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When viewed with the lunar surface at the bottom, Earth is tilted on its side with the South Pole to the left, and the equator running top to bottom. Little landmass can be seen through the swirling clouds, but the bright sands of the Namib and Saharan deserts stand out salmon pink against the blackness beyond. Just 368 years and 10 months after a man was burned at the stake for dreaming of worlds without end, here is Earth, a fragile crescent suspended over an alien landscape, the negative of a waxing Moon in the friendly skies of Earth. This is an unfamiliar, planetary Earth, no longer central; just another world. When Kennedy spoke of Apollo as a journey to an unknown celestial body, he meant the Moon. But we discovered Earth and, in the words of T. S. Eliot, came to know the place for the first time.

OUTWARDS TO THE MILKY WAY
    Newton’s laws are the keys to understanding our place in our local neighbourhood. Coupled with precision observations of the motion of the planets and moons, they allow the scale and geometry of the solar system to be deduced, and their positions to be calculated at any point in the future. The nature and location of the stars, however, requires an entirely different approach because at first sight they appear to be point-like and fixed. The observation that the stars don’t appear to move is important if you know something about parallax, as the ancients did. Parallax is the name given to a familiar effect. Hold your finger up in front of your face and alternately close each of your eyes, keeping your finger still. Your finger appears to move relative to the more distant background, and the closer your finger is to your face, the more it appears to move. This is not an optical illusion; it’s a consequence of viewing a nearby object from two different spatial positions; in this case the two slightly different positions of your eyes. We don’t normally perceive this parallax effect because the brain combines the inputs from the eyes to create a single image, although the information is exploited to create our sense of depth. Aristotle used the lack of stellar parallax to argue that the Earth must be stationary at the centre of the universe, because if the Earth moved then the nearby stars would be observed to move against the background of the more distant ones. Thousands of years later, Tycho Brahe used a similar argument to refute the conclusions reached by Copernicus. Their logic was completely sound, but the conclusion is wrong because the nearby stars do move relative to the more distant background stars as the Earth orbits the Sun, and indeed as the Sun orbits the galaxy itself. You just have to look extremely carefully to see the effect.
    Amongst the thousands of stars visible to the naked eye, 61 Cygni is one of the faintest. It’s not without interest, being a binary star system of two orange K-type dwarf stars, slightly smaller and cooler than the Sun, orbiting each other at the lethargic rate of around 700 years. Despite the pair’s relative visual anonymity, however, 61 Cygni has great historical significance. The reason for this quiet fame is that this faint star system was the first to have its distance from Earth measured by parallax.

 
     

     
    Friedrich Bessel is best known to a physicist or mathematician for his work on the mathematical functions that bear his name. Pretty much any engineering or physical problem that involves a cylindrical or spherical geometry ends up with the use of Bessel functions, and, in blissful ignorance, you will probably encounter some piece of technology that has relied on them in the design process at some point today. But Bessel was first and foremost an astronomer, being appointed director of the Königsberg Observatory at the age of only 25. In 1838, Bessel observed that 61 Cygni shifted its position in the sky by approximately two-thirds of an arcsecond over a period of a year as viewed from Earth. That’s not very much – an arcsecond