# Would the tropic and arctic climate bands switch if the Earth's axial tilt changed to 60 degrees?

At 4:56 in this video essay, Edgar states that at an axial tilt of 60 degrees, the tropic and arctic climate bands will be switched, so that equatorial regions would be cold and polar regions hot.

https://youtu.be/J4K3H9aNLpE?t=4m56s

Is this plausible? It seems to me that it should be more complicated than that - on a solstice, everything from 30- 90 degrees north or south would be dark, including one of the "tropical" poles, and everything on the opposite side of the planet from 30 - 90 degrees would have a full 24 hours of sunlight.

• You should really ask Physics or EarthScience.SE, but it seems plausible to me, since the poles are severely pointed towards the sun. Apr 23, 2018 at 4:43
• @RonJohn - Yeah, I really went back and forth on where to ask first. I actually drafted a question on EarthScience and deleted it before posting this here. But since Artefexian, the channel, is specifically about world building, I felt it was most appropriate here. Apr 23, 2018 at 4:48
• You're probably right. Only one pole will be 'tropical' at a time & the other will be cold & dark. The equator could be cold. But the two poles will which switch back and forth from 'polar' to 'tropical' over the period of a year. Where a year is the time to complete one orbit of its primary star. It is plausible, but, as you said, more complicated than a simple switch of climatic bands. Apr 23, 2018 at 13:12
• This is perfectly on topic here, but other more specialized sites might give you better answers or not at all since it is a fictional world. They can be hard on that issue alone. Apr 23, 2018 at 16:00
• For high axial tilt, the total amount of energy received from the sun over the course of a year is higher at the poles than at the equator. Presumably this is what the video is referring to. You are right that there would be extreme seasonal variation everywhere on the planet, though, so nothing would be analogous to the tropics on Earth. Apr 24, 2018 at 22:15

Note that I am using averages and it is also simplistic to avoid getting to much into details that would not have a big impact on the answer.

During the northern summer:

• At 60 degrees, the planet receives the most energy from the star. It is the warmest at that time of the year. At sea level, I would expect average temperatures in the 30s in humid climates and 40s in dry climates, based on what is observed on Earth. Of course, during daytime the temperature rise far above 40 in dry climates but the temperature gradient is much smaller in tropical climate (between the day and night).
• The pole would have a temperature climate similar to the ones we have here on Earth close to 45 degrees. Temperature ranges in the 18 to 22°C and can rise higher especially in the interior of large continent like Asia, given the climate is also dry there.
• The tropics too would have a fairly temperate climate at this time of the year.
• The equator in the other hand would be at a much greater angle, receiving much less direct sunlight. The quantity of energy received would be comparable to what Earth receives in the 80s degrees of latitude. Svalbard is one example and the climate of the warmest month is barely above 0° C.

During the southern summer:

• At 60° N, it is extremely cold. There would be no sunlight for several months. Actually, anything about 4 or 5° north of the equator would have a least of few days of complete darkness. I would expect something a lot colder than Antarctica or Siberia but I don’t have specific numbers.
• The tropics would be about as cold as our poles are in winter. Average temperatures in the range of -40° would be common.
• The equator would have “Nordic” climate like Scandinavia if they are near warm water currents or like Canada if it is not the case (Northwest Territories). The vegetation in that part of Canada is made up of taiga and tundra.

During the rest of the year, the temperatures are in a large transition from one extreme to the other.

Summary: Are Arctic and tropic climate switched?

Summer:

• Arctic: 30-40° C
• Tropic: 18-22°C and hotter if it is really dry

Winter:

• Arctic: -60°C and possibly colder
• Tropic: -40°C

Conclusion: The Arctic region is hotter in summer but colder in winter. It is not exactly a switch.

# No; the equator is always warmer than the poles

Earth has a 23 degree axial tilt. That means that the sun is never more than 23 degrees from the equator. The equation for incident solar energy ($E$) for any given day is

$$E = E_d\cos{A_i}$$ where $E_d$ is the incident energy of the sun overhead at noon and $A_i$ is the angle of the the sun above the horizon at noon. There are plenty of associated factors like cloud cover and refraction of light from various layers of the atmosphere, but we can ignore them for now.

On the Earth, over one year of sunlight, the total incident sunlight can be calculated as the percentage of the maximum possible sunlight ($E_{max}$); that is, the amount of energy you would receive if the sun was directly overheat at noon every day of the year (i.e. a planet with no axial tilt). We will define a year to be $2\pi$ units long, so $E_{max} = 2\pi E_d$.

The motion of the sun over the course of the year can be modeled by the sine (or cosine) function as $$A_i = \max\left[\frac{\pi}{2}, A_{tilt}\sin{t} + L\right]$$ where $t \in [0, 2\pi]$ are times within one solar year and $A_{tilt}$ is the axial tilt of the planet and and $L$ is the absolute value of latitude (north and south do not matter). Note that if $L$ is greater than $A_{tilt}$, then the location is outside of the tropics and the sun can never be overhead. Also note the max function is necessary, since if the sun is more than 90 degrees away, it is still giving zero light.

Plugging equation 2 into equation 1 and integrating over a year, we get

\begin{align} \frac{E}{E_{max}} &= \frac{1}{2\pi}\int_{0}^{2\pi}\cos\left(\max\left[\frac{\pi}{2}, A_{tilt}\sin{t} + L\right]\right)dt\\ \end{align}

The closed form solution of this indefinite integral is derived from the Bessel function with some added complexities due to the max function, but we can solve it numerically. For Earth, axial tilt is 23.5 degrees or 0.410 radians, and the solution is roughly 0.958. That is, the equator gets 95.8% as much sunlight as a planet with no axial tilt. A solution for the Tropic of Cancer (or Capricorn) at 23.5 degrees from the equator is 0.878. At 60 degrees (north or south) the value is 0.478, while at the pole it is 0.128. So far, this reflects reality pretty well.

Now, let us change the axial tilt of your planet to 60 degrees. The corresponding number for the equator is 0.743; and for the poles 0.294. You have succeeded in making the entire planet into a temperate or cooler climate; but you have not succeeded in making the poles warmer than the equator.

A general proof of this for any axial tilt can be seen by observing that the derivative of the integrated function is just the function itself. That function in turn is maximized by $L = 0$ for $A_{tilt} \in \left[0,\frac{\pi}{2}\right]$, so for any non-tidally locked planet orbiting the sun, the equator will receive the most solar radiation.

Indeed, topics by their solstice definition would move to 60 degree latitude (which is Northern Canada and Norway). But tropical ecosystems won't move there. In fact, there might be no tropics as we know them at all in the new Earth.

Today, Earth year-around average temperature is 14.6 degrees Celsius. Let's keep in mind that this average is not likely to change much.

Every summer, high latitudes will be awash in sunlight and weather will get quite warm. But every winter they will plunge into polar nights and all species that aren't adapted to it will die. The climate there may be similar to modern day highly continental one, like Kazakhstan or northern China.

Equatorial regions will be in a constant twilight, with the sun hanging low to horizon. But good thing is that these regions will get constant sunlight with 12 hour long days throughout the year. The climate there may be comparable to coastal Pacific Northwest.

Because there will be no constantly cold places, massive glaciers are unlikely to form, and if we start with modern day Antarctica and Greenland, the ice shields there will likely melt.

But the main key that will define the climate zones will be ocean currents. With high seasonal variations, the presence of absence of those current will define whether highly variable swings or smooth temperate stability will dominate. At the moment, it would be very difficult to predict how the current will change.