orbital cycles

Much of my undergraduate research dealt with orbital cycles, which are periodic wobbles in Earth’s rotation and orbit around the Sun that affect when, where, and how much Earth’s surface receives solar radiation. Because they affect the Earth’s energy budget (which is entirely dictated by solar input), these wobbles are capable of changing Earth’s climate. In fact, the ice ages of the past 5 million years are a direct result of these orbital cycles.

major disclaimer: These cycles are not responsible for global warming, which is caused by emission of greenhouse gasses by humans!

Anyway, along the way, I wrote a bunch of codes and made some visuals that might be of use to others, so I’ll share them here, along with a brief description of orbital cycles in case you’ve never heard of them before.

There are three orbital cycles:

eccentricity: This cycle changes the shape of Earth’s orbit around the sun, which goes from circular to elliptical and back every 100,000 years. When Earth’s orbit is elliptical, there are points when the Earth is closest (perihelion) and furthest (aphelion) from the Sun, meaning that the total amount of energy received is no longer constant throughout an orbit like it is for circular orbits.

Animation of eccentricity. Earth’s orbit is the black line, which goes from circular to elliptical and back. Also shown is apsidal precession, which is what causes the ellipse of Earth’s orbit to itself rotate around the Sun. The degree of eccentricity is exaggerated 10 times (Earth’s orbit is never as elliptical as shown above).

precession: Precession is the rotation of Earth’s spin axis. For Earth, this rotation takes roughly 23,000 years. Precession is important because it changes what season occurs when the Earth is closer or further from the Sun. Right now, our orbit is somewhat elliptical, and when we are closest to the sun, it is southern hemisphere summer, meaning that southern hemisphere summers are currently relatively warm. In roughly 11,000 years, it will be northern hemisphere summer when we’re closest to the Sun. If you’re following along, then you’ll understand that precession is completely irrelevant for an orbit that’s perfectly circular: because Earth always receives the same amount of energy from the sun in a circular orbit, the phase of seasons with respect to trajectory along the orbit does not matter.

Animation of precession. The black line is perpendicular to the plane of Earth’s orbit around the Sun. The red lines is Earth’s spin axis.

obliquity: Obliquity refers to the tilt of Earth’s axis of rotation with respect to the line perpendicular to the plane of Earth’s orbit around the Sun. This tilt is the reason that we have seasons, because it means that there are times when a hemisphere is angled towards or away from the Sun. The tilt angle changes from roughly 22 to 24.5° and back every 41,000 years, meaning that the degree of seasonality on the planet changes periodically.


Animation of obliquity. The black line is mean obliquity of 23.3°. The red line shows Earth’s spin axis. The range of inclinations is exaggerated by 5 times.

The code for generating these animations is in a Matlab script and assumes access to the mapping toolbox in Matlab.