Dot Physics

Parallax, what is it good for?

Very simply, parallax is an apparent motion of an object due to a change in observation position. Let me start with an example. Here are two photos. I took a picture of the cabinet in the background from two slightly different positions. In the foreground is a clone trooper that did not actually move.

Parallax.key

I added the dotted line so you could see how the clone trooper appeared to change positions with respect to the background. Here is a diagram of the camera in the two positions along with the toy.

i-eff519563290e8f7d67a873082219665-parallaxkey_1.jpg

Since the camera changed positions, the object that is closer appears to have moved with respect to the objects that are farther away. You don’t need a clone trooper toy to see an example of parallax. You can do this with your thumb. Hold your thumb out in front of your face at arms length. Close one eye and line your thumb up with some object in the distance. Then switch eyes that you are looking out of. Here is a diagram.

i-b4559318a6150bda669333abe9b8fd9e-parallaxkey_2.jpg

If you can’t tell from my drawing, this is a diagram looking down on a person.

So, how is this useful? Well, early astronomers like the Greeks knew about parallax. If you know the distance between the two viewing locations and if you measure the apparent change in position of the object you can calculate the distance of the object. Great, the Greeks could use this to show that the Earth is orbiting the Sun (rather than the other way around). If you look at a star now and then 6 months later, you have changed your observation location by twice the radius of the Earth’s orbit. The closer stars should move relative to the stars that are more distant.

When the Greeks looked for the parallax in stars, they measured none. This must mean that the Earth is not orbit the Sun. However, the closest star only changes its apparent position by about 1 arcsecond (that is like 0.0003 degrees). A very very difficult angle to detect and measure. So, when Aristarcus proposed that the Sun is so big that the Earth must orbit it, all the other Greeks made fun of him and called him names.

Comments

  1. #1 Tom
    November 6, 2009

    I couldn’t resist turning your clone trooper photos into a stereogram
    http://blogs.scienceforums.net/swansont/archives/4062

  2. #2 Cleon Teunissen
    November 6, 2009

    Did other greeks actually make fun of Aristarchus?
    Or is that detail a fancy, to make the story juicier?

    I know, drama is appealing: the one voice who turned out to be right after all. But we don’t know what Aristarchus’ considerations were.

    It seems to me the prevailing opinion at the time is a good example of what would later be called Occam’s Razor. Don’t go beyond what you need to account for the observations.

    I feel it’s not fair to fault the ancient greeks for not knowing what we know today. That’s like mocking the captain of the Titanic for failing to use radar.

    Cleon Teunissen

  3. #3 Rhett
    November 6, 2009

    @Cleon,

    I made up the part about making fun of him. You know, like Rudolph the Red Nose Reindeer….

    You make a good point though.

  4. #4 Cleon Teunissen
    November 7, 2009

    About the views of the ancient greeks and later.

    To my knowledge: among greek scholars it was generally understood that the Earth had to be spherical. For instance, it was known that when there is a lunar eclipse the shadow that the Earth casts on the Moon is always circular. There were other clues too, such as the one that Erastothenes used for his estimate of the Earth’s diameter.

    The solar system was thought of as a system of transparent spheres, each within the other, a sphere for each celestial body. I suppose the sphere that enveloped the Earth was thought of as extending to the Moon. I suppose the Earth’s atmosphere was thought of as having the same density everywhere in that sphere.

    The ancient Greek scholar’s concept of motion was derived from everyday experience: to sustain motion a sustained force is necessary. If you give a single push to a cart it will roll, but pretty soon the cart will come to a standstill again.

    (Galilei’s supposition, centuries later, was incredibly daring. Galilei based his theory of motion on a thought experiment, which is staggering. On Earth friction is never absent, but Galilei supposed that IF friction would actually be absent then motion would continue indefinitely.)

    In the ancient greek worldview logic dictated that the Earth could not possibly be orbiting the Sun, for if it would then Earth would have to plow through all of the atmosphere that filled the Earth sphere.

    Also it could be excluded that the Earth was rotating on its own axis. If a force would keep the Earth in rotation all the time, (counterclockwise as seen from the pole star), then giant winds would be coming in from the East all the time. Even if you would factor in that the Earth would drag along the atmosphere close to the surface you’d still be experiencing non-stop eastern winds.

    The copernican revolution was in a sense two scientific revolutions, each one dependent on the other. Only when the theory of motion is shifted to being based on galilean mechanics does it become possible to think of the Earth as rotating on it’s own axis, and orbiting the Sun. Each shift in view, the heliocentric celestial model and Galilean mechanics, made the other shift possible; it was only with the two shifts together that any self-consistent wordview could be conceived.

    The ancient greek scholars, like all scientists, weren’t going to endorse a self-contradicting worldview.

    Cleon Teunissen

  5. #5 Cleon Teunissen
    November 7, 2009

    Oops, misspelled the greek name: it was ‘Eratosthenes’.

    Cleon Teunissen

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