Why are there seasons? The Earth’s axis is tilted by 23.4° and always points the same way in space as the Earth goes round the Sun. So for half of the year the southern hemisphere leans towards the Sun (summer in Australia, in December) and the northern hemisphere leans away (winter). Six months later it is the other way round. Two things make summer hotter:

1. The Sun is higher in the sky. The same beam of sunlight spreads over a bigger area of ground when the Sun is low, so each square metre gets less energy (the sunlight on the ground is proportional to sin of the Sun’s height).

2. The days are longer, so the ground has more time to warm up.

Sun’s height at noon = 90° − |latitude − declination|

The declination is the latitude where the Sun is straight overhead at noon. It goes from +23.4° (June) to −23.4° (December). It is not the distance. The Earth is actually closest to the Sun in early January (about 147 million km) and furthest in early July (152 million km). That is a difference of only 3%, and it is summer in the south and winter in the north when we are closest. Set the tilt to “No tilt” and the seasons disappear: the day length is 12 hours all year and the Sun’s noon height never changes.

Moon phases. Half of the Moon is always lit by the Sun. What changes is how much of the lit half we can see from the Earth. At new Moon the Moon is between the Earth and the Sun and we see its dark side. At full Moon the Earth is between the Moon and the Sun and we see all the lit side. The Moon takes 29.5 days to go through its phases (a month), a little longer than the 27.3 days it takes to orbit the Earth, because the Earth has moved on round the Sun.

Eclipses. A solar eclipse happens at new Moon when the Moon’s shadow falls on the Earth. A lunar eclipse happens at full Moon when the Moon passes through the Earth’s shadow. If the Moon’s orbit were in the same plane as the Earth’s orbit, there would be an eclipse every month. But the Moon’s orbit is tilted by about 5°, so at most new and full Moons the Moon passes above or below the line from the Sun to the Earth and the shadow misses. An eclipse can only happen when a new or full Moon is near the two places where the Moon’s orbit crosses the Earth’s orbit plane (the nodes), which happens in two “eclipse seasons” each year. Look at the calendar: with the real tilt there are only about 4 eclipses a year altogether, but with no tilt every new and full Moon would have one.

What the picture leaves out. The orbits are drawn as circles, and the Moon’s distance and size are not to scale. The Moon’s orbit is tilted by an average of 5.1° to the Earth’s orbit, and its nodes slowly turn round (once in 18.6 years), which is included in the calendar. The calendar uses average motions, so it shows how often eclipses happen but not the exact dates of real eclipses.

Things to try. (1) Find the date when Sydney has its longest day. What is the noon height of the Sun then? (2) Compare Sydney, Darwin and the South Pole in June and December. (3) Set no tilt. What happens to the seasons? (4) In the second tab, find the phase when the Moon rises at sunset. (5) Count the eclipses in the calendar with the real tilt and with no tilt.