Chapter 2: almost finished.
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31
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..
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.\" MS Accents
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.\".AM
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.defcolor citation rgb 0.4 0.4 0.4
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.de CITATION1
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.de EXPLANATION1
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@ -3,4 +3,5 @@
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.2C
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.so universe-from-nothing/preface.ms
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.so universe-from-nothing/ch1_a-cosmic-mystery-story_beginnings.ms
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.so universe-from-nothing/ch2_a-cosmic-mystery-story_weighing-the-universe.ms
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.so universe-from-nothing/annex-events.ms
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@ -26,9 +26,6 @@ we currently know as Andromeda).
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.BULLET
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.UL "1925, Mount Wilson 100-inch Hooker telescope" ,
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the world's largest at the time.
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.FOOTNOTE1
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We now make ten times bigger telescopes and hundred times bigger in area.
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.FOOTNOTE2
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.BULLET
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.UL "1927" :
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Lemaître shows that the Einstein's equations suggest an expanding universe.
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@ -36,6 +33,9 @@ Lemaître shows that the Einstein's equations suggest an expanding universe.
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.UL "1930" :
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Lemaître proposes an universe beginning in a small point he called
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.I "Primeval Atom" .
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.BULLET
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.UL "1933" :
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Zwicky concludes that the Coma cluster is about 100 times more massive than the sum of the masses of its stars.
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.ENDBULLET
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.SH
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@ -66,6 +66,8 @@ star whose brightness varies over some regular period, indicating a change in di
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.BULLET
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.UL "Doppler Effect" :
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a wave coming at you will be stretched if the source is moving away from you, or compressed if the source is coming toward you.
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.BULLET
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.UL "Nuclei" :
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.ENDBULLET
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.SH
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@ -93,7 +95,7 @@ astronomer.
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.BULLET
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.UL "Henrietta Swan Leavitt" :
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Harvard College Observatory "computer".
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Discovered the relation between Cepheid variable stars' brightness and period of vacation.
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Discovered the relation between Cepheid variable stars' brightness and period of variation.
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.BULLET
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.UL "Edwin Hubble" :
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former lawyer, became astronomer.
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@ -104,12 +106,24 @@ discovered the Sun wasn't at the center of the Milky Way, and that our galaxy wa
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.BULLET
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.UL "Vesto Slipher" :
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astronomer, he measured the spectra of light coming from several galaxies.
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.BULLET
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.UL "Fritz Zwicky" :
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astronomer, analyzed in 1933 that galaxies in the Coma cluster were moving so fast they would have quit the cluster unless the cluster was 100 times more massive than the sum of the masses of the stars.
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.BULLET
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.UL "Tony Tyson" :
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physicist.
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Discovered the mass between galaxies through images from the Hubble Space Telescope.
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.ENDBULLET
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.SH
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Random explanations
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.PP
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.METAINFO1
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TODO: explain how we measure stuff with telescopes (resolution, focal, arcsecond unit, etc.).
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.METAINFO2
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Diffraction: behavior of waves when reaching an aperture.
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.PS
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@ -149,7 +163,7 @@ APERTURE: circle fill fill_light_source dashed
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# LEGEND.
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move; move
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move 0.6
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arrow to APERTURE chop 0 chop rad_aperture
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move to last arrow.s + (txt_x_shift,txt_y_shift)
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"Aperture, where light can pass through" ljust
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@ -168,6 +182,11 @@ move to last arrow.s + (0,space_between_arrows_y)
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arrow to LIGHT_SOURCE chop 0 chop rad_large_circle
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move to last arrow.s + (txt_x_shift,txt_y_shift)
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"Halo, thin light" ljust
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# let's cheat a little
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# Center the figure.
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false_line_x = 2.7
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line from LIGHT_SOURCE + (false_line_x,0) to LIGHT_SOURCE + (false_line_x,0)
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]
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move to CIRCULAR_DIFFRACTION_FIGURE + (0, -1)
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@ -1,12 +1,17 @@
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.NH
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.NH 1
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a cosmic mystery story: beginnings
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.PP
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.METAINFO1
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Contrary to the book, I'll describe things chronogically in the summary.
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Contrary to the book, I describe things chronogically in the summary.
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Some pieces of information (such as dates, explanations, events), absent from the book, are added for the sake of completeness.
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.METAINFO2
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1514: Nicolaus Copernicus suggests an heliocentric model.
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.EXPLANATION1
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Planets move around the sun.
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.EXPLANATION2
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Between 1609 and 1619: Johannes Kepler publishes his
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.I "laws of planetary motions" ,
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which fixes a few problems with the view of Copernicus on the matter:
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@ -19,6 +24,28 @@ The Sun is not near the center but at a focal point of the elliptical orbit.
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Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed (closely linked historically with the concept of angular momentum) is constant.
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.ENDBULLET
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Another way to express the same thing, with a direct citation from the book:
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.BULLET
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Planets move around the sun in ellipses.
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.BULLET
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A
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.I line
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connecting a planet and the Sun sweeps out equal
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.I areas
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during equal intervals of time.
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.BULLET
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The
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.I square
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of the
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.I "orbital period"
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of a planet is directly proportional to the
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.I cube
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(3rd power) of the
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.I "semi-major axis"
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of its orbit (or, in other words, of the "semi-major axis" of the ellipse, half of the distance across the widest part of the ellipse).
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.ENDBULLET
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1665: Isaac Newton uses a prism to see the sunlight disperse into the colors of a rainbow.
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He manages to obtain this result by only letting the light of the sun enter a room by a small hole in the window shutter.
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His conclusion: the white light contains all these colors.
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@ -27,12 +54,14 @@ His conclusion: the white light contains all these colors.
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Sunlight contains a spectrum of colors.
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.EXPLANATION2
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(around) 1815: another scientist
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1784: first observation of Cepheid variable star, which are stars whose brightness varies over some regular period.
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(around) 1815: a scientist
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.FOOTNOTE1
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His name is not given in the book.
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.FOOTNOTE2
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analyses the dispersed light: some colors aren't there.
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His conclusion: some materials in the outer atmosphere of the sun are absorbing the light of certain colors or wavelengths.
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His conclusion: some materials in the outer atmosphere of the sun are absorbing the light of certain colors or wavelengths.
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Known materials are tested to see what are the colors they
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.I absorb ,
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which includes: hydrogen, oxygen, iron, sodium, and calcium.
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@ -44,15 +73,13 @@ some part of the solar spectrum.
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Different materials, different parts of the spectrum.
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.EXPLANATION2
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1784: first observation of Cepheid variable star, which are stars whose brightness varies over some regular period.
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1842: Christian Doppler discovers the Doppler Effect.
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.EXPLANATION1
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Doppler Effect: a wave coming at you will be stretched if the source is moving away from you, or compressed if the source is coming toward you.
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.EXPLANATION2
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1868: another scientist
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1868: a scientist
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.FOOTNOTE1
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Again, not named in the book.
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.FOOTNOTE2
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@ -78,7 +105,7 @@ The spectrum of radiation of stars provides their composition, temperature and e
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1908-1912: Henrietta Swan Leavitt discovers a relation between the brightness of Cepheid variable stars and their pulsation period.
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.EXPLANATION1
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The light spreads out uniformly over a sphere whose area increases as the square of the distance.
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The light spreads out uniformly over a sphere whose area increases as the square of the distance (this is called the inverse-square law).
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Thus since the light is spread out over a bigger sphere, the intensity of the light observed at any point decreases inversely with the area of the sphere.
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.EXPLANATION2
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.NAMECITATION "TODO: find out who and when this was discovered"
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@ -89,9 +116,6 @@ Also, the observed brightness of stars goes down inversely with the square of th
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Therefore, comparing its known luminosity to its observed brightness gives us the actual distance to the star.
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.EXPLANATION2
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Knowing the distance between us and these stars leads to a new map of the world.
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Other galaxies will soon be discovered, as some stars are too far to be within our Milky Way.
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.\".CITATION1
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.\"If one could determine the distance to a single Cepheid of a known period, then measuring the brightness of other Cepheids of the same period would allow one to determine the distance to these other stars.
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.\".CITATION2
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@ -124,11 +148,26 @@ Gravitation is thought to be an attractive force: objects should then always col
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Also, the scientific community still thinks the universe as static, eternal and composed of a single galaxy (our Milky Way) surrounded by a vast, dark, infinite empty space.
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And without accurate knowledge of the distances with observed stars, nor better images, this idea seems consistent with the observations.
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1923-1924, with the period-luminosity relation and the measurement of Cepheid variable stars, Hubble determines that the distance with some Cepheids was too great to be inside our Milky Way.
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The universe contains
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.I "at least"
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another galaxy.
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He identifies a first galaxy (NGC 6822) in 1925, then the Triangulum galaxy (M33) in 1926, and Andromeda (M31) in 1929.
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1917: Mount Wilson 100-inch (2.5 m) Hooker telescope, the world's largest at the time (from 1917 to 1949).
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It will soon help to discover many things.
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For example,
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to prove the Andromeda nebula is external to our galaxy (1923, Edwin Hubble),
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that the Universe is expanding (1929, Hubble and Milton Humason)
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and to measure both its expansion rate and the size of the known Universe,
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to find evidence for dark matter (1930s, Fritz Zwicky),
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etc.
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.FOOTNOTE1
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We now make ten times bigger telescopes and hundred times bigger in area.
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.FOOTNOTE2
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1923-1924, with the period-luminosity relation and the measurement of Cepheid variable stars, Hubble determines that the distance with some Cepheids are too great to be inside our Milky Way.
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.FOOTNOTE1
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Hubble identifies a first galaxy (NGC 6822) in 1925, then the Triangulum galaxy (M33) in 1926, and Andromeda (M31) in 1929.
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.FOOTNOTE2
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.EXPLANATION1
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The universe contains other galaxies.
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.EXPLANATION2
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1925: Hubble publishes his study on spiral
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.I nebulae ,
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@ -136,14 +175,22 @@ where he identified Cepheid variable stars in them (including the
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.I nebulae
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we currently know as Andromeda).
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1925: Mount Wilson 100-inch Hooker telescope.
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1927: Georges Lemaître is the first person to suggest the universe was expanding.
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1927: Georges Lemaître is the first person to suggest the universe is expanding.
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This is his conclusion after solving the Einstein's equations for general relativity.
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1929: Hubble remarks that galaxies are moving away from each other.
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More importantly, the more distant, the faster the velocity.
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The relation is linear: a galaxy twice more distant is moving away twice as fast.
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.EXPLANATION1
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The universe is expanding.
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.EXPLANATION2
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1930: Georges Lemaître proposes that the universe began in a very small point, which he called
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.I "Primeval Atom" .
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.FOOTNOTE1
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This isn't accepted by the scientific community right away: actual observations were provided by Edwin Hubble beforehand.
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.FOOTNOTE2
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.SH 2
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Random facts: current state of knowledge
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@ -155,14 +202,30 @@ Our galaxy is one of the about 100 to 400 billion other galaxies in the observab
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Over 200 million stars already exploded within our galaxy, providing us the material resources necessary for life on Earth.
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Big Bang created light elements in massive quantities, such as hydrogen.
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However, heavier elements require the stars to be created (by their massive gravity), and their explosion to be dispersed accross the galaxy.
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No nuclei heavier than lithium were produced during the initial universe expansion (too hot).
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Heavier elements require the stars to be created (by their massive gravity), and their explosion to be dispersed across the galaxy.
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The universe expansion explains the abundance of light elements.
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.EXPLANATION1
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Life on Earth is, literally, made of stars.
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.EXPLANATION2
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A supernovae (the explosion of a star) occurs once every hundred years or so per galaxy.
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A supernova (the explosion of a star) occurs once every hundred years or so per galaxy.
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The last one in our galaxy was in 1604.
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Rare events, such as supernovae, happen constantly at the scale of the universe.
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Therefore, each night with a good enough telescope, you can expect to see a supernovae.
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Rare events, such as supernova, happen constantly at the scale of the universe.
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Therefore, each night with a good enough telescope, you can expect to see a supernova.
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Type 1a supernova (a certain type of exploding star) accurate luminosity can be infered by the duration they shine.
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Their
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.I observed
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brightness provides their distance (with the inverse-square law), which also determines the distance with their galaxy.
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Then, the redshift of the light from the stars in the galaxy indicates its velocity.
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Finally, comparing the velocity of the galaxy and its distance allows us to infer the
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.I "expansion rate of the universe" .
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Galaxies are more and more distant from each other, this is the general trend.
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In some cases, two galaxies may collide, but that is rare (again, rare events happen all the time).
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Independent estimates of the age of the oldest stars in our galaxy are consistent with the rate of the universe's expansion.
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The Big Bang is consistent with all the different ways we observed our universe, with independent methods.
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@ -0,0 +1,214 @@
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.NH 1
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a cosmic mystery story: weighing the universe
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.PP
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.METAINFO1
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Work in progress.
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.METAINFO2
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.METAINFO1
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This chapter is about the knowlegde and thought the scientific community had up to the 1980s.
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.METAINFO2
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.QUESTION "How will the Universe end?"
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Since the Universe isn't static, there are three main possibilities.
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The first one is the
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.I "Big Crunch" :
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the Universe will collapse, creating a reverse Big Bang.
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In the second case the Universe will
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.B almost
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stop expanding.
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Last possibility, the Universe will continue to expand at a finite rate.
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To know the answer,
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Gravity shapes solar systems as well as galaxies and
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.I clusters
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of galaxies.
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But the apparent gravity force cannot be explained only by visible objects, such as stars and planets.
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For example, the movement speed of stars (and hot gas) within our galaxy isn't explained only by the sum of gravitational forces of other stars, gas and planets.
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Also, the mathematical formulas leading to the explanation of the abundance of light elements (hydrogen, helium and lithium) in the universe
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.FOOTNOTE1
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TODO: explain these formulas.
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.FOOTNOTE2
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give an approximation of the total number of protons and neutrons must exist in the universe.
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Problem: there should be twice the amount of material we can see in stars and hot gas.
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.FOOTNOTE1
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Some of the non observed matter is contained in planets, since it is hard to see something that doesn't produce light.
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.FOOTNOTE2
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Second problem: even then, this isn't even remotely near enough material to explain the mass of galaxies.
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Invisible matter should represent ten times the mass of visible matter.
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So, this
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.I "dark matter"
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cannot be only made of neutrons and protons.
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.EXPLANATION1
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The Universe is mostly made of matter we don't understand.
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.EXPLANATION2
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Maybe this dark matter is made of a particle that can be identified through calculations or educated guess for example.
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This way, new experiments could be proposed to detect this dark matter, and learn more on what appears to be the main component of the universe.
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Later, to that end, we built machines on Earth to recreate an environment where these particles could be created (see the
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.I "Large Hadron Collider" ).
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We also created dectectors, deep in mines to avoid perturbations from all sorts of cosmic rays.
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.CITATION1
|
||||
The job of physics is not to invent things we cannot see to explain things we can see, but to figure out how to see what we cannot see.
|
||||
.CITATION2
|
||||
.NAMECITATION "Lawrence Krauss"
|
||||
|
||||
Knowing the abundance (and the nature) of dark matter is important to know how the Universe will end.
|
||||
Two possibilities are given in the book to make this calculation.
|
||||
First, in case this "dark matter" was created during the Big Bang, then its abundance could be estimated by ideas from the forces that govern the interactions of elementary particles.
|
||||
Second, by reusing some ideas from particle physics.
|
||||
.FOOTNOTE1
|
||||
In both cases: the chapter doesn't include an explanation of what these
|
||||
.I ideas
|
||||
could be.
|
||||
That's kind of a bummer.
|
||||
.FOOTNOTE2
|
||||
|
||||
.\" .CITATION1
|
||||
.\" If these particles were created in the Big Bang, like the light elements (hydrogen, helium and lithium), then we should be able to use ideas about the forces that govern the interactions of elementary particles (instead of the interactions of nuclei relevant to determine elemental abundance) to estimate the abundance of possible exotic new particles in the universe today.
|
||||
.\" .CITATION2
|
||||
.\" .NAMECITATION "Lawrence Krauss"
|
||||
.
|
||||
Einstein general relativity predicted that space is curved in the presence of matter or energy.
|
||||
This leads to our universe having different possible geometries depending on the total density of mass in the universe.
|
||||
.FOOTNOTE1
|
||||
This isn't explained further in the chapter how the general relativity actually indicates that.
|
||||
Second bummer.
|
||||
.FOOTNOTE2
|
||||
|
||||
The first possible geometry of our universe could be
|
||||
.I closed .
|
||||
It can be described as a
|
||||
.I "three-dimensional sphere" .
|
||||
A way to picture it is to imagine looking far enough in any direction and see the back of your head.
|
||||
In this case, the general relativity tells us the energy density of the universe is dominated by matter like stars, galaxies and this
|
||||
.I "dark matter" ,
|
||||
and will end in a Big Crunch.
|
||||
The second is the
|
||||
.I open
|
||||
universe.
|
||||
The universe will continue to expand at a finite rate.
|
||||
Finally, the
|
||||
.I flat
|
||||
universe, which expands but slow down with time without ever stopping.
|
||||
This requires the "dark matter" to be 100 times more massive than visible matter.
|
||||
|
||||
.QUESTION "How to get the density of mass in the universe?"
|
||||
The largest gravitationally bound objects are
|
||||
.I "superclusters of galaxies"
|
||||
that can contain thousands of galaxies (or more).
|
||||
These are so massive, most of galaxies are within a supercluster.
|
||||
Measuring the weight of a supercluster (which also includes its dark matter) and then estimating the density of superclusters in the universe leads to
|
||||
.I "weighting the universe".
|
||||
|
||||
.QUESTION "How to get the density of mass of a supercluster?"
|
||||
In one word: gravity.
|
||||
Gravity bends space, so bright objects behind something massive (such as a galaxy, or a cluster of galaxies) can be seen.
|
||||
So, gravitational lensing is a thing.
|
||||
Also, Fritz Zwicky analyzed as early as 1933 that galaxies in the Coma cluster were moving so fast they would have quit the cluster unless the cluster was 100 times more massive than the sum of the masses of the stars.
|
||||
Therefore, the speed of galaxies in a cluster can be some sort of metric to estimate the density of a cluster, too.
|
||||
|
||||
.METAINFO1
|
||||
Note: at the time, little was known of black holes, red dwarves, neutron stars, etc.
|
||||
A good chunck of the missing mass actually comes from these objects, with little to no light emissions.
|
||||
.METAINFO2
|
||||
|
||||
In 1998, the physicist Tony Tyson shows that the mass of a cluster mostly comes from between the galaxies.
|
||||
He used magnified images of a distant galaxy from the Hubble Space Telescope to calculate its mass.
|
||||
The mass was computed with a mathematical model of the cluster of the galaxy, using laws of general relativity, and calculating a lot of paths.
|
||||
.FOOTNOTE1
|
||||
From what is actually written in the book, this seems almost like an exhaustive computation.
|
||||
An evolutionary algorithm maybe?
|
||||
Too bad there isn't much details: Krauss said the model was based on general relativity but the actual algorithm (to some extent) could have been interesting to learn.
|
||||
.FOOTNOTE2
|
||||
Finally, once the model produced an image like the one the observation, the model was used to determine the mass of the cluster.
|
||||
The result was, as stated before, that the mass of the cluster mostly comes from between the galaxies, not from stars or hot gases.
|
||||
More precisely: there is 40 times more mass between the galaxies than within, which is 300 times more mass than within stars alone with the rest of visible matter in hot gas around them.
|
||||
|
||||
.CITATION1
|
||||
[...] more recent observations from other areas of astronomy have confirmed that the total amount of dark matter in galaxies and clusters is far in excess of that allowed by the calculations of Big Bang nucleosynthesis.
|
||||
Dark matter must be made of something that isn't normally on Earth nor in stars.
|
||||
.CITATION2
|
||||
.NAMECITATION "Lawrence Krauss"
|
||||
|
||||
Dark matter should be all around us, including basically everywhere on Earth.
|
||||
It should be comprised of an elementary particle (or several particles) and experiments are done to detect it.
|
||||
As already said: deep in mines and with the LHC.
|
||||
Since it doesn't interact electromagnetically (therefore, it doesn't absorb, reflect or emit light), we assume that its interactions with normal material are extremely weak.
|
||||
Dark matter could, for example, traverse anything.
|
||||
Therefore, it will be difficult to detect.
|
||||
Removing most of the cosmic rays of the equation is necessary and this is why the dark matter detection is expected to be made deep in mines.
|
||||
The LXC also has a great chance to detect dark matter, by recreating what is thought to be an environment near the conditions of the early universe.
|
||||
This is done by smashing protons together with an incredible energy.
|
||||
Direct observation is not necessary, an imbalance between the energy used to smash protons and the result could be an indicator that something emerged from the experiment.
|
||||
|
||||
.METAINFO1
|
||||
The book is from 2009, since then the LXC actually produced results.
|
||||
However, as the time of this writting (october 2021), still no direct confirmation that dark matter actually exist.
|
||||
.METAINFO2
|
||||
|
||||
.SH
|
||||
Random facts
|
||||
.PP
|
||||
.PS
|
||||
.ps 7
|
||||
reset
|
||||
mag_massive_obj_x = 1.4
|
||||
mag_massive_obj_y = -1
|
||||
.
|
||||
rad_obs = 0.3
|
||||
rad_massive_obj = 0.5
|
||||
rad_mag = 0.4
|
||||
rad_dist = 0.27
|
||||
.
|
||||
.defcolor lightgreen rgb 0.9 1.0 0.9
|
||||
.defcolor lightblue rgb 0.9 0.9 1.0
|
||||
.defcolor bloatcode rgb 1.0 0.1 0.1
|
||||
down
|
||||
OBSERVER: circle rad rad_obs "Observer"
|
||||
move
|
||||
MASSIVE_OBJECT: circle rad rad_massive_obj "Massive" "object"
|
||||
move 1
|
||||
TARGET: circle rad rad_dist "Distant" "object"
|
||||
move to MASSIVE_OBJECT + ( mag_massive_obj_x, mag_massive_obj_y)
|
||||
MAGNIFIED1: circle rad rad_mag "Magnified" "distant" "object"
|
||||
move to MASSIVE_OBJECT + (-mag_massive_obj_x, mag_massive_obj_y)
|
||||
MAGNIFIED2: circle rad rad_mag "Magnified" "distant" "object"
|
||||
.
|
||||
line from MAGNIFIED1 to OBSERVER chop rad_mag chop rad_obs dashed
|
||||
line from MAGNIFIED2 to OBSERVER chop rad_mag chop rad_obs dashed
|
||||
.
|
||||
rad_correction = 0.32
|
||||
spline -> from TARGET to MASSIVE_OBJECT.e + (rad_massive_obj-rad_correction,0) to OBSERVER chop rad_dist chop rad_obs
|
||||
spline -> from TARGET to MASSIVE_OBJECT.w + (-rad_massive_obj+rad_correction,0) to OBSERVER chop rad_dist chop rad_obs
|
||||
.
|
||||
move to TARGET + (0,-0.7)
|
||||
.ps 14
|
||||
"Gravitational lensing"
|
||||
.PE
|
||||
.
|
||||
According to Zwicky, gravitational lensing can be useful for:
|
||||
.BULLET
|
||||
testing the general relativity;
|
||||
.BULLET
|
||||
using galaxies to magnify distant objects;
|
||||
.BULLET
|
||||
determine the mass of a galaxy or a cluster.
|
||||
.ENDBULLET
|
||||
.
|
||||
.SH
|
||||
Anecdotes
|
||||
.PP
|
||||
Einstein became famous mostly because he predicted sunlight curving around the Sun during an eclipse in 1919.
|
||||
It wasn't because of its famous mathematical equation in 1904:
|
||||
.EQ
|
||||
E = mc sup 2
|
||||
.EN
|
||||
|
||||
Einstein predicted that gravity could help see objects beyond other objects, through lensing.
|
||||
Gravity bends space, so bright objects behind a massive object can still be seen.
|
||||
This is practical: objects can be seen by gravitational lensing via galaxies or cluster of galaxies.
|
||||
However, Einstein thought at the time that his prediction was useless since he only thought of star by star lensing.
|
|
@ -39,5 +39,5 @@ Lastly compiled the
|
|||
(day/month/year, you know, like in any sane civilization).
|
||||
.br
|
||||
.UL Status :
|
||||
preface OK. Just starting.
|
||||
preface and chapter 1: OK. Chapter 2: just starting.
|
||||
.AE
|
||||
|
|
Loading…
Reference in New Issue