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J. Perelman
"Entertaining physics". Book 2.
Chapter 9. Reflection and refraction of light. Vision


If, while keeping the angular size, we wished to portray on paper the constellation URSA major, that would get the figure shown in the figure below. Looking at it from a distance top view, we see the constellation of the way it draws us to the heavenly arch. That is to say, the map of the Big dipper with the conservation of angular dimensions. If you are familiar with the visual impression from this constellation, is not only a figure, namely the immediate visual impression, looking at the attached picture , it looks like you are reliving this impression. Knowing the angular distance between the main stars of all constellations (they are given in the astronomical calendars and detailed handbooks), you can draw in the "natural form" of the whole astronomical Atlas. It is enough to stock up on millimeter paper and count on drink every 4.5 mm per degree (square circles, depicting stars, it is necessary to draw proportional to the brightness).

The constellation URSA major with the conservation of angular dimensions.
Keep the figure at a distance of 25 cm from the eye.

Let us now turn to the planets. The apparent size them as stars are so small that the naked eye they seem radiant points. This is understandable, because no one planet (except Venus in the period of its greatest brightness) does not seem to the naked eye at an angle for more than 1 minute, i.e., the limit value at which we can distinguish the object as the body sizes (at a smaller angle each item seems to be the point without outlines).

Here are the values of the different planets in angular seconds; against each planet shows two numbers - the first corresponds to the smallest distance of the lights from the Earth, the second - largest:

  • Mercury 13 - 5
  • Venus 64 - 10
  • Mars 25 - 3,5
  • Jupiter 50 - 31
  • Saturn 20 - 15
  • The Rings Of Saturn 48 - 35

To draw these values in the "natural scale" on paper there is no possibility: even the whole angular minute, i.e., 60 seconds, is responsible, at a distance top view of only 0.04 mm - size, indistinguishable to the unaided eye. Draw so planetary disks as they appear in the telescope that magnifies 100 times. The figure here is a table of visible sizes of planets at high magnification.

If you hold the drawing at a distance of 25 cm from the eye, then drawn on it planetary disks will appear to us in size exactly what is visible planet in a telescope that magnifies 100 times.

The lower arc depicts the edge of the lunar (or solar) disk in a telescope with a 100-fold magnification. Above - mercury at least its distance from the Earth. Even higher Venus in different phases; in the near to us the position of this planet is absolutely not visible, as it faces the Earth unillumined half*; then it becomes visible narrow hammer, is the greatest of all planetary disks"; later phases of Venus is still decreasing, and full disk has a diameter, 6 times less than that of a narrow Crescent.

Above Venus depicts Mars. To the left you see him in the greatest proximity to the Earth; therefore shows us his trumpet its 100-fold magnification. What can be discerned on this little disc? Imagine the same circle multiplied by 10, and get a glimpse of what he sees astronomer studying Mars in the most powerful telescope with 1000-fold magnification. Is it possible to have such a close space to grasp with certainty such subtle details, like the proverbial "channels", or to notice a slight change in color associated though with vegetation at the bottom of the "oceans" of this world? It is not surprising that evidence of some observers significantly at odds with the testimony of others, and some consider an optical illusion that seemed to be clearly seen by others.

Giant Jupiter with its satellites occupies a very prominent place in the Pasha table; his drive significantly more disk other planets (excluding sickle Venus), and the four main satellites scattered along the line, equal to almost half of the lunar disk. Here Jupiter is depicted in the greatest proximity to the Earth. Finally, Saturn with rings, and the largest of its moons (Titan) is also quite noticeable object in the moments of greatest intimacy to us,

After telling the reader it is clear that every visible object seems to be the smaller, closer than we imagine. And Vice versa: if for some reason we exaggerate the distance to the subject, and the subject will seem to be correspondingly large.

The following is an instructive story of Edgar Allan PoE, describing such an illusion. The seeming nepravdopodobna he's not fantastic. I became once a victim is almost the same illusion, and many of our readers will probably recall similar cases from their own lives.

*It can be seen in this position only in those extremely rare moments when it is projected on the Solar disk in the form of a black circle (the so-called "transit of Venus").

Entertaining physics J. Perelman


System Orphus


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