The Tropical Year: 31.6888 nHz

One of the most important cycles we live by is the tropical year, measured from equinox to corresponding equinox (or solstice to corresponding solstice). The tropical year lasts, on average, 365.2422 days (365 days, 5 hours, 48 minutes, 45 seconds), which means that it is an oscillation with a frequency of 31.6888 nanohertz (nHz). This is the cycle of the seasons.

Spring, summer, autumn, and winter are the conventional seasons, but the tropical year may be split up into more than or less than four seasons, and these need not be of equal length. In northern Australia, a frequent division is “the dry” (May to September), “the build up” (September to December), and “the wet” (December to April). Local Aboriginal people, however, may recognise as many as six seasons.

The Sidereal Year: 31.6875 nHz

A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the stars. This is the time that it takes for the sun to move through the “signs of the zodiac.” Because of the precession of the equinoxes, the sidereal year is 365.2564 days, which is about 20.4 minutes longer than the tropical year. As a result, ancient rules assigning dates to the signs of the zodiac are now completely wrong. The sidereal year corresponds to an oscillation of 31.6875 nanohertz.

The Synodic Month: 391.935 nHz

A synodic month is a cycle from new moon to new moon or full moon to full moon. This period actually varies by several hours, but it averages out to 29.530588 days (29 days, 12 hours, 44 minutes, 3 seconds).

In 432 BC, Meton of Athens noted that 235 synodic months (6939.7 days) is almost exactly equal to 19 years (6939.6 days). This period is called the Metonic cycle, and is used for predicting solilunar events such as the date of Easter.

The synodic month is also strangely similar to the average menstrual cycle (28 days), and this is reflected in the word (“menstrual” derives from the Latin mēnsis = month).

The Week: 1.65344 µHz

The week has an origin among the ancient Hebrews. It also has a Babylonian origin (the relationship between the two origins is unclear). The Babylonians related the 7 days of the week to the sun, moon, and 5 visible planets. They also related them to various gods. Our days of the week derive from the Babylonian week, via Greece and Rome: Sunday (Sun), Monday (Moon), Tuesday (Tiw, god of war = Mars), Wednesday (Woden = Mercury), Thursday (Thor = Jupiter), Friday (Frigg = Venus), and Saturday (Saturn).

Early Christians related the two week concepts together, pointing out that the day of the Resurrection (the day after the Jewish Sabbath) corresponded to the day of the Sun in the Roman system. The week corresponds to an oscillation of 1.65344 microherz.

The Sidereal Day: 11.6058 µHz

A sidereal day is the time that it takes the earth to rotate once around its axis. It often surprises people to discover that this time is 23 hours, 56 minutes, 4.1 seconds. It can be measured by the time to go from a star being overhead to the same star being overhead again.

The Solar Day: 11.5741 µHz

A solar day (24 hours, give or take some seconds) is the time from noon to noon. It is longer than a sidereal day because, while the earth is rotating around its axis, it is also moving around the sun. To put it another way, the sun is not a fixed reference point for the earth’s rotation. The difference between the sidereal and solar days mean that the stars seem to rise about 3 minutes and 56 seconds earlier every night.

The Seasons

It’s solstice time in a few days, so here is an infographic on the seasons (click for hi-res image):

Infographic constructed using R (with DescTools::DrawCircle, rasterImage, layout, and the suncalc package for day length calculation). Images used are a diagram by “Colivine,” paintings by Arthur Streeton and Joseph Farquharson, and two photographs of my own.

Phenology wheels

Recently, somebody pointed me at phenology wheels, which are a popular tool for nature study among teachers and homeschoolers. Nature study is all about careful observation and finding patterns, and phenology wheels help with both. Every month, students draw a picture of what they see in the garden or on a nature walk, and the completed phenology wheel then shows an annual pattern. Other activities are possible – see this University of Wisconsin-Madison Arboretum document.

The picture below shows a pair of partially complete mother/daughter phenology wheels from the very useful Nature Study Australia website (they are using the central circle to show indigenous seasons). It is helpful to outline each month’s section in felt-tip pen:

Mother and daughter phenology wheels from

I’ve generated blank wheels for the Northern Hemisphere and for the Southern Hemisphere, and produced a partially complete wheel of my own (from a European perspective):

Like nature journals, this is an activity both fun and educational!

Credits: lavender watercolour painting by Karen Arnold, sunflowers by Vincent van Gogh, butterfly from here, font is Jenna Sue, wheel constructed using R (with DescTools::DrawCircle, rasterImage, and the showtext package).

World Solar Challenge: Weather in Darwin

One very helpful input to race strategy in a solar car race is weather expertise. How much sunshine can we expect? And when can we expect it? In 2013, Solar Team Twente took along an expert from the Joint Meteorological Group of the Royal Netherlands Air Force to help with that. This year, Punch Powertrain Solar Team (team 8) is taking along an expert from the the Royal Meteorological Institute of Belgium, who will be blogging his insights and experiences.

For those without his specialist expertise, forget everything you thought you knew about Spring and Summer, Autumn and Winter. Darwin has 7 seasons, as the Larrakia People tell us, and the World Solar Challenge begins towards the end of Dalirrgang (the “Build Up” – click image above for multimedia tutorial). Dalirrgang is a kind of overture to the rainy season (the “Wet”). Traditionally, Dalirrgang is the time to hunt the Magpie goose (photo by Djambalawa below).

Long-term weather forecasts suggest that the World Solar Challenge this year might in fact begin on a partly sunny day, with a little rain, but that’s very uncertain, this far ahead.

No wonder it’s cold down here

Here in Australia, it’s the middle of winter. And, as Bad Astronomy reminds me, we’ve also just had aphelion, Earth’s furthest point from the sun (152 million km, compared to 147 million km at closest approach). The diagram below exaggerates the elliptical nature of Earth’s orbit, but it gives the general idea:

For the current distance to the sun, see Wolfram’s calculator or the live diagram of the solar system at Fourmilab, which includes images (green lines show orbits below the plane of the ecliptic):

Live Solar System image

A season on Saturn

This photograph, taken on May 6 last year by the Cassini spacecraft, shows Titan in front of Saturn’s rings. The rings are seen almost edge-on, but leave their shadows on the planet. The bluish tinge in the southern hemisphere indicates oncoming winter (and seems to be due to processes similar to those giving Earth a blue sky). Given that I’m writing this in Australia, where it’s autumn, the photograph seems appropriate for the season.