**Astrophysics Corner, Part 15 – Changing a Planet’s Rotation Axis Tilt: the Effect on the Sun’s Altitude and the Length of the Day at Different Altitudes**

In an earlier blog, I noted that
solar panels on a planet are affected by both the latitude of the
location that the panels are placed and the tilt of the planet’s
axis of rotation, relative to its orbital plane.

- The latitude of the location of the panels is obviously important. Essentially, the solar flux that is experienced on the surface varies with the latitude of the site as the sine of the sun’s elevation above the ground. The farther from the planet’s equator, the smaller that angle will be.
**That will be further compounded by the tilt of the planet’s axis, relative to the plane of its orbit around the star. The greater the tilt, the more the elevation of its sun will vary throughout the year, so the solar panels output will be greater or lesser as the season’s progress.**

Earlier, we looked at how the
latitude of the location of the observer (person or solar panel)
influenced the altitude of the sun and the length of the day. In
this blog, we will be a bit more speculative and discuss how the tilt
of the rotation axis affects the length of the day, the altitude of
the sun (or the planet’ s star in the case of planets other than
the Earth) and the distribution of solar energy on that planet.

__Case 1 - 23.5 Degree Tilt (Standard Earth tilt)__

Below is the standard picture, the
Earth with a 23.5 degree tilt. These are the relative positions of
the Earth and Sun in the Northern hemispher mid-summer. It is
pretty clear from the picture that the North Pole will be bathed in
sunlight for an entire rotation (day) at this time of the year, and
that northern areas in general will have longer days than southern
areas. It is also clear that the sun’s rays will be perpendicular
to the ground at mid-northern latitudes, which means the sun will be
directly overhead then. Thus, longer, hotter days.

If we reverse the picture above, the
northern hemisphere will now be in relative darkness, as it is in
mid-winter. The sun’s rays will hit at a very oblique angle in the
north, thus providing relatively little energy per square meter.
The situation will, of course be the opposite in the south, which
will be experiencing the long, warm days of summer.

As for the spring and fall
equinoxes, we have to imagine the sun being out of the picture (where
the reader’s head is now) looking down on the Earth. It is obvious
then, that the sun will warm the north and south equally, and there
will be no difference in the length of the day.

The next two graphs show the altitude of the sun at mid-day, and the length of the day, at various latitudes throughout the year.

The final two graphs show the
effective power of the sun at various latitudes, throughout the year
and aggregated over the year. As you can see, the sun’s power
drops off almost linearly with latitude.

__Case 2 - 0 Degree Tilt (Straight Up and Down Planet)__

Now, let’s imagine tilting the
Earth’s axis, or alternatively, being on a different planet with 0
tilt.

In this case, it is clear that the
strength of the sun’s rays will not very throughout the year, at a
given latitude, nor will the length of the day vary. It will always
rise at the same time, climb to the same height in the sky at noon,
then sink to the horizon at the same time and place.

If we multiply the sine of the angle
of the sun by the number of hours of daylight, to get a measure of
how much effective sunlight falls at different latitudes, we get the
graphs below. As you can see, the effective solar insolation at
various latitudes never changes. Furthermore, it is linear with
latitude.

There will be no seasons - hot
places will always be hot and cold places will always be cold. Kind
of monotonous. Assuming the planet had an atmosphere and oceans like
the Earth’s, one suspects that there would have to be steady,
strong winds and currents redistributing the heat from the equator to
the poles year round. It might be quite a wild place to live.

__Case 3 - 90 Degree Tilt (Tipped Over Planet)__

The other extreme is the 90 degree
tilt, such that the equator and the line through the poles have
effectively swapped places.

Now, it is obvious that the length
of the day will vary drastically throughout the year. At summertime
at the North Pole, the sun will be up all day, directly overhead. In
fact, the North Pole will have 24 hour days half the year, and 0 hour
days the other half of the year. The situation will be the reverse
at the winter solstice. The equator will have 12 hour days
year-round, but even relatively “tropical” latitudes a few
degrees above the equator will experience very large differences in
the length of the day throughout the year.

As before, when we multiply the sine
of the angle of the sun by the number of hours of daylight, to get a
measure of how much effective sunlight falls at different latitudes,
we get the graphs below. In this case, the solar insolation at the
North Pole is actually much higher than at the equator in mid-summer.

Interestingly, although seasons
would vary tremendously at any particular latitude during the course
of the year, on an annual basis, the energy of the sun is distributed
quite evenly throughout the planet. The form of the function
approximates a quadratic quite well, with the maximum solar energy
being at the mid latitudes, dropping off towards the poles and the
equator. So, the weather would probably be quite strange, with
great temperature shifts from season to season, but not very much
rebalancing of heat between low latitudes and high latitudes.

__Heat Balances by Tilt__

Perhaps the most interesting result,
is the variation in the planet’s heat balance between the equator
and the poles, when different axis tilts are applied. I ran the
simulation for a number of other planet tilts, and the results are in
the graph below.

It appears that the equator gets
about the same amount of solar energy over the course of a year,
regardless of the planet’s tilt. But the amount of solar energy
gained by higher latitudes is strongly dependent on the planet’s
tilt.

- The stronger the tilt, the more solar energy falls on the poles. This means that the planet has a more even heat balance over the course of a year.
- The stronger the tilt, the more solar energy the planet appears to capture over the course of a year, via the combined effect of length of day and altitude of sun at the various altitudes. This seems a bit counter-intuitive, but that’s the result that the simulations give.

So, if humanity
ever wants to build a planet, scout for alternative planets, or just
change the tilt of the Earth, we might want to keep this in mind.

Actually, it is
thought that the presence of the moon maintains the Earth’s axis
tilt at a near constant level. If the moon weren’t so large and so
close, the Earth’s axial tilt would vary over geologic time,
something like how a spinning top can wobble. But the moon is slowly
drifting away from the Earth, as its orbital momentum is stripped
away due to tidal interactions with the Earth. So, in some distant
future the Earth might actually go through these large variations in
axial tilt. Wouldn’t that be interesting.

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