Lunar eclipse part 2: lunar orbit precession

Precession is the way in which the axis of a rotation changes orientation. In other words, it's the way in which the axis around which an object spins is itself rotating through space. Watch this lovely film of the Moon rotating around the Earth https://www.youtube.com/watch?v=jWCBhVfeAQU Notice that the Moon always has the same axis of rotation relative to the Earth and that the Moon orbits the Earth at an angle relative to the plane of the the Earth's orbit around the Sun. Despite this fixed orbital angle, the Earth's journey around the Sun moves this axis through 360 degrees during the year. So the Moon stays fixed relative to the Earth but not relative to the Sun. An eclipse of the Moon occurs when the Sun, Earth and Moon are in line. You'll see from the animation that most months the tilted orbit means that when the Moon is behind the Earth it is too high to be in its shadow.

Emmy Noether on In Our Time

Last week's In Our Time on Radio 4, presented by Lord Bragg of Wigton, is about the mathematician and physicist Emmy Noether. Understanding the mathematics of Noether's Theorem is one of my lasting ambitions. She proved that the fact that doing the same experiment tomorrow and getting the same results, showing symmetry in time, is a consequence of Conservation of Energy; that doing the same experiment in different places and getting the same result, showing symmetry in space, is a consequence of Conservation of Momentum. For me, the best bit is in the epilogue on the podcast, where the difference between global symmetry and local symmetry is explained. https://www.bbc.co.uk/programmes/m00025bw

Lunar eclipse part 1

I saw part of last week's lunar eclipse but my photographs didn't work. This new camera doesn't work well in low light levels. There's a great composite image showing the stages of the eclipse at https://apod.nasa.gov/apod/ap190122.html However, the nagging question remained about why it doesn't happen every month. The shadow that the Earth casts into space is there all the time so why doesn't the Moon end up in it every month? I know that the answer is that the Moon's orbit is at an angle to the shadow but then why does it clip it some months but not others? I decided to start by calculating the length of the shadow cone that the Earth casts behind it. I used the method of similar triangles to get a length of 1.4 million km. This is the dark central shadow or umbra. The diagram has been simplified by ignoring the outer paler shadow or penumbra. The Moon is 0.4 million km from the Earth so definitely in range. Next up will be to put the Moon's orbit onto the diagram and then find out about precession.

A surprising carbon dioxide graph

This picture is from a display at a local attraction. It caught me by surprise. In the resources that I use to teach climate in class, the graph I use finishes at the point 290ppm and labels it "today". That graph does date from the 1990s I think. I was shocked to see that the new graph has reached 400ppm. And I have found the source of this graph: NASA https://climate.nasa.gov/climate_resources/24/graphic-the-relentless-rise-of-carbon-dioxide/ I know that the data going back 450000 years comes from air trapped in bubbles in ice. See the start of the film The Day After Tomorrow for footage of this going on. But now we seem to be a long way above any level from the last half a million years.

Hoar frost or rime ice?

This wire fence at Watchtree was amazing. But is it hoar frost or soft rime? Both produce spikes like this. Hoar frost is formed when the air becomes supersaturated with water vapour. At any given temperature, the air can hold a certain amount of water vapour invisibly before becoming saturated and forming condensed water droplets (ie fog). As the temperature drops, the air can hold less water vapour. Normally, this means that fog forms (it's how clouds form as water vapour condenses in rising air as it cools). Under certain conditions, the excess water vapour doesn't condense - the air holds too much water vapour for its temperature and is supersaturated. If that hits a surface that is below freezing point, it freezes instantly to become hoar frost. For rime ice, the water vapour condenses first in the air before freezing onto the object. This makes rime more directional. If there is a breeze, then the spikes grow into the wind. Since there were spikes on the far side of the fence but not the near side, this may be rime.

Fog bow at Watchtree

If you look at these two pictures, you might be able to discern two halves of a white arc. It was clearer through my polarising sunglasses and by tilting my head from side to side I could see that it was polarised because it disappeared with my head tilted at certain angles. With my hand as shown in the bottom picture, I am measuring 25 degrees. https://oneminuteastronomer.com/860/measuring-sky/ The radius is bigger than this. https://www.atoptics.co.uk/droplets/fogform.htm gives the radius as between 30 and 45 degrees, which sounds correct. When a rainbow is formed, larger droplets of water refract light giving the colours. Here the droplets are much smaller and diffraction dominates. https://www.metoffice.gov.uk/learning/optics/rainbows/fogbow

Measuring specific latent heat

 We did an experiment to measure the specific latent heat of fusion, which means the change of state from solid to liquid. We packed a glass funnel with ice and inserted an electric heater. We measured the voltage and the current and caught the melt water in a beaker. We ran the experiment for 900 seconds (15 minutes). We calculated the energy put in by the heater using the formula E=ItV. we measured the mass of the melt water and calculated the specific latent heat by doing E/mass in kg. Specific latent heat is measured in joules per kilogram.

One problem is that the warmth of the air in the room can melt water too. To find out how big an effect that is, a second funnel should be packed with ice but the heater not turned on. The mass of melt water from this can be subtracted from the mass from the main experiment. We could call this part of the experiment the CONTROL.

Janna Levin TED talk

I've been reading Black Hole Blues by Janna Levin which is the story of the LIGO experiment to discover gravitational waves. She's done a good TED talk explaining the idea of how colliding black holes can make space ring - although it was clearly done before the major discovery was announced. https://www.ted.com/talks/janna_levin_the_sound_the_universe_makes

Magnetic braking

This apparatus lets an aluminium wedge swing freely between the poles of a strong magnet. We would not expect aluminium to attract to a magnet. It is like any pendulum and swings for a long time before friction dissipates its energy and it stops.

This aluminium wedge swings once or twice before stopping. What's the difference? Both wedges cut through the flux lines that go between the north pole and the south pole of the magnet. By Faraday's Law an EMF is induced that is proportional to the rate of flux cutting. The EMF causes circular currents to flow, which are called EDDY CURRENTS and which I have drawn onto the aluminium. They act like electromagnets and are repelled by the magnetic poles as they swing in, slowing the motion. They are attracted as they come out, also slowing the motion. It doesn't work on the first pendulum because the slots cut into that pendulum reduce the size of the eddy currents. The "repelling in and attracting out" is a consequence of Lenz's Law which is a magnetic version of the law that says you cannot create more energy. The eddy current electromagnets cannot push to make it go faster as that would be creating more energy.

Wavelength of a wall

We found Andy Goldsworthy's "Taking a Wall for a Walk" in Grizedale Forest. The wavelength is not constant but is about 8 metres. So I was wondering about the frequency. But the wall is not moving so there is no group velocity with which to calculate the frequency. We could resort to De Broglie's equation and get the momentum, which would be Planck's constant / wavelength but that won't get us frequency. See https://physics.stackexchange.com/questions/62522/de-broglie-wavelength-frequency-and-velocity-interpretation for further discussion.

Why is my plant held up by a clamp stand?

My Amaryllis is in flower and very top heavy. The flowers are not evenly distributed around the stem and the stem is not straight. A force (weight) x distance from the pot means that there is a torque twisting the plant which means that it keeps falling over. The clamp provides an equal and opposite torque, meaning that the resultant torque is zero and the plant stays upright.

The indicator light on my cooker

Here's the indicator light for my oven. The light is on when the oven is cold and goes out when the oven reaches the correct temperature.

 We made a similar device by putting a thermistor in a potential divider with a 1000 Ohm resistor. We then put an LED in parallel with the thermistor.

 When the thermistor was cold, the LED was on. The thermistor had a bigger resistance than 1000 Ohms and so took a big enough share of the battery voltage to light the LED.

When placed in hot water, the resistance of the thermistor went right down so it took only a small share of the battery voltage and the LED went out. I assume that on the oven , the fixed 1000 Ohm resistor is actually variable, set by the dial to give a different trigger point for each temperature.

Newton's Laws and Oxford United at Fleetwood

Oxford United were brilliant in the second half at Fleetwood. Here's the warm up beforehand. A full description of the kicking of a football is a thing to behold. As the foot hits the ball, the ball exerts a force on the ball to decelerate and stop the ball according to Newton's Second Law. Then a reaction force from the foot acts on the ball by Newton's Third Law. This reaction force then acts to accelerate the ball forward according to Newton's Second Law. Or we could pursue an analysis using momentum. Newton wrote his Second Law as "resultant force = rate of change of momentum". As the foot hits the ball, the ball deforms so there is a definite time frame over which the foot is decelerated. If the force exerted by the ball on the foot is constant, then force x time = change in momentum. Force x time is called IMPULSE. The same impulse must act on ball and foot, so the ball will have the same change in momentum, provided no external force acts. Since momentum = mass x velocity, the ball can have the same momentum as the foot but a different velocity due to differing masses.

What causes the Aber Falls?

These are the Aber Falls near Bangor in North Wales.

On the way up, there is a hut with a lovely geological model of the area. The lower part of the valley is on Ordivician mudstones which erode more easily.

The highest part is made of volcanic rock.

The falls photographed seem to lie on a fault where magma has got in producing an intrusive igneous rock called microdiorite. This was very hot and has baked the surrounding rock - making metamorphic rock. The result is a harder rock that is more resistant to wear than the surrounding mudstones so there is a step down which the Falls proceed. The model is a wonderful explanation of the landscape.

Aeolian Harp - wires in a gale on South Stack

My last attempt to model the note produced by wind across overhead transmission wires failed. We experienced the effect again during a gale on South Stack off Anglesey. The note is low, down towards 100 Hz. Then I found this article by the great physicist, James Jeans https://books.google.co.uk/books?id=SUbCAgAAQBAJ&pg=PT94&lpg=PT94&dq=how+does+the+wind+in+the+wires+make+a+note&source=bl&ots=j_1AwDO2_z&sig=SUibbG1dTpoA9Pfo1QRCGTurY2w&hl=en&sa=X&ved=2ahUKEwjT0M2t99nfAhX-ThUIHXfCDdkQ6AEwFHoECAkQAQ#v=onepage&q=how%20does%20the%20wind%20in%20the%20wires%20make%20a%20note&f=false His analysis is for a 40 mph wind over half-inch rigging on ships. That would be the same sort of thickness as one of these power cables and the winds were strong enough to blow us over so would be close to 40 mph. He comes up with a figure of 261 Hz. That sounds about right. From experiment, he gets a vortex forming every time the air travels a distance of 5.4x the diameter of the cable. He calculates the distance traveled by the air in one second, works out how many diameters of rope that is and then divides by 5.4 to get the frequency. This is an Aeolian harp effect. Now I want to see one! https://en.wikipedia.org/wiki/Aeolian_harp

Density of carbon dioxide

I found this information at the Findhorn Community in Scotland. They are using a tree to illustrate the volume occupied by one tonne of carbon dioxide. A 10 metre diameter sphere has a volume of 523 cubic metres. There are 1000 litres in 1 cubic metre so 523000 litres in the sphere. At room temperature and pressure, one mole of a gas occupies 24 litres. This means there are about 22000 moles of carbon dioxide. One mole is 12 + (2x16) = 44 grams. So the mass of gas in the sphere = 968000 grams which is 968kg so almost 1000kg or 1 tonne. It works.

Benchmark on a milestone at Whinlatter

Before there were trig points on hill tops, there were benchmarks. The up arrow points to the level line. They started with an agreed place that was at sea level and worked by the process of levelling from one benchmark line to the next https://en.wikipedia.org/wiki/Levelling Originally, Victoria Dock in Liverpool was the defined sea level but after 1921, it moved to Newlyn in Cornwall - and then sea level was fixed there between 1915 and 1921. It won't be the same now! https://en.wikipedia.org/wiki/Ordnance_datum This benchmark is defined relative to Cockermouth. In 1899, it was 834.9 feet above Victoria Dock, Liverpool. This must have been from a chain of measurements over 100 miles. To be to one decimal place after that distance, the uncertainty in each measurement must have been very small. https://www.bench-marks.org.uk/bm65397

Looking for boulder clay on Walney Island

I'd heard that Walney is made of glacial deposits. Looking on the beach at Biggar Bank, I noticed a lot of pebbles made of rocks from further north. Then I noticed that the source of the pebbles appears to be the crumbling bank behind the beach. But this doesn't look like the glacial deposits I've found at Boggle Hole on the east coast and at St Bees. There the low cliffs are of more more clay like stuff with quite angular samples in. Here the rocks look like normal beach pebbles. I'm guessing that whatever the original origin of these pebbles, they have been in the sea previously. Perhaps an older shingle bank was more recently covered with vegetable matter than laid down top soil and that it is now eroding. Since these pebbles are not angular, I don't think this is a glacial deposit.

Longshore Drift from south to north at Silloth

In Clarence Ellis's book The Pebbles on the Beach he says that longshore drift moves material from south to north on the west coast due to the wind-driven waves coming predominantly from the south west across the Atlantic and then up into the Irish Sea. The exception is apparently the stretch of coastline in Cumbria from Walney to St Bees where the movement is north to south. The photograph shows a view looking west at Silloth. Notice that the pebbles have piled up much higher on the left of the groyne. That means that material is moving from south to north as predicted.

Big kaleidoscope installation in Grizedale Forest

Each viewing section of this device consists of three mirrors. At each corner, there seem to be 5 images formed. An odd thing seems to be happening. The upper left mirror seems to reflect the right hand mirror and in then itself reflected in the bottom mirror. I think I'll have to make a model of it to understand it. The complication is probably the fact that it tapers inwatds.