Friday, 4 August 2017

Why are science teachers so obsesssed with units?

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Have you ever felt like feeding your teacher/ lecturer their text book because, after spending hours pouring over the pointlessly dry and complex physics problem they set, they gave you no marks – even though you got the answer right – because you forgot to put the units?

If you haven’t…. congratulations! You either are a robot from the future, sent back in time to make everyone else feel bad about themselves*, or you have something to blackmail your physics teacher with. Something big. Because I still make that mistake from time to time, and I have freaking PhD in Physics.

But there’s a good reason why you should make the effort not to forget the units - not just in school but in life. Imagine I asked you to do me a favour and buy me "a milk, just a milk, one milk - go, go, go, right now," from the shop down the road. Once you got there you'd find that ‘a milk’ could mean this….

A milk.

...or it could mean this…..

Another milk

…or this….

A recyclable milk

You might be a bit surprised and upset, when you get back, to find I actually mean one of these:


You might be a bit mad. You might ask ‘why has this idiot wasted my time and sent me on a wild goose chase without telling me exactly what he wanted?’ You might be concerned that you were sharing a room with a madman who expected you to get highland cows from the corner shop. And, If I then told you it was to demonstrate why you need to put units on your exam questions, you’d probably shout at me and throw the milk at my head**.  

So it’s a good thing this is just happening in our imaginations. 

But it is exactly why your teacher is being so pedantic about the units - because not putting in units opens has caused some very expensive misunderstandings: NASA once crashed a $115 million space probe into the planet Mars, because a computer program gave them information in kilometres when they expected it in miles - and didn't put 'km' after the number to let hem know.
Result: Flat spaceship at the bottom of yet another crater on Mars.

Mars actually has this crater, it's not CGI or anything. Mars is literally laughing at us. Courtesy of NASA.

No-one wants to explain to their boss why they just blew a hole in the planet Mars (or, as a more realistic example, why the expensive door they ordered for the office is too big for its frame) so getting students to put the right units on things is just one of those life-skills teachers try to get you in the habit of doing.

So, while your teacher may or may not be mean, pedantic, dull, or weird smelling, give them a break on this one thing: Putting the right units after your answer really is worth the effort to do.

Which units?

What units to use? Elephants are what my daughter (she's six) recommended, but elephants are frowned on as units of weight, length, or smell, because you have to fed them so much, take them for walks, and pay vet bills. 

Nor do they fit into a pencil case very well. Courtesy of the BBC.

So in physics we mostly stick to the SI units system, which is a collection of units for basic things that can be used in combinations to cover most situations. For example distance is measured in meters, and time is measured in seconds, so speed, which is distance travelled per unit of time, gets the unit of meters per second, or m/s, or sometimes even ms-1 (they all mean the same thing, it’s just different styles of writing ‘meters per second’). 

Below is a table of the S.I. units.  I really recommend you do your best to learn them – it's worth the time, even for things outside of Physics exams:

Unit nameUnit
Definition Dimension
metre m length
  • The distance travelled by light in vacuum in 1299792458 second.
kilogram[n 2] kg mass
  • The mass of the international prototype kilogram.
second s time
  •  The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
ampere A electric current
  • The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length.
kelvin K thermodynamic temperature Θ
mole mol amount of substance N
candela cd luminous intensity
  • The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

* That seems a very petty reason to actually go back in time but, if you are, I'm not going to give you a hard time about it. You might turn out to have a secondary mission to kill anyone who finds out about the first mission.

** If you actually turned up with a cow, which is very unlikely but not entirely impossible, I would call you 'Master'. Whether you wanted me to or not.

Friday, 30 June 2017

Answers for authors: What would a real space battle be like?

Above: A full solar eclipse, seen from space. It has nothing to do with battles in space, it's just cool.

"What would a real battle in orbit be like?"

There are two ways to think about this question*:

What would two nations of Earth fighting in space be like?

What would Earth fighting off an invasion from extraterrestrials be like?

Let's look at the first one this post and save the alien invasion for next time - although bear in mind that much of what we're about to look at could apply to aliens with similar technology levels to Earth's.

As far as I can find out** no armed confrontation has ever taken place in space.  But there has been a hell of a lot of military activity in Earth orbit, and the information released on it gives us some material to work with

Why fight in space?  
Everything that gives modern western forces their technological and tactical edge uses space-based systems: Drone surveillance, Reaper drones, battlefield communications, guided smart bombs... even tanks depend on satellites. The images of Russian troop movements around Ukraine came from them, and the weapons that destroyed Saddam Hussein’s military wouldn’t have hit their targets without them
Even presidential phone calls rely on a small fleet of them — the Advanced Extremely High Frequency constellation

What kinds of examples can we look to?
Since it's a real field of warfare today, we have something to base our pace battle on - and a motivation for it: Dominate space and you can dominate the air, the land, and the sea. 
It's easier to find information on older military operations in space, so let's start with some fairly odd gems from the cold war:: 
  • The Soviet Almaz space station, built to orbit over American territory and take pictures, was fitted with an R23M cannon, in case any sneaky Apollo astronauts decided to board it and leave the cosmonauts hogtied with gaffa tape like floaty space pinatas. The design was abandoned, as the gun's recoil during test firings kept changing the space station's orbit.
  • Ronald Reagan initiated the 'Star Wars' program (officially called the Strategic Defense Initiative) - essentially a series of satellites and ground bases toting various advanced weapons - never really produced much, as the idea was way ahead of the era's technology. But it laid a lot of foundation for future military missions.
  • In the 1950's and '60's the US experimented with using nuclear weapons to wipe out enemy satellite arrays – a nuke produces no shockwave in space, but emits a pulse of rapidly changing electric and magnetic fields that cook the chips of any computer caught in the blast radius. The tests, called operation Fishbowl, were so successfully they created a miniature aurora, and took out six satellites... as well as most of the electronics on the island of Hawai below.
  • The Space Shuttles, those great symbols of peaceful American space exploration, were re-designed (on the insistence of the National Reconnaissance Office) to fly on highly secret military missions, often with military crew. On one occasion astronaut Ken Mattingly, who was also a rear admiral by the time he retired, was ordered to file false flight plans and travel documents to cover up taking the shuttle on a secret mission. 
In more modern times, and since the retirement of the Space Shuttle, in-space military shenanigans seem to have become more oriented around robotic missions. I say 'seems' because the world's military leaders aren't keeping me up to date on their deep space black ops for some reason. Even so, since tracking satellites and spaceships is a hobby anyone with a telescope can do, we know it still goes on:
  • The Russian satellite known as Kosmos 2499, and Object 2014-28e, was launched on a rocket meant to be carrying three communications satellites. Only later was it revealed to have been carrying 'object 2014-28e' as well. Once in orbit the mysterious satellite did something very odd: It chased down other Russian space satellites, and rendezvoused with the spent booster stage that placed it into orbit.  
  • US air force has been operating its small fleet of Boeing X37B unmanned mini-shuttles since April 2010, smashing records for length of time spent in space, and performing "classified missions in support of long term goals". It is certainly possible an X37B could chase down a satellite and damage it with a weapons in its payload bay.
  • In 2008 the Chinese decided to fly small satellite, called BX-1, close to the International Space Station. It then performed a mission in the space around a Chinese space station that had many of the hallmarks of an anti-satellite weapon test.
Is that a Virgin Galactic launcher, or a missile? The truth is it all depends on where you aim it, and Richard Branson is building a fleet of these so... be nice to him, OK? No stealing his lunch money or anything like that...
The problem is that there are also many totally peaceful uses for satellites that can do these things – for years space agencies around the wold have been developing small satellites that could rendezvous with, refuel, repair older satellites, and safely de-orbit dead ones. But as Bob Christy’, who used to track Soviet spy sats for the US, told Financial Times magazine:
“People talk about them being inspectors, but if you have the ability to manoeuvre up to another satellite in space to inspect it, you also have the ability to destroy it.”
Putting up a fight:
To add some defence to this potential space offence, Princeton university (among others) think it's certainly possible to fit countermeasures to satellites: Better manoeuvring thrusters, jamming devices, decoys, or even cannons like the old Soviet Almaz space station, are all rumoured to been tested. And a report (linked here), dating from the Reagan administration, lays out the approaches being considered at that time - including laser and particle based beam weapons.

A real incident to work from?
There has been an incident where one nation's anti-satellite weapon (accidentally) destroyed another nation's spacecraft: On January 11 2007, 865km above the Chinese mainland, a weather satellite was blown to smithereens by a missile fired from the Xichang spaceport. More than 2,300 pieces of shrapnel— each lethal to anything it hit — were released into orbit. Think a small version of the orbital debris storm in ‘Gravity’.

If you just went 'what?' go and watch the movie 'Gravity'. Go on, this is a blog post, it's patient. 

Done? Like that, but smaller – more of a space squall than a storm - but it took out the Russian BLITS satellite.

In effect the incident was ignored - and BLITS was so small and inexpensive the worst Russia was likely to do was sue. But it's a salutary lesson: A full on battle in Earth orbit would have a huge potential for collatoral damage

Sooner or later, every space fairing nation would lose.

Fighting in space and cyberspace:
But there's an element here that we're missing: Although blowing up or sabotaging enemy satellites is fun, cool, and looks great on your CV, the most energy efficient way to shut them down is to hack them.  Where it can be done not only can you deprive an enemy of the satellites use you can use it to send them misleading data – although you might want to hold off on the satellite readings of flying Scotsmen with laser powered bag pipes, for fear of giving your game away a wee bit.

A recipe for a realistic space battle?
So we know there is some gearing up being done, and the elements for an in-space battle are there -  but it looks like a battle in space isn't likely to be much like Star Wars, with space ships close enough to see each other exchanging bright beams of energy. Instead, some general possibilities seem to be:  
  • Nothing would happen for ages, and no other vehicles would be visible. Then you'd explode - hit by a missile, or debris moving too fast for the human eye to see, fired from the ground or another craft too far away to see. 
  • ASAT missiles would be fired at those craft in a low enough orbit to be hit, and clouds of debris (intentionally released and just from casualties) would pose a constant threat. If the battle went on for long enough, eventually just being in orbit would be seriously risky.
  • There might be chases, as a saboteur satellites tried to close with a target. Both would, again, be too distant for human eyes to see for most of the chase. The target might defend by trying to manoeuvre away, jam the attackers signals to ground, deploy decoys, or perhaps even use physical weapons like Almaz's  cannon to shoot it's pursuer to bits.
  • There could also be standing decoys, designed to fool ASAT weapons into hitting a worthless target, being deployed ahead of the battle.
  • Satellite constellations, ground stations, and other spacecraft like the X37B, would be trying to jam each other electronically
  • In an all out conflict nukes would be being set off as EMP weapons.
  • Hackers, probably working from the ground, would be trying to take control of, and subvert each others satellite networks 
Above: An X37B being checked after landing. The HazMat suits are because the hydrazine used in it's manoeuvring system is toxic by the way.  At least... I assume that's what it's for. Imagine if you farted in one of those things.
I'm not a soldier - so all I can say is that this is a possible image of war between modern day human forces in space. All of it would be trying to gain advantages for air, sea, or land forces. It would be battle of silent, often almost invisible and instantaneous, destruction. It would be largely fought between robotic satellites and remote controlled spacecraft, responding to pre-programmed instructions, or general commands from ground bases - Human reflexes and co-ordination simply aren't up to the speeds and distances involved, once vehicles got close to each other. The best thing a manned vessel in orbit could do is return to Earth immediately - out there it would be nothing more than a target.

But what about the green four eyed elephant in the airlock? What if we had to fight off an extra-terrestrial invasion?

I'll save that for next week.

*That's a big ol' lie,  there are zillions,  but keeping it to the two that pop into my brain fastest keeps the post to a readable length,  and gives us a blog sized entry to the topic. 

**That doesn't mean it's never happened, just that it was kept quiet if it did. 

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Sunday, 6 March 2016

Critical angle and total internal reflection

We have already seen that when a ray of light travels from air into glass its direction is changed (have a look at this post for a refresher): The angle between it and the normal line ( the line at right angles to the boundary between the two substances) gets smaller in the denser medium. When the light goes back, the opposite happens: The angle gets bigger. 

Above: A light ray entering something denser.

Above: A light ray going from something dense to something less dense.

That leads to something slightly odd: If the ray's angle to the normal line is already pretty big inside the glass, it's possible for it to become bigger than 90 degrees as it moves into the air.

Which looks like this:

 Above: Video courtesy fo QuantumBoffin.

Even though the surface isn't a mirror, the light cannot get out of the glass! In fact you might well have seen this if you've ever swum underwater:

Above: Look at the surface of the water. It's reflective, like an upside down mirror. But the world above hasn't been mirrored off, the camera is just being held at a viewing angle where total internal refraction occurs.

This effect is called 'total internal refraction', and the maximum angle to the normal line that an incoming ray can have, before it undergoes total internal refraction, is called the 'critical angle'. To find the critical angle we use this equation:

Where n1 is the refractive index of the material the ray is entering, and n2 is the refractive index of the material the ray is leaving.

The use for total internal reflection you're probably most familiar with is the 'cat's eyes' on the road*. Have you ever noticed how real cats eyes reflect light, and seem to glow from the inside?

Like this: Cute, yet ever so creepy. You just know they're planning on eating you.

This effect inspired Percy Shaw to build an artificial version, for marking the edges and middle of roads. An actual cat has a layer of reflective cells at the back of the eyeball, that let it 're-use' incoming light to see better, but a lot of modern versions use a transparent block with lots of tiny cube shaped facets embedded into one face. In this type of reflector, light enters the smooth face, and then bounces around the back surface as a result of a total internal reflection - like this:

Above: Video courtesy of Thorlabs.

Another use is in tracking criminals, by their footprints!
Revision questions:


What is the critical angle for a ray of light passing from inside a body of water to the empty air above? Water has a refractive index of 1.3, and we'll assume air has an index of 1.


How does the critical angle change if a sheet of glass with refractive index 1.5 is placed on top of the water?

Answers here.

*If I were a bad man I'd make a roadkill joke there, but I'm not so... whoops.

Saturday, 20 February 2016

Things that waves do, part 2: Diffraction and interference

We've looked at reflection and refraction.... so what other things do waves do? Well there are two important ones.

We covered many of the ideas behind this before, in this post, but to recap: Remember how every wave is a moving oscillation in whatever medium it's moving through? When two waves meet, or pass through each other, they add together. So, at every point along the two waves where they meet, the amplitude is the amplitude of one wave plus the other wave.

That's nice and simple - just remember that where the wave drops below the X axis it has a negative sign - and a negative added to a positive actually subtracts from it. This means that we can get waves interfereing destructively (decreasing each other's amplitude) like this.... 

Above: Destructive interference.

....or we can get waves interfering constructively (increasing each other's amplitude), like this....
Above: Constructive interference.

When two waves are coherent (see this post for an explanation of coherence and phase), and have zero phase difference, they have the same sign along their whole length so you get the most increase in amplitude. When two waves are 180 degrees out of phase (so their peaks align with their troughs) you get the most reduction in amplitude.
Once we extend this idea to waves on a 2D surface, or  a 3D volume, we will start to see more complicated patterns arising - and we'll look at that after the diffraction section below - but it all stems from these basic principles.

The formal definition of diffraction is:

"The process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge."

This is a fairly counter intuitive property of waves, and a fairly important one. Imagine we've got an ocean wave passing through a small gap. If the gap is bigger than the length of the wave then the wave passes through fairly unaffected...

But if the gap is smaller than the wavelength than the waves doesn't pass through cleanly, it sploshes through....

... and on the far side of the barrier the 'splosh' acts like water falling straight down: It produces a new set of circular waves. The effect is called diffraction, and it actually happens in all types of waves. The 'how' of a light wave going 'splosh' is a bit complicated - in fact for non-ocean waves the 'splosh' is just a good metaphor, but the diffraction effect still happens anyway! 
In fact the incoming waves don't need to 'splosh' very hard to produce this effect, they just need to have a wavelength that is big compared to the size of the gap they're trying to get through -  so even a big gap can cause diffraction if the waves passing through are also big. The Open University has a nice demonstration that uses a water tank:

The smaller the gap is compared to the wavelength, the closer to a semicircle the diffracted waves get. But some diffraction happens even when the slit is very large, as shown below.... 
That's important to get, because it will help with the next part about diffraction: Diffraction can happen even when the 'slit' only has one edge. If we go back to ocean waves we can actually see how this isn't ridiculous - watch a few seconds of this video, showing storm waves hitting a section of sea wall:

See how the waves 'splosh' off the edge of the sea wall, creating circular patterns of backwash?  Something similar happens to any wave hitting an object with an edge: The wave diffracts off the edge, now going in a different direction, and this lets the wave reach areas it couldn't get to just travelling in a straight line. And, just like all kinds of diffraction, longer wavelengths diffract more than shorter ones.
A good example is a person with  two radios, one shortwave and one long wave, trying to send a signal to the other side of a very tall wall. The short wavelength radio waves only diffract slightly, and so cannot reach the receiver:

...But longer wavelengths diffract much more, and do reach the receiver....
...which is why you can usually get your favourite radio station, even when there're houses or even hills in the way.

Just before we move on, it's important to point out (because it's sometimes an exam question) that no property of a diffracted wave is changed by the process, other than it's direction.
The last thing we need to know, that makes diffraction very interesting (and ultimately leads to the weirdest area of physics, quantum mechanics), is that it only occurs with waves. That makes it a good test for whether or not something is a wave, and early scientists used an experiment that combined diffraction and interference to test whether light is wave. The experiment was set up like this:
 ....if you look at the white screen you can see that at certain points the light waves interfere constructively, and at others they'll interfere destructively - so on the screen, if light is a wave, we should see some areas that are dark, and some areas that are light. And, if you actually do the experiment, you'll see something like this:
That's definitely a pattern of light and dark, which the old times scientists took as proof that light is a wave.for a hit more on exactly how their ingenious experiment was done with their simple technology, check out the video below. 

Friday, 5 February 2016

Radiation and half life crib sheet (and practice questions).

Half-life and radiation factsheet:

General information:

Radioactivity happens because:

1.       Some atoms are unstable, and break apart or loose smaller particles to become more stable atoms – this called the ‘activity’.

2.       Activity is measured Becquerel’s.

3.       When atoms decay they give off radiation.

4.       The amount of time for half the radioactive atoms to decay into stable atoms is called the half life.

5.       Radiation ionises atoms ((knocks off an electron from them) which is damaging to DNA.

Types of radiation are:

How penetrating?
What is it?
What’s its charge?
What’s a use?
Weighting factor
Alpha particle
Will be stopped by a few cm of air, or skin. Least penetrating.
Two protons and two neutrons bound together
Used in smoke detectors
Beta  particle
Will go through air and thin metal, like aluminium, but not thick or very dense metal like lead.
An electron
Measuring  the thickness of paper in industry
Gamma ray
Will go through thick metal sheets, concrete, or rock. The most penetrating.
A very high energy photon (an electromagnetic wave, like light or radio waves)
Radiotherapy, to kill cancer cells

Natural sources of radiation are everywhere, most are natural radioactive atoms in the air (like radon gas), the rocks and soil (like Uranium ore), or dissolved in water. Some radiation comes from stars or other objects in space, and is called cosmic radiation.



Activity is defined as ‘The number of atoms to decay per second): the equation for this is:

Where A is activity in Becquerels, N is the number of atoms that decayed, and  t is the time in seconds their decay took.

Doses of radiation:

Radiation is measured in two ways:

Absorbed dose, which is measured in Greys (or more often milligreys). The equation for Absorbed dose :

Where D is absorbed dose in Greys, E is the amount of energy the radiation carried in Joules, and M is the mass of the thing absorbing the radiation in kg

Equivalent dose takes into account how damaging  each kind of radiation is, by multiplying the absorbed dose by a weighting factor (a unitless number picked by observing how much damage each type does). It’s equation is:
Where H is the equivalent dose in, W is the weighting factor, D is the absorbed  dose in Greys. Equivalent dose’s  unit is Sieverts.

Half-life and radioactivity practice questions:

1: Three kinds of radioactive source give off three different kinds of radiation.
·         Source A gives off radiation that goes through  aluminium sheet but is stopped by  a lead brick
·         Source B gives off radiation that is stopped  by aluminium sheet, but travels through several centimetres of air
·         Source C gives off radiation that is stopped by several centimetre of air.
Which source is giving of which type of radiation?
2: A chunk of radioactive material has a half-life of twenty three seconds. 
a)    How many whole half-lives does it go through before its activity has dropped to 6.25% of the original value? Hint:  1 whole half-life takes the activity to 50%, 2 half-lives takes the activity to  25%, and so on – you can draw a table of  half-lives vs % of activity if it helps.
b)    How many seconds before the activity level drops to 25%?
3: A 4 Kg cat gets hit with 50 joules of radiation.
a)    What is its absorbed dose?
b)    The radiation is alpha particles, with a weighting factor of 20. What is the cat’s equivalent dose?
4:  A radioactive source is made of 10,000,000 radioactive atoms. After 2 seconds 1,000,000 have decayed. What’s its activity in Becquerel’s?