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Distance travelled ~ 442'521'600 km: day 172

Today Kate Humble and some of the 23 Degrees team are in Aswan, Egypt. They are there to reveal something fascinating about the Summer Solstice and the tilt of our planet.

The Earth's tilt reveals itself every time we step out in the Sun but none more so than today on the solstice. The angle between the Sun and the Earth was first worked out over 2000 years ago. It was a discovery made near the city of Aswan, at the bottom of an ancient well by a Greek scientist and philosopher, Eratosthanes.

Eratosthanes was a poet, an athlete and a true polymath. He invented the word geography and even created a map of the world. He tried to write a chronology of world history and he invented the leap day. He also proposed a simple algorithm to work out prime numbers and all the time he was the head librarian of the library at Alexandria, the greatest treasure trove of knowledge of its time.

The story goes that 250 BCE on the summer solstice Eratosthanes was in Aswan and at midday, he looked down to the bottom of a well and saw his reflection staring back at him. Now as with most geniuses he noticed something that the rest of us would have missed. Something that told him about the very nature of our relationship with the sun.

When Eratosthanes looked at his reflection in the water in the well, he noticed he threw no shadow because the Sun was directly overhead. Now to most people that wouldn't have meant much but for Eratosthames it was an important revelation. Let me explain. Eratosthames didn't live here in Aswan, he lived 500 miles north in Alexandra. You might ask why that's significant. Well history has it that he noticed that when he was in Alexandria at the same time, on the Summer solstice on a previous year he did cast a small shadow. In fact he'd measured its length and angle.

So when he saw there was no shadow in Aswan he realised that at the very same moment, midday on the solstice, the Sun's position in the sky was different in Alexandra to Aswan. So, by calculating the angle of the shadow he cast in Alexandria, and its distance to the well here, Eratosthenes was able to estimate the circumference of the earth with an astonishing 98% accuracy. And using the same data, he was able to establish the tilt of the Earth's axis, obtaining a value of 23° 51' 15". A pretty amazing result without GPS and modern computing methods.

From watching the position of the Sun, Eratosthanes observed something else. After June 21, shadows appear here once again at noon, and over the coming days, they lengthen. So this day and this place marks the most northerly apparent position of the Sun due to that 23 ½ degree tilt. But tracing a line of latitude, west to east, across the planet one can see the same thing. Aswan sits just above a hypothetical line of latitude, a line we know as the Tropic of Cancer. A line that circles the world at 23.4 degrees above the equator.

The northward drift of the Sun in our sky that begun at the Spring Equinox on March 21 ends now on the Summer Solstice. From this day on, in the northern hemisphere, the hours of daylight will start to reduce and the Sun will track a lower arc in the sky.

Kate and the team are visiting a well reputed to be the very same well that Eratosthanes looked down all those years ago, to tell the story of this remarkable man and his discovery about the tilt of our planet.

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Distance travelled ~ 429'657'600 km: day 167Ìý

In this blog post we are going to show you how you can calculate the exact tilt of Planet Earth by using your shadow. You can only do this at a certain time of the year, the Summer Solstice, and that moment is fast approaching. Ìý

This year Summer solstice is on 21 June. This is the longest day of the year and also for us here in the northern hemisphere, the time when the Sun is highest in the sky. Astronomers regard it as the start of summer for the northern hemisphere winter for the southern.

So what's the Summer Solstice got to do with measuring the tilt of the Earth, I hear you ask. Well, the orientation of the Earth to the Sun is defined by angles, and on June 21 the physics align so that you can use the position of the Sun in the sky at 1pm BST to accurately measure the tilt of the Earth. It still works around 2 days before and 2 days after so you have a few days to try this out.

Here's a tip - measure from the balls of your feet to the top of your shadow and remember be careful and don't look directly into the Sun.

The first important angle is Solar Zenith. This is the angle between the Sun and straight up and it's marked in green on the figure below. We can find this because the smaller this angle is - or the higher in the sky the Sun is - then the smaller your shadow. To work this out we use . If you know about tan, then your height is the adjacent side and your shadow is the opposite side of a square-angled triangle.

Figure 1.

Next we need latitude. This is essentially the angle between the equator and your position on the Earth. You can see from the figure above that if you take the green angles away from the pink angle then you get the yellow angle. This angle between the equator and the place on Earth where the Sun is straight above you is called the "solar declination". But on the solstice it's exactly the same as the tilt of the Earth - convenient.

How to find your latitude?
There are loads of ways of getting your lattitude -a gps device maybe on your phone or satnav, or endless websites can provide you with this. Some are as simple as putting in your postcode.

Most importantly the 23 Degrees team would love to hear how you get on. Send us your calculations, photos or videos of you doing the challenge on the Solstice, or maybe a photo of your shadow. Shadows have long been a key indicator to our Earth's position in it's orbit around the Sun.

Continue the conversation and put #solstice in your tweets!

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