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Going Around in Circles

It is a new year. What is so new about it? Anyone born before 2008 will have been here before, at least on a cosmic scale. We inhabitants of the Earth have completed one orbit of the Sun since the last bout of New Year’s parties. Presumably that is something worth celebrating, though I am not sure what contribution anyone made to this stellar achievement, except that even the thinnest and tiniest of us has a mass and hence adds to gravity’s sum. If going around the Sun is worth celebrating, that would seem to imply that the heaviest people deserve the most congratulation. Perhaps that would justify them eating and drinking a little bit more during the celebrations, and hence creating an oddly virtuous circle.

Although the Earth goes around the Sun, you could argue we are not back where we were. Our whole solar system is moving, as it spins around our Galaxy, the Milky Way. On that measure, it will be another 220 million years before we are back here again. I cannot imagine anyone is planning a party for that anniversary. On top of that, the entire Milky Way is moving towards something called the Great Attractor. The Great Attractor is not what you get if you advertise that the Beckhams, Brangelina, TomKat, Lindsay Lohan and Sam Ronson will be attending a wife-swapping party, though the respective influence on galaxies and paparazzi are similar. The Great Attractor is a superdense gravity anomaly about 250 million light years away. Although the Milky Way is heading for the Great Attractor at a rate of something over 500 km/s, we will not be getting there anytime soon, and when we do, it is not sure if this will be a cause for celebration.

Returning to our own cosmic backyard, Einstein showed we do not go around the Sun in a fixed elliptical orbit, as previously thought. His general theory of relatively explained that the route of the orbit is also turning through space, tracing a path like a celestial spirograph. Einstein’s theory correctly predicted that the perihelion, the point where a planet is closest to a star during its orbit, keeps changing. Each year, it arrives earlier than the year before. Earth’s perihelion now occurs in January. That is fortunate for everyone suffering the winter in the Northern hemisphere, as otherwise it would be even colder. However, the change in the Earth’s orbit is only very slight, meaning it will take about 21,000 revolutions before we are back where we began and start to retrace the same route.

The advancing perihelion may not be enough to poop a New Year’s party, but Einstein had plenty more reasons to undermine any annual festivity. To begin with, the changing perihelion is only one manifestation of the curvature of spacetime. Because time is not independent of space, it elapses at different rates depending on where you are and where you are going. Imagine three friends. One of them is going to blast off in a rocket that will take him as far and as fast as he can go into deepest space. The other two are less adventurous, and decide to stay at home. The astronaut launches at precisely midnight on New Year’s Eve; NASA are trying to save costs on fireworks displays. A year goes by, and the two homebodies are holding a party. They count down to the new year, and then send a goodwill ‘instant’ message to their pal in space. Thanks to magical technology, their message really does arrive an instant later. However, the atomic-powered chronometer on the astronaut’s spaceship will say that the year is not yet over. Because he has been moving at speed, his clock undergoes time dilation relative to the party-goers on Earth. This means that the clock on the rocket seems to run relatively slow if seen by people on Earth. This is one strange consequence of the measurement of time not being independent of location in space.

If you think time dilation sounds odd, you have only heard the half of it. If the roles were reversed, and the astronaut instead sent the ‘instant’ message back to his buddies on Earth, they would find that their Earth clocks were running slow, relative to the astronaut’s. How can the clocks on the rocket, and on Earth, both be slow relative to each other? Although we said the rocketman was moving away at high speed, all motion is only relative. From the perspective of the astronaut, he is stationary and it is the planet Earth, with all its inhabitants including his two friends, that is moving away at speed. It does not matter that he is alone and there are lots of people on Earth, it is just as meaningful to describe the Earth’s movement relative to the rocket as it is to describe the rocket’s movement relative to the Earth. From the astronaut’s point of view, the Earth has been moving at high speed, and hence clocks on Earth are all dilated. That way, he finds himself celebrating the new year before anyone else.

So where does that leave us? Well, it leaves us exactly where we began, not just at this moment or for today, but all year and every year. All motion is relative, so it is just as true to say the Sun goes around the Earth as it is to say the Earth goes around the Sun. From our perspective, the Earth is motionless. That is lucky, as otherwise we would fall off. When we celebrate going once around the Sun, we have not gone anywhere at all. New Year’s parties are less of a home-coming and more of a never-going-away-in-the-first-place. However, it does at least mean that the Earth, or more precisely the bit of it where you are, (or more precisely still, the bit of it where I am) really is the centre of the universe. What is more, it is not just the centre of the universe now. It always has been the centre of the universe, and always will be. Now that is something I can celebrate all the year round.

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