Earth and Sun – Bartosz Ciechanowski
Bartosz Ciechanowski
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October 16, 2019
Earth and Sun<br>The day-night cycle and the cycle of the seasons have been an important part of human civilization for millennia. Today the discoveries from centuries ago are well known, but despite the superficial simplicity of Earth revolving around its axis and orbiting the Sun, the interaction between those two actually forms a fairly complex system.
This blog post will talk about space and how our planet moves through it, so it’s only fitting if we embed ourselves in the cosmos itself.
Over the course of this article I’ll try to explain how the Sun and the various motions of the Earth end up making our planet look like in the demonstration below. You can drag the globe around to see it from different perspectives and use the sliders to change the date and time:
It’s hard to talk about Earth and Sun without referencing a few dimensions and dates. They’ll be shown in imperialmetric units (e.g. 1 mi1 km) and an Americanan international date format (mm/dd/yyyydd/mm/yyyy), but you can switch to the more universalAmerican units if you prefer.
The time of day will be presented in Coordinated Universal Time, or UTC for short, which is roughly a local time in Greenwich in London, UK. This time standard is not adjusted for daylight saving time which is very convenient as it will let us look at the sunlight for the same time of day at different dates.
Size
Let’s start by visualizing how enormous the Sun is. In the picture below you’ll find the Earth and the Sun placed next to each other. The Earth is the tiny blue dot on the right side of the Sun:
The Sun is almost a perfect sphere with a radius of 432,170 mi695,700 km. The Earth’s shape resembles an ellipsoid with an average radius of 3958.8 mi6371 km. As such, the radius of the Sun is 109 times larger than that of the Earth. Naturally, the Sun doesn’t look that large in the sky, but that’s because the Sun is quite far away from the Earth. Before we see how far away the Sun is we first have to discuss a simple shape that is the base of all planetary orbits – an ellipse.
Ellipse
There are multiple ways to define an ellipse, but in the context of space it’s most convenient to speak of it in terms of focal points. An ellipse is a figure consisting of points for which the sum of distances to its two focal points is constant. That’s certainly a mouthful, so an interactive diagram will paint a better picture:
The small cross represents the center of an ellipse while the two white disks show its focal points. The total length of blue and red segments is the same for every point on the ellipse. The dashed line is called the semi-major axis of the ellipse while the dotted line is the semi-minor axis.
The defining property of an ellipse is the ratio between a distance c from the center to a focal point known as linear eccentricity, and a distance a from the center to the “far point” of the ellipse i.e. the length of its semi-major axis. In the demonstration below you can adjust that ratio with a slider:
This ratio is known as eccentricity. When an eccentricity is equal to 0 an ellipse becomes a perfect circle, for eccentricity of 1 an ellipse with a fixed major axis length degenerates into a linear segment.
Orbit
You may have already heard that the orbit of the Earth is an ellipse and that the Sun is located in one of the focal points of that ellipse. This situation is often visualized like this:
The small cross in the middle shows the center of the ellipse while the small rings, one of which is directly in the center of the Sun, symbolize the focal points. There are two important points on the orbit: the perihelion is the point at which Earth is closest to the Sun, while at the aphelion Earth is the furthest away from the Sun.
Technically, the Sun is not in one of the focal points of the ellipse, but instead the objects in the Solar System revolve around its center of mass. However, the Sun’s mass is so dominant that the actual focal point is fairly close to the Sun’s center.
What we’ve seen above paints a convenient picture, but the actual relative sizes are very different. Below you’ll find a visualization of the Earth’s orbit around the Sun with proper scales. The tiny yellow dot in the middle depicts the Sun. At your current viewing scale the Earth is pretty much invisible, it has a diameter of pixels, so instead its location is shown by an arrow. You may also be barely able to tell that the orbit is elliptical. Its eccentricity is equal to 0.0167 and the Sun is very close to the center:
If you pay a close attention to the position of the Earth at the beginning of a calendar year and compare it with the beginning of the next year you’ll notice that the Earth hasn’t returned to the exact same...