Friday, April 09, 2010

One more trip around the sun

Over the Hedge

In this week's Over The Hedge comic strips, Hammy the squirrel convinces his friends and a few garden gnomes to enjoy a theme-park style ride around the sun, hurtling through space at a nausea-inducing 66,600 miles per hour.  Not only that, but as they hurtle around the sun, they are also spinning at the alarming speed of roughly 800 miles an hour, and the Solar System itself is moving around the Milky Way Galaxy at a mind-bending 492,000 miles per hour (read here if you need reminders on what the solar system and Milky Way are).   Yet, in the end, their chairs don't seem to go anywhere.

This apparent non-motion of us and the Earth were one of the big stumbling blocks for humans in accepting that the Sun is the center of our Solar System, not the Earth.  The Earth seems so solid and still, and the sun appears to move.  It's no wonder the ancients thought the Sun traveled around the Earth!  So, how do we know that the Earth is moving?
The ancient Greeks were one of the first civilizations to consider a model of the Solar System where the Earth went around the Sun.  The Greek philosopher Aristarchus proposed this model, and he realized that if the Earth went around the sun, then the stars should appear to move a little bit in the sky as the Earth traced out its orbit.  This motion is called parallax, and although you may not know it, your brain uses parallax all the time -- we call it depth perception.  But the basic idea is that if you move, things around you will appear to move too, but the amount they appear to move depends on how far away they are.  Nearby things move a lot, further things move a little.  Go ahead and try it -- look at some things close to you and move your head from side to side or forwards and backwards, and you'll see them move relative to one another.

The stars should move in the same way, but Aristarchus failed to measure any parallax.  Aristarchus claimed this meant the stars were really far away, and so moving too little for the human eye to perceive.  The Greeks had calculated (incorrectly) the Earth-Sun distance as about 5 million miles, so the lack of a parallax would mean that the nearest stars would have to be at least 30 billion miles from the Earth, a distance far larger than the Greeks were willing to consider, so the natural reaction  of other Greek philosophers was that the stars didn't appear to move because the Earth wasn't moving.

When Copernicus and Galileo again proposed the Sun-centered model of the Solar System, the lack of parallax from stars was a major argument against the idea that the Earth moves around the Sun.  Sure, there was plenty of evidence in favor of Copernicus's model, but the lack of stellar parallax was embarrassing.  And astronomers realized that, if they could measure parallax, they would also know how far away the stars were. Astronomers worked hard measuring the positions of stars at different times of the year (when the Earth was at different parts of its orbit).

The first breakthrough came in 1725, when British astronomer James Bradley discovered that a star in the constellation Draco moved by 40 arcseconds a year.  Arcseconds are a measure of angle: a full circle is 360 degrees, each degree contains 60 arcminutes, and each arcminute contains 60 arcseconds.  The tiniest angles the human eye can see are about 1 arcminute, or 60 arcseconds.  So, the star in Draco was moving an amount just below the human eye's ability to see without a telescope.  The problem was, the motion Bradley saw was in the opposite direction that the star's parallax should have been. Two years later, Bradley figured it out.  He wasn't seeing parallax, but an effect we know call the aberration of light.

Again, you probably have noticed this effect of aberration in your own life.  If you've ever been outside in the snow (or rain) when there is little wind, the snow appears to be coming straight down from the sky.  Yet if you get in your car and start driving, the snow appears to be coming from a spot not straight overhead, but at an angle.  The faster you go, the bigger the angle from overhead.  If you go really fast (like in an airplane), the snow appears to be coming from straight in front of you.

Light works the same way.  Light from a star nearly overhead will appear to be coming from an angle depending on how fast we are moving relative to the star.  If the Earth is moving in a circle, then the star's apparent position will also trace out a tiny circle over the course of a year.  This is exactly what Bradley saw.

The aberration of starlight was the first proof that the Earth was moving relative to the stars.  By tracing out this aberration for stars around the sky, you can prove that the Earth's motion is a near circle around the sun, just the motion predicted by the Sun-centered model of the Solar System.  The Earth-centered Solar System could not predict the aberration of star light, and was now dead.

But still, the stars should show parallax.  It took another century for the first parallax of a star to be observed and measured.  In the 1830s, astronomers started observing  the star 61 Cygni, a fairly faint star in the constellation Cygnus.  61 Cygni drew their attention because it appears to move across the sky at a rate of 5 arcseconds a year; over a human lifetime of 60 years it moves a full 5 arcminutes, measurable with the unaided eye.  That fast motion could be explained if it is one of the closest stars to our Solar System.  And, in 1838, German astronomer and mathematician Friedrich Bessel measured its parallax: one third of an arcsecond in size, or only about 1/200th the smallest angle that the unaided eye could see!  No wonder nobody had detected it before -- Bessel needed both a telescope and special measuring equipment to detect that tiny parallax.   The distance to this star thus works out to be a whopping 67 trillion miles (11.4 light years), or 2000 times further than Aristarchus had estimated.

The parallax of 61 Cygni was additional proof that the Earth was moving around the sun, and it had only taken 2000 years to discover after the prediction was made.  Since then, parallaxes have been measured in hundreds of thousands of stars, each star making little tiny ovals in the sky as the Earth's viewpoint toward these stars changes.

One other proof that the Earth is moving comes from measuring the Doppler shifts in the light from stars.  If the Earth is moving around the sun, for part of its orbit it will be moving toward a given star at 66,600 miles per hour.  Six months later, the Earth will be moving away from that same star at that speed.  This speed should be detectable in the spectra of stars (the splitting of a star's light into its component colors), and we do, in fact, see this change.

All three of these pieces of evidence, aberration of starlight, parallax, and Doppler shifting of starlight, are explained by the motion of the Earth around the sun.  More than that, these are proofs of the Earth's motion around the sun.

And, perhaps best of all, if you don't believe me, you  can see and measure all three of these effects with your own telescope.  To be sure, these are tough measurements, and the measurements will take you a few years to finish.  You'll need some pretty accurate equipment: a telescope with very accurate pointing, a camera that can take sharp pictures, and a stable spectrograph that can make accurate and precise measurements of Doppler shifts.  Such equipment is already used by many amateur astronomers. I don't think that such projects would be worth the time, money, and effort to replicate a result that has been proven many times over; it's probably as exciting as sitting under a tree for 365 days.   But it is completely possible for anyone to do, and I think that's cool.

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