in an upcoming post.  I’m going to concentrate on the flora in this one: what should vegetation look like on your planet, assuming it has vegetation at all?

Flowers come in all shapes and sizes and colors.  The local quality of light may make some differences, but you are pretty much free to choose what you want in this regard.  However, leaf color is probably going to be determined by the star you’ve picked.

Stellar spectra

Light curves from three types of stars

The figure shows a schematic diagram, representative only,  of the spectrum of different classes of stars.  This shows the relative amounts of power which the star emits as a function of the wavelength of light.  Human eyes are insensitive to most light: our eyes are most sensitive in the wavelength region in which our sun emits the most light.

On Earth, leaves are green because Earthly chlorophyl absorbs blue (shorter wavelength) and red (longer wavelength) light predominantly.  Why this is so is a little bit tricky.  The chemical pathways by which plants absorb light and convert it into energy are complicated, and involve no less than about 8 photons per reaction.  Red light has low energy photons but can be used directly for photosynthesis.  Blue light has high-energy photons, but can be “down-converted” to lower energy to make them useful for photosynthesis.  Because of this, photons of wavelengths which appear blue and red to our eyes are used for photosynthesis on Earth and are absorbed, while middle wavelength photons, i.e., green light, is reflected,  leading to leaves being green.

Vegetation under different stars is probably going to look different.  Dr. Nancy Kiang and her colleagues at NASA have investigated the most likely chemical pathways for energy uptake for vegetation on planets circling other stars.  Note that the M-class star emits less light in toto than the sun does.  Dr. Kiang and her group theorized that plants on worlds circling M-class stars would need every available photon; if they absorb all light, they would appear black.  On the other hand, planets circling F-class or brighter stars would have too much light, especially in the short wavelength spectral region.  They might have to reflect the blue light, leading to blue-looking leaves.

These are just a few of the details which the science fiction writer needs to keep in mind.  In the next post, we’ll discuss how the distance of the planet determines the length of the year.

For the budding SF writer, part 2: Local color

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Now that we’ve fixed where the planet is going to be, we need to think about what life is like on the planet – quite literally.  There are milions of details to consider – let’s just pick one to start out with.  Let’s think about the star and how that’s going to affect what you see when you look around.

Everything starts with the star.  Luckily for the writer, stars are all pretty simple in some respects.   The star’s luminosity determines its color, which will determine how things look on the planet — at least, to any human visitors to it.  Remember, if we have an Earth-like planet at some distance D from the star, how bright the star is relative to our sun (L) will be about D*D, although there will be some adjustments for atmospheric composition and albedo (see my previous post.)

Here’s a table summarizing the information  on stellar coloration as a function of luminosity:  this is only data for what are called “main sequence” stars, that is essentially middle-aged stars which “burn” hydrogen into helium in their cores.  If you want to use a star in its old age, or a newly forming protostar in a story, you have to dig a little deeper.

L Color
.01 Red
.1 Orange
1 Yellow
10 White
100 Blue-white
1,000 and higher Blue

As stars get increasingly dim, a larger fraction of their light will be in the infrared spectrum, that is in long wavelengths which we can’t see.  As they become increasingly bright, more of their light will be in the ultraviolet – still invisible to they eye, but at shorter wavelengths than we can see.  (This can also lead to obvious complications for humans visiting such planets.)

There’s a lot of room for play when you start thinking about the color of different things on the planet.  Let’s start with the sky.  Earth’s sky is blue because light from the sun is scattered by air molecules.  They scatter short wavelengths (that is, bluer light) more readily than longer wavelengths (i.e., red light), which is what gives the sky its characteristic blue tint.  When you look at the sky, you’re seeing light which has been scattered.Because of this, the coloration of various features of sky light should more or less mimic the properties of the star: skies on planets with reddish stars should be blue, but less blue than our own sky – maybe greenish blue or green?  Detailed computer simulations could show if this were true.   Particles in the atmosphere due to smog, pollen or volcanic eruptions will change the sky color; for example, fire from smoke or volcano can make the sun or moon appear green or blue when seen through it (hence the phrase, “once in a blue moon”, which doesn’t mean the second full moon in a month.)  Atmospheric refraction warps the appearance of the rising sun and moon: thicker atmospheres will warp them more, thinner ones less.  It’s again something to have fun with when thinking of story details.  The green flash is due to atmospheric refraction and layering of the atmosphere when the sun sets over a flat landscape like the ocean: an ocean planet with the right atmosphere could have an extended green flash every night…Now that we’ve gotten the sky colors, let’s go on to the landscape, and think about what plant life and ground cover will look like, in the next post on this subject.

For the budding SF writer, part 1: Where to put your planet

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Note: What I write here was covered in Poul Anderson’s 1960-something essay, “How to build a planet”, plus other sources.  However, it’s worth restating.

This is the first in a series of posts for non-scientists who want to use science in their science fiction stories effectively.  I’m going to start with a venerable one, how to design a planet suitable for Earth-like life.  There’s a simple rule which makes it very easy to begin, although you have to tweak it (nothing’s ever too simple.)  Imagine you have a planet circling a star.  Let’s say that the star is L times as bright as our sun, and the planet is D times as far away from the star on average as Earth is from our sun. For example, since Mars is about 140 million miles on average from the sun, and Earth is about 93 million, D for Mars is about 1.5.  (I’m rounding)  In order for the planet to be roughly the same temperature as the Earth (which is to say, suitable for Earth-like life) there is a relation between D and L:  L should be approximately equal to D*D (that is, D-squared.)  That is, if D=1, L=1*1=1.  If D=2, L=2*2=4; if D=1/3, L=(1/3)*(1/3) = 1/9.

People usually start the other way, by picking a star and then calculating the distance, but doing it this way makes the math something you can do in your head.  The reason for this rule is that the light from the star (the main source of energy warming the planet) spreads out in all directions, and decreases as the square of the distance from the star.  If you have two planets in orbit around the same star, and one is twice as far from the star as the other, then the illumination of the second is 2*2=4 times less than the illumination that the first one gets.  By using the rule that L=D*D, we compensate for that.

This is a good place to start when you’re thinking about where to put your planet, but a bad place to stop.  There are many caveats to the simple rule.  First of all, it assumes that the orbit is roughly circular – the orbits of many planets aren’t.  Secondly, it ignores planetary albedo, the average amount of light which the planet reflects back into space.  Earth’s averge albedo is about 30%, meaning that it absorbs about 70% of the light from the sun.  Planets with higher albedos need to be moved closer to compensate.

Finally, it ignores the effect of the atmosphere.  Earth’s atmosphere traps heat due to a mild greenhouse effect due to a number of gases in the atmosphere; it warms up the planet by about 30 degrees Celsius on average.  Venus has a runaway greenhouse effect because its atmosphere is 95% carbon dioxide; its surface temperature is about 450 degrees Celsius, far, far warmer than it would be if position is all we needed to worry about.  Take the advice given to any starting writer: pay attention to your story’s atmosphere!

In the second post in this series we’ll discuss how L determines the type of star which the planet circles.