Starts With A Bang!

Dreaming of the Sun: A Holiday Story

We are going on day 12 of the Portland snowpocalypse now, and I haven’t seen the Sun in 12 days. Which means I missed the shortest day of the year on December 21st: the winter solstice. The winter solstice is a special day for the Sun in the Northern Hemisphere of Earth, because it’s the day where the Sun is in the sky for the shortest amount of time, and also remains the lowest above the horizon as compared to any point during the year.

As the days progress, that arc the Sun travels through the sky gets higher and wider, and the days get longer, and the Sun’s rays get warmer and more powerful. Anthropologically, this is why there are a lot of very old holidays that take place right after the Winter Solstice: as the Sun’s path stops descending in the sky and starts rising again, it’s clear that a new year of growth and prosperity will follow the winter, even as temperatures drop and lakes freeze and snow falls and Portlanders drive insanely. That’s something worth celebrating!

But what about astronomically? Is this really something people would notice? Heck, is the seasonal “rise and fall” of the Sun something that we could notice today? Let’s do an experiment. Throughout the year, at different times, what if you went outside and photographed the Sun at exactly the same time of day on different days? Would you be able to see any differences? Would it rise in the spring, peak in the summer, fall in the autumn and bottom out in the winter? Let’s take a look:

Wow. Not only does the Sun rise and fall, it makes a “figure-8″ pattern! Yes, that lowest point you see is the Winter Solstice, and yes, the highest point is at the Summer Solstice. This is the reason why your shadows appear longer in the winter and shorter in the summer. But why the figure-8 shape? There are three factors you need to consider to calculate this:

1. The shape of the Earth’s Orbit around the Sun.
2. The tilt of the Earth’s axis as it rotates.
3. The difference in angle between the semimajor axis (the imaginary line between perihelion, which is closest approach to the Sun, and aphelion, a planet’s farthest point from the Sun) and the solstices.

The Earth’s orbit is nearly circular, but not quite. It’s 1.6% closer to the Sun during perihelion (which happens during early January) and 1.6% farther away from the Sun during aphelion (which happens in early July) than average. The Earth is also tilted on its axis at about 23 degrees as it orbits the Sun. The solstices are tilted, just by a couple of degrees in orbit, relative to the Earth’s perihelion and aphelion. Plug this data into a computer to simulate what the pattern of the Sun will look like, and here’s what you get:

Now, that’s a pretty figure 8!

But is this how it works for all planets? Let’s take a look at Mars. Mars is quite a bit more elliptical than Earth, as instead of 1.6% variations in proximity to the Sun, it’s 9% closer at perihelion and 9% farther away at aphelion. Mars is also tilted similarly to Earth, at about 25 degrees as it orbits the Sun. But the way Mars’ orbit lines up with the solstices is very different from Earth, so instead of a figure 8 shape, you’d get a teardrop shape:

For a fancier artist’s rendition (which is more accurate in this case), the analemma of Mars would more closely look like this:

In fact, the analemmas for the different planets can all be calculated based on those three pieces of information above. Here are the results:

• Mercury: a single point (because a day on Mercury takes exactly two years!)
• Venus: an ellipse
• Earth: figure 8
• Mars: teardrop
• Jupiter: ellipse
• Saturn: teardrop with a teeny-tiny loop at the end
• Uranus: figure 8
• Neptune: figure 8
• Pluto: a very large figure 8

So that’s more information than you ever wanted to know about the Sun, but it was too cool not to talk about it. Hope you enjoyed it, and hope you’re enjoying whatever holidays you celebrate at this time of year! So, in an acknowledgment to my Southern Hemisphere readers who bear with me despite my Northern Hemisphere bias, here’s a season’s greetings especially for you!