omenti

the moon's going to be okay

You've probably heard that an old Space X rocket will crash into the Moon on the forth of March.  It's very likely and a good excuse to look at a few other things.

 

The object in question is the second stage of a Falcon 9 that was used to take the Deep Space Climate Observatory to L1, the first Lagrange point in the Earth-Sun system.¹  The observatory monitors the Sun, specifically the solar wind, from a vantage point a million miles closer to the Sun.  In addition to science, it it gives about an hour's warning for satellites in orbit as well as power stations who need to prepare for large solar storms. 

 

The Falcon's second stage has been looping around the Earth and Moon in an unstable orbit making a few close approaches to both Earth and Moon.  This type of orbit crashes into either the Earth or Moon or is perturbed into a solar orbit.  Exactly where is difficult to predict, but almost certainly it will be on the far side of the Moon.  Too bad as it might be visible through a telescope if it were to hit an area in the night side of the Moon's near side.  

 

That brings up another point.  The far side of Moon is the part away from us. We see the dark side, at least some of it, all the time except when the Moon is perfectly full. 

 

The Moon's rotation is tidally locked with the time it takes to make an orbit.  Initially the Moon wasn't and rotated at a faster rate. Over millions of years tidal forces slowed it down to the point where it became locked.  Roughly speaking the Moon is slightly egg-shaped rather than a perfect sphere.   If the long axis through the Moon isn't pointed at the Earth, a torque is exerted which moves it back into position. Once locked it would take a large force to unlock the rotation. 

 

The Moon's far side is only the dark side when we see a full Moon from Earth.  If you're interested in how bright the Moon's surface is, the far side tends to be much brighter than the side we see.  And the elliptical orbit of the Moon permits us to observe a bit more than half of the Moon's surface over about a month, although only half at once.

 

A few other neat things about the Earth-Moon system.  The two bodies orbit a common point, or barycenter, about 1,700 km below the Earth's surface. (the barycenter for our solar system is sometimes outside the Sun, currently it's on the inside).  

 

And finally the average distance from the Earth to the Moon is increasing at about the rate your fingernail grows. Tidal forces are also slowing the Earth's rotation.  There's a point where a day on the Earth will be the same as the lunar day - something like 46 days long.  It's a bit in the future though..  long after the Sun becomes a red giant and incinerates the Earth and long after before the Sun explodes forming a planetary nebulae.  The Earth and Moon will have vanished long before, but planetary nebulae are beautiful.

 

 

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¹ In a two-body system like the Earth and Sun, there are five points where the gravitational force on an object  exactly equals the centripetal force necessary for that object to move with the bodies.  L1 is closer to the Sun and great for a solar observatory, L2 is behind the Moon and a great place for a telescope like the James Webb Space Telescope. (note the little orbit around L2 - it turns out the JWST orbits L2, rather than sitting there so the Earth doesn't shield it from the solar energy it needs to operate.  L3 is where the anti-Earth of science fiction would live.. (except it's unstable, so not really), an L4 and L5 are useful points on our orbit to put solar observatories that look at the Sun from an angle other than head-on.

 

 

 

 

skiing!

a minipost

With Beijing approaching I started into a piece on skiing, but the number of drawing needed to illustrate carved turns, sidecut radius, reverse camber, self-turning, plowing and so on was daunting.  Looking around I found a good, not very technical, discussion of downhill skiing. The discussion falls apart on freestyle and ski jumping. I'll save freestyle for later as it's a rich area.  But I know a little about ski jumping.

 

The point of ski jumping is to jump as far down a hill as possible while showing style. Contestants are judged on how far their landing is from a critical line know as the K line (kritisch is critical in German).   The main hill at the PyeongChang Olympics was K98 - the K line was 98 meters from the end of the jump.  The long hill was K125.

 

The first phase is the in-run.  A ski jumper releases from a metal bar at the top of the ramp and begins to turn  gravitational potential energy from the height they're at for kinetic energy.  They crouch to lower the area their body presents to the oncoming air.  Aerodynamic helmets and tight fitting suits are used and their arms are out behind them.   Ski jumps have refrigerated ceramic tracks that form a very slippery layer of ice.  New snow or warm sunlight can dramatically change frictional drag and ski waxes are picked for specific conditions.

 

The ski jumper has a good deal of speed and momentum as they reach the takeoff table at the end of the ramp.  It may look angled up, but that's an illusion. It's still slightly down and the jumper needs to change from the crouch they've been in and physically jump into the air.  You don't just fly off.  The timing and power of the jump are critical elements.

 

 The ski jumper/ski combination is a glider at this point subject to three forces:  gravity, aerodynamic drag, and lift.  They've changed from a minimal aerodynamic profile to something more like an airfoil with greater surface area and the best possible shape. The skis move to form a V shape and  with the ski jumper in control of the angle of each ski (a total of six angles) and their hip and chest angles. Their arms are held slightly apart from the body to add some additional area while keeping aerodynamic drag at a minimum.   The best lift to drag in competition is about 1.6 - for every meter a ski jumper drops, they travel 1.6 meters forward. A common sea gull has a L/D of about 10 and modern airliners are in the 15 to 18 range.  

 

The V ski position revolutionized the sport in the mid 80s. Sorting out all of the angles and learning how to  change them for differing conditions is necessary for winning.  The aerodynamic problem is still very computationally difficult, so large low speed wind tunnels as well as racks on top of vans are used for experimentation and training.

 

You might think that a heavy jumper, coming off the ramp with greater momentum, would have an advantage, but the force of gravity is more important and lighter jumpers fly farther.   There were body mass index requirements, now lighter skiers are penalized with shorter skis that reduce lift.  Ski jumpers still tend to be very thin.

 

The flight is rarely more than four meters above the ground, the flight plath roughly following the hill's downward slope. Landings are highly technical and judged for style.  The transition from the V flying configuration to parallel skis one foot ahead of the other requires timing, strength and balance. 

The longest ski jumping events are on K185 and longer hills - "ski flying"  It's not an Olympic event, but shows off the flying portion:

 

But one of the most memorable performances was that of Eddie the Eagle in the Calgary 88 games.  (it won't embed .. watch at the link) You can place last and be the most celebrated athlete Calgary.  If you've stood at the top of a ramp, you get an appreciation of what it must take to even try it.

 

flavors of augmented reality

Augmented reality has been with us for a long time.  Glasses and contact lenses turn the eye into a two element lens to correct issues with our eye's lens.  We use sunglasses to change the intensity and/or polarization of incoming light.  Some of these are responsive to changes in the scene around us.  Some of us wear hearing aids.  A few use assistive animals like seeing eye and epilepsy dogs. 

 

Some of these applications like glasses have fixed characteristics. Others like dogs can be highly adaptable.   Apple offers good example of computationally adaptive AR with AirPods and the cameras on iPhones and iPods.  The technical press tends to describe AR as overlaying a computational display - often information from the cloud keying on local state information like who you are, what you're interested in, your location, and so on.  

 

As it happens reality is much richer than what we experience with our senses.  Visible light is only a tiny segment of the electromagnetic spectrum and soundscapes are much richer. There can be any number of useful and recreational explorations into the larger reality - science does this all the time.  Wearable AR can open up wider videos into the incredible richness of reality itself.

 

It's been interesting watching Apple's shift in how they position their watch.  At first there seemed to be an assumption that it was a fashion accessory like a normal watch with some extra complications.  After a few generations it evolved into a health and safety wearable.  Initially Apple's visual AR device will probably offer simple visual overlays that you might see on a smartphone but with time I suspect it develop a strong health component that will be a major attraction.  People with serious glaucoma could get a view of the areas their eyes are missing.  As displays get better perhaps a visual AR wearable could replace glasses entirely matching your prescription and becoming a computational tool with the tricks we see in computational photography.  "zoom to the moving target and slow motion..." or "reduce glare from the water.."    It's easy to sit down and come up with a dozen ideas that aren't games.  The list gets even richer when you start linking in other sensors. 

 

We'll see wearable AR used in many modes, but I suggest the augmentation of local reality will be very important in ways we don't yet appreciate.  There are a lot of hurdles that make me think early devices will be crippled, but after a decade this could be a very rich area indeed.

 

 

 

 

 

orbits

It's almost Perihelion Day!   I may wish people Happy New Year, but the beginning of a calendar year is artificial, so I celebrate a specific point in our orbit every year.

 

The orbit of the Earth is elliptical. Not terribly so, but enough we're about 5.1 million kilometers closer to the Sun in early January than we are in early July.  The closest point is the perihelion and the furthest, the aphelion.  The exact time of perihelion varies from year to year - this year it's the 4^th of January at 6:52am UT or 1:52am EST.  Californias get to celebrate on the 3^rd.

 

At perihelion the Earth is at its fastest speed in our orbit - 30.29 kilometers per second.  At aphelion, the slowest point, we've slowed by about a kilometer per second.  Given its closeness, the apparent disk of the Sun has about 7% more area at perihelion than it does at aphelion.  That seems to bother people as it's Winter in the Northern Hemisphere.  In fact the Earth is a bit more than 2°C colder at perihelion than at aphelion - an artifact of the distribution of the continents and a bit of physics.

 

There more land in the Northern than the Southern Hemisphere.  Water has a higher heat capacity than land.  Think about a desert.  During the day it can get scorching hot, but it rapidly cools off at night.  The ground doesn't hold heat as well as water.  In July the Northern Hemisphere has long days that allow the land to heat up for longer periods raising the temperature of the air above it and raising the average temperature of the Earth in the process.   In January the Southern Hemisphere is getting the most sunlight, but most of it falls on water, which doesn't heat up as much as the land. 

 

There are some interesting rabbit holes one can get into and much can be learned by studying the positions of bodies in our solar system and people have been doing it for thousands of year.   Some civilizations were very sophisticated in calculating and predicting astronomical events even though their models of the solar system were wrong.  An early computer that makes your jaw drop is the Antikythera mechanism.  People have been studying it for over a century and Scientific American has a fine summary of what's currently known about the device.

 

In 1900 diver Elias Stadiatis, clad in a copper and brass helmet and a heavy canvas suit, emerged from the sea shaking in fear and mumbling about a “heap of dead naked people.” He was among a group of Greek divers from the Eastern Mediterranean island of Symi who were searching for natural sponges. They had sheltered from a violent storm near the tiny island of Antikythera, between Crete and mainland Greece. When the storm subsided, they dived for sponges and chanced on a shipwreck full of Greek treasures—the most significant wreck from the ancient world to have been found up to that point. The “dead naked people” were marble sculptures scattered on the seafloor, along with many other artifacts. Soon after, their discovery prompted the first major underwater archaeological dig in history.

One object recovered from the site, a lump the size of a large dictionary, initially escaped notice amid more exciting finds. Months later, however, at the National Archaeological Museum in Athens, the lump broke apart, revealing bronze precision gearwheels the size of coins. According to historical knowledge at the time, gears like these should not have appeared in ancient Greece, or anywhere else in the world, until many centuries after the shipwreck. The find generated huge controversy.

...

 

A more technical discussion appears in a recent article in Nature (open access)

 

A Model of the Cosmos in the ancient Greek Antikythera Mechanism

Tony Freeth, David Higgon, Aris Dacanalis, Lindsay MacDonald, Myrto Georgakopoulou & Adam Wojcik

The Antikythera Mechanism, an ancient Greek astronomical calculator, has challenged researchers since its discovery in 1901. Now split into 82 fragments, only a third of the original survives, including 30 corroded bronze gearwheels. Microfocus X-ray Computed Tomography (X-ray CT) in 2005 decoded the structure of the rear of the machine but the front remained largely unresolved. X-ray CT also revealed inscriptions describing the motions of the Sun, Moon and all five planets known in antiquity and how they were displayed at the front as an ancient Greek Cosmos. Inscriptions specifying complex planetary periods forced new thinking on the mechanization of this Cosmos, but no previous reconstruction has come close to matching the data. Our discoveries lead to a new model, satisfying and explaining the evidence. Solving this complex 3D puzzle reveals a creation of genius— combining cycles from Babylonian astronomy, mathematics from Plato’s Academy and ancient Greek astronomical theories.

 

Back to now.  Happy Perihelion Day to all of you!

and a comment

I'm  not fond of the idea of the Earth making a circuit every year as, the Earth never comes back to the same spot in any reference frame.  It's roughly close enough for most, but in four dimensional space time it's something of an approximate helix expanding out along the time axis.  You can never go home. Good enough reason to look forward!