Monday, 15 February 2016

Super-Seasons on Earth and Pluto

On Earth, one hemisphere experiences summer when the closest pole is pointing at the sun, and winter when it's pointing away. The yearly variation in the distance to the sun does not have much effect; most Northerners are surprised to find out that the sun is closest in January. On Pluto,  the seasons are more extreme because there is a much greater axial tilt and much greater orbital eccentricity, leading to seasonal variation not experienced on Earth. There is a cycle of hot and cold summers in each hemisphere, corresponding to the alignment of the solstices and the perihelia. I call these superseasons, and in this post I will discuss superseasons on Earth and Pluto.

Northern winter if Earth were as tilted as Pluto.

For the purposes of this article, I am going to pretend that spring and autumn do not exist.

A Recap of Earth's Seasons

There is a pretty good video here about the astronomical contributors to Earth's seasons. Earth's 23.5 degree axial tilt means that when the Northern hemisphere is pointed at the sun, days in that hemisphere are longer and more energy is absorbed from the sun. Above the Arctic circle there is permanent daylight, and the sun appears directly overhead on the Tropic of Cancer. When the Southern hemisphere is pointed at the sun, the opposite happens, and the Arctic is in permanent darkness. Astute readers will recognize these two extremes as "summer" and "winter." It's the axial tilt that gives us our seasons.

The Earth's orbit is also slightly eccentric, meaning that in January Earth is about 3% closer to the sun than in July, although this does not have as big an effect. Where I live, the sun gives me 7% less light in the summer compared to the winter, but it does so for twice as long each day, so summer tends to be warmer in the winter despite the sun being farther away.

The eccentricity axis of Earth's orbit slowly precesses around the sun, mostly due to the influence of Jupiter. This is a 21,600 year cycle, so in about 11000 years, the sun will be closest in Northern summer, and we will have more extreme seasonal variation. There are other long-term periodicities that contribute to varying climate patterns, which together make up the Milankovitch cycles.

Seasons on Pluto

Compared to Earth's 23 degree tilt, Pluto's axial tilt is a whopping 120 degrees with respect to its orbit (the fact that it's greater than 90 degrees means that North on Pluto is defined as slightly "upside down" compared to Earth). This basically means that at certain times of the year one of the poles can be pointing almost directly at the sun. On average, somewhat counterintuitively for Earth-dwellers, the polar regions on average get about 20% more sun exposure than the equator over the course of a year. On Earth, the equator receives about twice as much sun on average as the poles. This also means that the equivalent of the Tropic of Cancer on Pluto would actually be above the Arctic circle.

Average yearly sun at different latitudes on Earth (left, source) and Pluto (right, source). Note that the scale on the Earth graph is about 1000x that of the Pluto graph.  Earth is a lot closer to the sun. North Pluto gets slightly more sun because of the currrent superseason.
In addition to being more tilted, Pluto's orbit is a lot more eccentric than Earth's. At its closest, it is about 30 times as far from the Sun as Earth is; at its farthest it is about 50 times as far. Because the power received from the sun is proportional to the square of distance, this means it gets about 3 times as much heat from the sun when at perihelion compared to aphelion.

An eccentric orbit is a lot like a good marriage. Pluto's orbit is much more eccentric than Neptune's, and at this scale Earth's orbit is roughly circular (circle added for comparison, orange not to scale).


With the combination of extreme axial tilt and large eccentricity, we can imagine "multiplying" summer and winter by "close sun" and "far sun" to get four extreme seasons: summer with a close sun (hot summer), summer with a far sun (cold summer), winter with a close sun (hot winter) and winter with a far sun (cold winter). We're just focusing on the extremes ignoring the mild seasons of spring and autumn, as well as periods where the sun is in between perihelion and aphelion.  On Earth, I guess these could correspond to summer and winter during an ice age, and summer and winter in an interglacial period, ignoring the fact that the Southern hemisphere exists (to the three percent of my readers from Australia, I'm sorry). This pattern of hot and cold summers and winters corresponding to the alignment of the perihelion with the solstices, I'm calling "superseasons."

Diagram of the superseasons.

The syncing of the moon's perigee with its phase, two cycles that differ by about a day, is also responsible for the "supermoon" phenomenon, although I think perigee-syzygy is a better term.

On Pluto, there is a much bigger effect. In years with a hot summer, the hot hemisphere receives roughly three times as much sunlight in the summer than the cold hemisphere does. This is made more extreme by the large axial tilt: rather than just a small region around the pole being enshrouded in light, roughly half the hemisphere is above the "polar circle," corresponding on Earth to everything North of Florida or South of Rio de Janeiro experiencing a midnight sun in the summer and eternal darkness in the winter. Even without the superseason effect, this makes seasonal variation more extreme than on the Earth.

Although there is an extreme seasonal variation on Pluto, it actually doesn't affect the temperature that much: only by about ten degrees from summer to winter. This doesn't seem to make much difference by human standards but it can determine how the different types of ice on Pluto's surface sublimate into the atmosphere. An interesting question is whether a hot winter is warmer than a cold summer. Based on what I have read, the perihelion-aphelion cycle has a stronger effect on the temperature than the summer-winter cycle.  Depending on the superseasonal phase, the temperature cycle and the light cycle might by quite out of sync. This is analogous to the fact that the coldest day on Earth is actually a month or two after the winter solstice, although not due to the same phenomena.

Right now, Pluto is in "superspring" where neither the Northern nor Southern hemispheres reach summer particular close to or far from the sun, which means that over its current 274 year orbit, both hemispheres get roughly the same amount of sun. This can be seen in the graph I showed earlier in this article, where the North just gets a little bit more sun. Pluto reached perihelion around 1990, and according to the analyses of Earle et al., there was a significant drop in the received sunlight within a few years of that, which as I understand is basically due to the equator becoming more aligned with the sun. Now it is getting both closer to the sun and closer to summer, so it should be cooling down.

Two images from Earle's paper. Left: predicted insolation for the whole planet for the past orbit.  Right: predicted average insolation at different latitudes averaged over the last 1.3 million years, showing the North receives a lot more light on average. Also note that the equator gets the least amount of sun.

The timescale of Pluto's superseasons is about 2.6 million Earth years or 8400 Pluto years. For the past 1.3 million years, Pluto's Northern hemisphere has been the one closer to the sun in the summer. In the same paper that I've mentioned a few times, they calculated the sunlight received as a functon of latitude and averaged it over the past 1.3 million years. They found that for the last 4200 of Pluto's orbits, the North has received 50% more sunlight than the South. When they average over 2.6 million years, this asymmetry vanishes as the entire superseason cycles through.

The idea of two separate time-scales modulating the temperature, on Earth the 365 day year and the 21000 year apsidal precession, is similar to how the climate of Westeros operates in Game of Thrones. There are summers and winters, but they are of variable length and intensity. Just having a periodicity like on Earth or Pluto wouldn't explain the random length of their seasons, but these guys simulated the seasonal cycle on a planet around a binary star to show that it could lead to apparently random seasonal length variations.

Heart of Darkness

It was recently discovered that Pluto has a big icy heart just North of its equator. This makes that section of the planet slightly more reflective, which adds a bit of complexity to the superseason cycle. When plants are more reflective they absorb less sunlight, making it harder to heat them up. In Northern summer close to the sun it might be slightly colder than Southern summer close to the sun, because more of the sun is reflected. This gives a range of four types of summer on Pluto: hot Northern summer, hotter Southern summer, cold Southern summer, and colder Northern summer. However, because of how recently this was discovered, the exact details of how much effect the heart has have not been computed yet. I hope to update this once the articles are published.

Giant mirror just above the equator.

Having written all this down, the main thing I've learned is that the phase of the superseason on Pluto leads to a strong asymmetry between the two hemispheres which simply is not seen on Earth. Earth's superseasons contribute to long-term climate shifts, but when there's an ice age there's an ice age in both hemispheres.

Thursday, 11 February 2016

Radiation Pressure: A Classical Depiction

A question I see a lot asks how light can exert a pressure on something or impart momentum if it has no mass. Because momentum is typically introduced as the product of mass and velocity, this is a seemingly cromulent question.

Radiation pressure can be simply understood in terms of electromagnetic wave phenomena without delving into special relativity or introducing photons. We simply recall that A. electromagnetic waves consist of transverse electric and magnetic fields, perpendicular to each other and the direction of wave propagation and B. surfaces are made of protons and electrons. B. isn't necessary, but it helps me visualize it.

An electromagnetic wave approaches an object made of free protons and electrons. The wave I found on google images, it apparently comes from someone named Amanda McPherson at University of Alaska.

Consider the wave hitting the surface. What does the electric field do? It makes the protons and electrons accelerate in or opposite its direction, in the plane of the surface, giving them a velocity. The electrons, being 1800 times less massive, will end up moving a lot faster*.
The electric field (red arrows) makes the protons move slowly in its direction, and the electrons move quickly in the opposite direction.

Then, what does the magnetic field do? If the particles are stationary, it does nothing, but since the electric field set them in motion, the magnetic field couples to their velocity and provides a force. The force is perpendicular to the magnetic field, and perpendicular to the direction of motion (which was the direction of the electric field, perpendicular to the magnetic field), meaning that it creates a force in the direction of wave propagation, making the electrons move in that direction, driving the whole object forward.
The magnetic field (blue arrows) couples with the velocity of the electrons, and changes their direction towards that of the wave propagation. I have neglected the force on the protons, because their velocity is so much slower.

So there you have it. An electromagnetic wave hits a surface, the electric field sets the electrons in motion in the plane of that surface, the magnetic field couples to that motion and forces them in the direction of the wave, causing a force on the entire object. Thus, radiation pressure arises.

My Ph.D. is in physics, not graphic design.

There are a few space probes that have solar sails that use this principle for propulsion, including the Japanese probe IKAROS (whyyy would they call it that?!). I think one of the best descriptions of some of the additional nuances is this old xkcd blag post on the subject.

*This makes the most sense if the surface is metal, so that the electrons are unbound to the nuclei.

Saturday, 6 February 2016

Article about secondary forces

I wrote another article on PhysicsForums about secondary forces: tidal forces for gravity, van der Waals forces for electromagnetism, and the residual strong nuclear force. Check it out.

This person experiences a tidal force because gravity is stronger at their feet than at their beret.