The Paradox of Perfection

Why perfectionists are rarely happy with their accomplishments.

Seasons on Steroids

Here on Earth, we're fortunate enough to orbit the Sun along a nearly a circular path. The result is a fairly stable climate system with a globally averaged temperature that is more or less constant year-round. Nevertheless, our planet's rotation axis is tilted at about 23.4 degrees relative to the plane of our orbit. This physical configuration allows for the seasonal cycle that we can observe each year. In Northern Hemisphere summer, the North Pole is angled towards the Sun, allowing the hemisphere to receive more light over one day. This allows for warmer weather. Meanwhile, the South Pole is angled away from the Sun and receives less Sunlight, making it colder.

A diagram depicting how the tilt of Earth's spin axis (the red arrow pointing from the South Pole through North Pole) creates seasons.  Position 1: Northern Hemisphere summer, Southern Hemisphere winter. Position 2: Northern Hemisphere autumn, Southern Hemisphere spring. Position 3: Northern Hemisphere winter, Southern Hemisphere summer. Position 4: Northern Hemisphere spring, Southern Hemisphere autumn.

As discussed in my previous post, the presence of a second star can gravitationally perturb planets into more elliptical orbits. Kepler's first law of planetary motion states that all planets orbit their star in an ellipse, with the central star at one focal point. The magnitude of how elliptical an orbit is is specified by a quantity called eccentricity. An eccentricity of zero (e = 0) corresponds to a circular orbit, whereas an eccentricity between zero and one (0 < e < 1) corresponds to an elliptical orbit. Within this range, higher eccentricity corresponds to an orbit that is more elliptical.

Four color-coded orbits of equal max. diameter (to scale) for eccentricities 0, 0.25, 0.5, and 0.75. The bottom left plot displays the radiative power per area received by the planet over time for each orbit (1 Solar Constant = average value for Earth). The bottom right plot displays the orbit-averaged value for a given eccentricity.

In an elliptical orbit, the planet can approach the star more closely, thereby receiving more radiation and reaching higher temperatures at the distance of closest approach. Much of the orbit, however, is spent further out than for a circular orbit of the same diameter. Averaged over one orbit, the amount of radiation received by the planet increases with eccentricity. So what does this all mean? Supposing that Earth's orbit were more elliptical, global temperatures could rise and fall (potentially significantly) over the course of a year. These global seasons could be quite extreme for planets in binary star systems.

This summer, I was able to run some preliminary models. Using initial conditions for a simplified Earth, I simulated how the climate would behave under orbital eccentricities of 0.4 and 0.6.

The above map shows monthly averaged surface temperatures for a planet at month of closest approach for an orbit with e = 0.4. Maximum temperatures exceed 340K (67C = 152F). Yikes! How can we better understand what this map means for humans? Thanks to biological evolution, humans have been able to adapt to warm climates by means of sweating. When sweat evaporates off our skin, it draws heat from our body, thereby cooling us down. This effect can be measured using what's called the wet-bulb temperature. In essence, this is the coolest temperature that our bodies could reach by sweating, and depends on environmental humidity.

The above map, then, can be used as a proxy when examining basic human adaptability to climate (Sherwood & Huber 2010). When the wet-bulb temperature approaches body temperature (37C = 98.6F), a human can no longer shed heat into their surroundings, and internal temperature rises. Prolonged exposure to environmental wet-bulb temperatures exceeding 35C (95F) can thus pose the risk of heat stroke. We can then make a map showing regions that are deadly for humans.

The above map depicts wet-bulb degrees Celsius above 35C. Luckily, our orbit is circular, but if you were to travel to a similar planet at e = 0.4, you may want to invest in air conditioning!

As would be expected, temperatures get even higher for e = 0.6. Spoiler alert: A/C won't help.

Some PhD students just want to watch the world burn.