| Stellar Parallax: The Astronomical Chicken
Distances from Stellar Parallaxes.
Despite the emphasis which I gave it in the previous section of the notes, stellar parallax does much more than merely demonstrate that the Earth moves around the sun, allowing us to look at stars from differing perspectives. It is also the fundamental tool for determining the distances of the stars.
Look again at the figure on page 525 of your textbook. The measured shifts tell us the size of the parallactic angle. (For all real stars, this angle is fantastically smaller than that shown because of the remoteness of the stars.) Once we know how far the Earth is from the sun (a distance of 150,000,000 km, which we call one Astronomical Unit), we can use simple geometry and the properties of triangles to work out the distance of the star for which the parallax has been noted and measured.
Perhaps you were clever enough to realise that it is necessary, in principle at least, to take into account the fact that some of the background stars in the field of view will themselves display parallactic shifts, of smaller size thanks to their larger distances. In general, though, any nearby star will be seen against a backdrop of others so much farther away that this is not a severe problem. The real difficulty is the tiny size of the angles to be measured. Even for the nearest star outside our own Solar System, the parallactic angle is less than one second of arc. [See page 31 of your textbook for a reminder about the units we use in the measurement of angles.]
As we saw in the previous section, there are
of proving that the Earth orbits the sun -- the phenomenon of aberration, for instance. But none of them provides or depends in any direct way upon this critical extra piece of information, the distance of the star under scrutiny. For that reason, parallax measurements are correctly seen as being of fundamental importance in astronomy and astrophysics.
The Astronomical Chicken.In many texts, analogies are drawn between stellar parallax measurements and the human binocular vision which gives us depth perception. This is a little misleading. As we saw in an earlier discussion, provides the brain with two simultaneous but slightly-out-of-register images which can be interpreted to yield depth perception. By contrast, stellar parallax work requires images which are taken months apart, images which are then intercompared to derive the critical information, so there is no real depth perception. A more apt analogy might be to the behaviour of a chicken (according to a discussion I have lately read; I cannot vouch for its correctness!). Chickens have eyes on either sides of their heads, which means that they have no binocular vision at all and thus no depth perception. Perhaps you have noticed that chickens walk with abrupt jerking motions of their heads. The suggestion has been made that this allows the chicken to synthesize a binocular image in the following way: the chicken fixes one eye on the ground by cocking its head to one side; it focuses on an interesting piece of grain; and it steps forward slowly and then abruptly snaps its head into a new position, with a suddenly different perspective. It has been argued that the quick change of position gives it two different images to consider, with implicit distance information because of the parallax effects. In this sense, then, astronomers are acting like astronomical chickens, saving one image from June (let us say) to compare with the image from January. And it works! Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Sunday, 25 February, 2018.)