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Please note!

    Listed below are questions submitted by users of "From Stargazers to Starships" and the answers given to them. This is just a selection--of the many questions that arrive, only a few are listed. The ones included below are either of the sort that keeps coming up again and again, or else the answers make a special point, often going into details which might interest many users.


For a list including questions not listed here, click here. You may also Link from here to a listing of questions arranged by topic.



Items covered:

  1. About asteroids hitting Earth.
  2. The swirling of water in a draining tub.
  3. Dispensing water at zero-g.
  4. Robert Goddard and World War II.
  5. Asymmetry of the Moon's orbit.
  6. Measuring distance from the Sun.
  7. Who owns the Moon?
  8. Acceleration of a rocket.
  9. Rebounding ping pong balls (re. #35)
  10. Rebounding ping pong balls and gravity-assist
  11. Why don't we feel the Sun's gravity pull?
  12. How hot are red, white and blue (etc.) stars?
  13. How does the solar wind move?
  14. The shape of the orbit of Mars
  15. What if the Earth's axis were tilted 90° to the ecliptic?


  16. Mars and Venus
  17. Where is the boundary between summer and winter?
  18. The Ozone Hole
  19. What keeps the Sun from blowing up?
  20. Those glorious Southern Skies!
  21. Should we fear big solar outbursts?
  22. Planetary line-up and the sunspot cycle
  23. What are comet tails made of?
  24. If light speed sets the limit, why fly into space?
  25. Does precession mis-align ancient monuments?
  26. Why does the Earth rotate? Why is it a sphere?
  27. What's so hard about reaching the Sun?


  28. Where does space begin?
  29. Gravity at the Earth's Center
  30. Radiation hazard in space (3 queries)
  31. "Danger, falling satellites"?
  32. The Lagrangian L3 point
  33. Distance to the Horizon on an Asteroid
  34. Overtaking Planets
  35. Falling Towards the Sun
  36. The Polar Bear
  37. Are the Sun's Rays Parallel?
  38. More thrust in reverse than going forward?
  39. The varying distance between Earth and Sun
  40. Mission to Mars
  41. Kepler's calculation
  42. The Appearance (Phase) of the Moon


  43. Stability of Lagrangian points
  44. Can an Asteroid Impact Change the Earth's Orbit?
  45. Can Gravity Increase with Depth?
  46. Lightspeed, Hyperspace and Wormholes
  47. Why do Rockets Spin?
  48. Around What does the Sun Revolve?
  49. Why are planets in nearly the same plane?
  50. The Shapes of Rockets and Spacecraft
  51. Space Debris
  52. Teaching Nuclear Fusion
  53. Contribution of different elements to Sunlight
  54. Jewish Calendar
  55. Spaceflight Without Escape Velocity?
  56. Who first proposed a round Earth?
  57. Does Precession change the Length of a Year?
  58. The Analemma
  59. Changes of the Polar Axis of Earth
  60. Van Allen Belt and Spaceflight
  61. Nearest Star Outside Our Galaxy
  62. (a) Why are Satellites Launched Eastward?
          What is a "Sun Synchronous" orbit?
     (b) Why are satellites launched from near the equator?

  63. How Tall Can People Get?
  64. Gunpowder and Rockets
  65. Precession
  66. Solar Sails
  67. (a) Distance to the Big Dipper
     (b) Big Dipper star names



  68. Was Moon landing a hoax?
  69. Clockwise or counter-clockwise?
  70. Isotopes in Center of Earth
  71. Density of the Sun's corona and the "Scale Height"
  72. Did Tesla extract free energy from thin air?
  73. What does "lapse rate" mean?
  74. Motion of the Sun through space
  75. Teaching about tides
  76. Distance to the Horizon
  77. Can geocentrist theory still be possible?
  78. Can Earth's rotation reverse, like its magnetic polarity?
  79. Why is the Earth round?
  80. The De Laval Nozzle
  81. Why 23.5 degrees?
  82. What is Gravitational Collapse?
  83. Can Earth capture a second moon?


  84. How far does the Earth's gravity extend?
  85. How far is the Moon?
  86. Twinkle, twinkle little star-- How I wonder, what you are.
  87. Teaching about seasons
  88. Space Launches by Cannon--A
  89. Space Launches by Cannon--B
  90. The Southern Pole of the Sky
  91. Do Astrologers use Wrong Positions for Planets?
  92. Why does the Moon have bigger craters?
  93. Why does Gravity Exist?
  94. Atmospheric "Thermals"--Triggered by Electric Forces?
  95. What would happen if Earth rotated faster?
  96. Where do gravity of Earth and Sun balance?
  97. The Ultimate Astronomy Tool
  98. High Temperature in Cold Outer Space


  99.   Refraction of sunlight and starlight by the atmosphere
  100.   Advice to a would-be astronomer
  101.   The effect of the Color of Light on the Output of Solar Cells
  102.   What is "radiation"?
  103.   Height of the Atmosphere
  104.   How does the upper atmosphere get so hot?
  105.   History of the use of De Laval's nozzle on rockets
  106.   Why don't Space Rockets use Wings?
  107. Distance of horizon on Mars
  108. Stopping the rotation of Earth?
  109. The equation of a parabola
  110. When does Jewish Sabbath start in the far north?
  111. Where is the center of the global landmass?
  112. What if our Sun was a much hotter star?
  113. Finding the north direction


  114. Why not use a heat shield going up?
  115. When and where can rainbows be seen?
  116. The unusual rotation of the planet Venus
  117. Why not use nuclear power for spaceflight?
  118. "Doesn't heat rise?"
  119. Have any changes been observed on the Moon?
  120. Why isn't our atmosphere flung off by the Earth's rotation?
  121. Can kinetic energy be reconverted to work?
  122. Does any location get the same number of sunshine hours per year?
  123. Speed of toy car rolling off an inclined ramp
  124. Acceleration due to gravity


  125. Re-entry from Space
  126. Balancing a Bicycle
  127. Is Absolute Zero reached on the Moon?
  128. Why isn't Longitude measured from 0° to 360°? "Constellation" or "Asterism"?
  129. "Position of the Stars when I was Born"
  130. Rotation of the Earth's Core"
  131. How hot is the Sun?
  132. How much weaker is gravity higher up?
  133. Eclipse of Venus?
  134. The Big Bang


  135. Thanks for the "Math Refresher" in Spanish
  136. The Pressure of Sunlight
  137. How is the instant the seasons change determined?
  138. Operation of Ion Rockets
  139. Physical Librations of the Moon
  140. The De-Laval Nozzle
  141. Why does the space shuttle rotate at take-off?
  142. Cold Fusion
  143. What if a Neutron Star hit the Sun?
    Why did the Moon appear Red?
  144. Centrifuge for Whirling Astronauts
  145. What Holds Galaxies Together?
  146. View of Earth and Moon from Mars
  147. Appearance of the Moon (1)
  148. Appearance of the Moon (2): Does it "roll around"?
  149. Altitude of the tail of the Big Dipper
  150. Sudden decompression, 5 miles up


  151. Do Negative Ions make you Feel Good?
  152. Shape of the Earth's Orbit
  153. Questions about the Solar Corona:
                       (1) Why don't its particles separate by weight?
                       (2) What accelerates the solar wind?
  154. Why does the rising Sun look so big?
  155. Drawing a Perpendicular Line in Rectangular Coordinates
  156. Unequal Seasons
  157. Is the Big Dipper visible from Viet Nam?
  158. Holes in a Solar Sail
  159. Consequences of no more solar X-rays
  160. Science Fair Project on the Size of the Earth
  161. Superposition of Waves
  162. The Sun and Seasons
  163. If the Earth's Rotation would   S t o p...     (1)
  164. If the Earth's Rotation would   C h a n g e...     (2)
  165. What if the Earth stopped in its orbit?
  166. Fast Trip to Mars     (1)
  167. Fast Trip to Mars     (2)


  168. Spacecraft Attitude
  169. What makes the Earth rotate?
  170. Energy from the Earth's Rotation?
  171. How were planets created?
  172. Does Precession of the Equinoxes shift our Seasons?
  173. "Zenial Days" on Hawaii
  174. Sun's Temperature and Energy Density of Sunlight
  175. Teaching about energy in 8th grade
  176. About the jetstream
  177. What would a breach in a space station do?
  178. Gravity at the Earth's center
  179. Freak waves on the ocean
  180. Citation on "Bad Greenhouse" web page
  181. How can radio waves carry sound?
  182. Do Cosmic Rays produce lightning?
  183. Star positions shifted by the atmosphere
  184. The equation of time
  185. Launch window of the Space Shuttle


  186. No "Man in the Moon" from Australia?
  187. Picturing the Sun from a different distance
  188. What makes the sun shine so brightly?
  189. Re-entry from orbit
  190. Effects of weightlessness on one's body
  191. Blimps on Mars
  192. Planet Mars "huge" in the sky, in August 2005?
  193. Astronomy and telescopes for ones' own children
  194. Does the solar wind have escape velocity
  195. Astronomy for cliff-dwellers of New York City
  196. Portable star finder
  197. What if the Moon was closer? (2 questions)
  198. Why doesn't the Moon have an atmosphere?
  199. Telling a 3-year old about the atmosphere (2 questions)
  200. Three-color vision


  201. Superconductors work, universe expands--with no energy input. Why?
  202. Shuttle orbit and Earth rotation
  203. Worrying about Wormholes and Black Holes
  204. What should I study?
  205. The greenhouse effect
  206. Separation between lines of latitude and longitude
  207. Motion of air: hot to cold, or high pressure to low?
  208. Removing "Killer Asteroids"
  209. Strange light seen from Hawaii
  210. Is the Sun attached to another star?
  211. What if the Sun turned into a black hole?
  212. Do absorption lines have a Doppler shift?
  213. What are "Electromagnetic Waves"?
  214. Why are the two daily tides unequal?
  215. Why air gets cold higher up--a wrong explanation


  216. Any limits to Newton's 2nd Law
  217. Gravity at the Earth's center
  218. Does the Earth follow a "squiggly" orbit?
  219. Third grader asks: how far to zero gravity?
  220. "How does inertia affect a rolling ball"?
  221. What determines the quality of a telescope?
  222. Why design maps around curved lines?
  223. "Drag" by the Sun on the Earth's motion
  224. Does precession affect the time of summer? (2 questions)
  225. Newton's law or Bernoulli's?
  226. Does the universe have an axis?
  227. Frictional electricity
  228. Syllabus for catching up on physics
  229. Parabolic reflector
  230. At what distance does Earth start looking spherical?
  231. Is the Sun on fire?
  232. Confusion about the "Big Bang"
  233. How did Tycho calibrate his instruments?


  234. Gases that fill balloons
  235. Asian tradition on the start of winter
  236. Why our year starts at January 1
  237. Sticking a hand out of a window...
  238. One year of continuous sunlight?
  239. Shielding out radio waves
  240. The way gravity changes with depth
  241. The Sun's Axis
  242. "Gravity Particles"?
  243. A "short stay on Mars"
  244. Weight and mass
  245. "The Moon Hoax"
  246. Shuttle re-entry from space
  247. Energy levels: plus or minus?
  248. How can such small targets be accurately hit so far away?
  249. A teacher asks about compiling lesson plans
  250. Why the Moon has its phases
  251. How can a spacecraft self-rotate?
  252. Stability during a rocket launch
  253. Boiling point of water in space


  254. Konstantin Tsiolkovsky
  255. The Color Indigo
  256. Electromagnetic Waves and Electromagnetic Induction
  257. Why do orbits curve?
  258. The "Sundial Bridge" in Redding
  259. (a) Temperature in space
      (b) Exposure to the space environment: Freeze or burn?
  260. Remote sensing of Thunderstorms
  261. What keeps Electrons away from the Atomic Nucleus?
  262. The Stars on the Winter Solstice of 2012
  263. Mars Sunset
  264. Gravity at the Center of Earth
  265. The Big Bang
  266. "How Often are Stars Born?"
  267. The Path of Lightning
  268. Launching a Rocket from an Airplane
  269. The Equation of Continuity
  270. The Four Corners Monument
  271. Which among the brightest stars is closest to N Pole?
  272. Gravity Assist
  273. Is the Centrifugal Force "Real"?
  274. How do we know Earth is bigger than the Moon?
  275. Sound Waves on the Sun?
  276. What if we had to give up use of Satellites?
  277. Rotation of Venus
  278. "Proper Motion" of Stars
  279. Doppler Shift from the Big Bang
  280. Science Fiction scenario for a Flight to Mars
  281. Motion of the Moon


  282. "Iridium" flares
  283. Discovering Planets outside the Solar System
  284. Landing speed of airplane
  285. The Hubble Constant
  286. Are Summer Nights Darker?
  287. "Space Elevator"
  288. Black Holes
  1. Don't use Diesel fuel in a gasoline car!
  2. How bright is our Sun when seen from space?
  3. What is a "field"?
  4. Outer limits of the Solar System
  5. Gravitational Energy
  6. Stresses on a Railroad Bridge
  7. The constellation of Cassiopeia
  8. Tracking of radioactivity carried by winds
  9. Why can't the space shuttle reenter "slowly"?
  10. "The Standard Model of the Universe"
  11. About the Maya Calendar
  12. Are light sabers possible?
  13. Can the heat of sunshine make the Earth expand?

  14. About Mountains
  15. "Will the World end in 2012?" (a,b)
  16. Advice to graduating High School Student
  17. Could a (heat resistant!) ship float on the Sun?
  18. Reducing the fuel weight of the Space Shuttle?
  19. How do Rockets Land?
  20. The Earth's Spin reduced by Global Warming
  21. Circumnavigation of the Sun
  22. Are nuclear forces merely gravity at very close distance?
  23. Changing the Earth's Rotation
  24. Why are planetary orbits eccentric?
  25. Forces on Comet-dwellers
  26. Nuclear reactors and bombs
  27. Why doesn't magnetism affect electro-magnetic waves?
  28. Is humanity changing the climate, or is it the Sun and the Earth's magnetism?
  29. Advice to home-schooling parent
  30. Science of Clothing
  31. Calculating a Collision
  32. The Coriolis force and more
  33. Why isn't the solar system stratified by density?

  34. Tapping Atmospheric Electricity
  35. Global Disaster in 2012?
  36. What's the difference between speed and velocity?
  37. Effect of Gravity on Electromagnetic Waves
  38. Why is North the reference, not South?
  39. The lowest 700 km of our Atmosphere
  40. Doomsday 2012?
  41. Where does a Flying Bird get its Support?
  42. Why does Sun seem to move?
  43. Why don't waves disturb each other?
  44. Does the Moon's motion Change?
  45. Big Dipper and Weather
  46. What IS the Ecliptic?
  47. Precession, Greenhouse and more...
  48. Latest Sunrise, Earliest Sunset
  49. Falling off the Earth's Bottom?
  50. Rolling down a slopea>
  51. Pelton Wheel Efficiency
  52. Energy loss rate of our Sun
  53. The Sun's distance
  54. Why does sunlight have a continuous spectrum?

  55. Harry Paul Sprain's perpetual Motion Device
  56. Can the plasma that fills space help spaceflight?
  57. Spiral arms of our galaxy
  58. What powers a glider?
  59. UFOs
  60. Maximum speed for propeller-driven airplane?
  61. The speed at which gravity spreads
  62. Layers of the Earth
  63. Why doesn't the sky fall on us?
  64. Imagine a non-rotating Earth
  65. Flying east with a 1° error
  66. US Flag on the Moon
  67. Rope stretched across a long lake...
  68. About studying electronics in the USA
  69. Publish Stargazers as a book?
  70. Charging of Earth by lightning:   +   or   –  ?
  71. If no stars were seen--could Earth's orbital motion be discovered?
  72. Local Solar Time in Iceland
  73. Is orbital motion same as free fall?
  74. Build a straight tower in warped space?

  75. The 2011-2 sunspot maximum
  76. Is Earth adding mass?
  77. Shape of a "bottle rocket"
  78. Fantasy spaceflight vs. reality
  79. Telling a 7-year old about stars "dying"
  80. (1) Why is lightning jagged?     (2) What did Tesla do?
  81. How can the north wall of my house be in sunlight?
  82. Heating the inside of Earth
  83. Dawning of the Age of Aquarius
  84. Why is hydrogen the fuel of choice?
  85. Gamma ray bursts
  86. Counter-clockwise swirling motion in the atmosphere
  87. Leap years on the Jewish calendar
  88. Earth axis tilt and climate (1)
  89. Earth axis tilt and climate (2)
  90. Does the Sun move?
  91. Can the Sun interfere with the visibility of the Big Dipper?
  92. Why can't we feel the Earth's rotation?
  93. Is our galaxy held together by a central black hole?
  94. Why don't gas planets just evaporate?
  95. Source of the Sun's energy
  96. Point of gravity equilibrium
  97. Solar system motion through the Galaxy
  98. Spaceflight by waiting for the Earth to turn?
  99. Does Earth rotation affect size of creatures?
  100. The year 2012
  101. Are our galactic arms winding up or opening up?
  102. Advice to a home-schooling mother
  103. Are all stars we see suns?


  104. Newton's 3rd law
  396A Posssibility of Asteroid Hitting Earth (1)
  396B Posssibility of Asteroid Hitting Earth (2)
  1. Author's IQ
  2. Global Warming caused by Sun getting nearer?
  3. The year 2012
  4. Empty space behind North Star?
  5. The year 2012 and the 26,000 year cycle
  6. "Quarter Squares"
  7. Do Rockets need "something to push against"?
  8. Sunrise-Sunset asymmetry
  9. Re-entry from orbit
  10. Earth Axis and Gravity
  11. The year 2012
  12. Choosing an Aerospace Career
  13. Advice for "new" physics teacher
  14. Paradox of Time Travel
  15. Is 7th grade Earth science boring?
  16. Air Resistance
  17. Experimenting with Microwave Oven
  18. Is the Sun losing mass?
  19. Sun's position at noon, south of equator
  20. Fred Hoyle's theory of the Sun's Corona
  21. Why don't Protons and Electrons combine?
  22. Days in a Year
  23. Position of the Moon in the sky

  24. Earth crossing Galactic Equator?
  25. Is the geocentric theory ruled out?
  26. Does the Southern Sky have a Pole Star?
  27. What is the fate of starlight energy?
  28. Double-slit diffraction of particles
  29. Does the Sun overhead reduce effective weight?
  30. Evidence for Global Warming ?
  31. Distances to the Equator
  32. Weight on the Equator and at the Pole
  33. Why doesn't gravity overcome buoyancy?
  34. The Prime Meridian
  35. Is L2 in the Earth's Shadow?
  36. In what direction is Israel from NY?
  37. Is the World Overpopulated?
    Magnetic Energy
  38. Magnetic Carnot Cycle
  39. Defining the Equator

  40. Second Moon for Earth?
  41. The year 2012 and a distant companion of our Sun
  42. Distance between two points on a sphere
  43. Getting sucked I by Gravity
  44. The work of Nikola Tesla
  45. Firing a cannon straight up
  46. Does one see half the sky--or more, or less?
  47. Why are nights dark?
  48. The origin of the Solar System
  49. Flying to other planets
  50. The heat of the Sun's corona
  51. Crossing our galaxy's equator
  52. Newton's 3rd law--in statics and dynamics
  53. Barycenter of Earth-Moon system
  54. What if Earth rotated in only 10 hours>




If you have a relevant question of your own, you can send it to
stargaze["at" symbol]phy6.org
Before you do, though, please read the instructions



     

188.   No "Man in the Moon" from Australia?

Fascinating site. One quick question, if I may.

    Having lived in the southern hemisphere for 2 years, the 'man in the moon' from my UK childhood is becoming a distant memory. In fact I can't find any reference to the face I was seeing. Would the moon surface be different in appearance in Australia and New Zealand than in Britain?

Reply

    You are absolutely right: the Moon does look different from Australia or New Zealand, and you may miss there the "Man in the Moon" arrangement of dark areas ("seas" or maria). That is not because the Moon moves, but because the "up" direction there may be almost the reverse of what it is in the northern hemisphere. Our mind always relates appearances to what we consider "up" or "down."

    Asian cultures, by the way, do not see "the man in the Moon" but rather "the rabbit in the Moon," and have a legend about that. Ask Google or some other search engine about that, if you wish.
 

189.   Picturing the Sun from a different distance

Here's a question for you that I could not find already answered on your very impressive and very useful web site.

    Where can we find some actual (normal visible light) photographs of the sun taken from outside the near-earth environment? There seem to be no photos of the sun available, taken, for example, from a point half-way between the earth and the sun, or taken from the vicinity of Saturn, Jupiter, Uranus, Neptune or Pluto. Voyager 1 and 2, Pioneer 10 and 11, and numerous other deep-space spacecraft, from the USA as well as from Russia and from the ESA, surely must have taken some photos of the sun. Where can we find them? Why has NASA never released them?

Thank you very much.

Reply

There is no advantage in taking pictures of the Sun from a different distance. You get the same result from a telescope.

    There does exist a considerable advantage in taking pictures from a different angle. For instance, when a sunspot group disappears around the edge ("limb") of the Sun's disk, it takes two weeks before we get any information on what has happened to it. The capacity of observing the Sun from other angles does not exist yet (spacecraft designed for planetary observations are not designed to look at the bright Sun) but NASA is planning a "Stereo" mission to look at the Sun from two somewhat different directions and get something of a 3-D view.
 

190.   What makes the sun shine so brightly?

What makes the sun shine so brightly?

Reply

What makes the Sun shine? Its heat, because all hot objects shine--like filaments in lightbulbs.

    What makes the Sun hot? Energy is released in the core of the Sun by nuclear processes, which combine atoms of hydrogen into atoms of helium. Four hydrogen nuclei (aka protons) combine to form one of helium, with some energy left over, and that energy provides the heat.

    Many chemical reactions require a higher temperature (boiling an egg, for instance), and so do nuclear reactions. The temperature required for the solar energy release is enormous, and creates enormous pressure. Only near the center of the Sun can these conditions exist, with the weight of the higher layers of the Sun keeping the energy-release region confined. If that confinement did not exist and it had the chance to expand, it would cool down and all nuclear energy release would end.

For more, see
http://www.phy6.org/stargaze/Sun7enrg.htm

                Response to reply:

thanks but my assignment was due like three days ago and i kinda didnt get your answer in time so thanks anyway. love jane  

191.   Re-entry from orbit

I am 17 years old. I go to school at Father Lopez Catholic High School where I run cross-country and track and play soccer. I have a few questions for you:
  1. What concept of physics causes the space shuttle to get so hot that it almost burns up when returning to earth? 2
  2. What one word describes this concept?
  3. What kind of energy is present during reentry?

Reply

    You probably mean "process', not "concept" (concepts are in your mind, processes occur in nature). The process involved is a shock, a piling-up of air around the shuttle, since the shuttle moves too fast for air to flow out of its way. The shock heats the piled-up gas, but luckily, most of the heat is then radiated away, since anything hot glows and radiates light--e.g. a flashlight filament. Only a small fraction of the heat reaches the heat shield tiles, although, since radiation is beamed in all directions, some of it will hit the shuttle, too.

    The amount of kinetic energy which must be given up (as radiation) is tremendous. The shuttle starts at 24 times the speed of sound, while a rifle bullet may have twice that much, maybe 3 times. So pound for pound, the shuttle may have 100 times more energy. Lead bullets melt when they hit a sandbag, so getting rid of that energy is a tricky feat indeed.
 

192.   Effects of weightlessness on one's body

    I was wondering how does going up into space have an imapct on your body if you are up there for a certain amount of time. How does it affect your health? what changes occur for males and what changes occur for females and both?

Also how are these problems fixed if nessecary?

Reply

Dear Australian friend

    Many of these problems were addressed on the space station "Skylab". Astronauts tend to lose weight, muscle tone and bone--in a way which somewhat resembles problems of patients who are bedridden for a long time. Exercises help prevent these from occurring. I am not sure about more subtle effects--you will have to search on the web.

About weight loss, see
http://www.phy6.org/stargaze/Sskylab.htm

    The principles used in measuring the mass of astronauts in a "weightless" environment, see the end of the section preceding
            http://www.phy6.org/stargaze/Smass.htm
and perhaps the one following
            http://www.phy6.org/stargaze/Smasscom.htm  

193.   Blimps on Mars

    I'm trying to figure out lofting capacity for various gases on Mars, so I can more realistically visualize a lighter-than-martian-atmosphere-craft. What with the different gravity, different atmospheric pressure, and different atmospheric composition, I figure that the lofting capacity of various gasses would be different.

    Unfortunately, I'm getting hung up on that lifting gas. I suspect that Helium will be in short supply on Mars. On earth, it is a byproduct of natural gas, but on Mars, there should be little, or no natural gas, and helium would have to be mined by itself.

    My idea however, is that since the atmosphere is mostly CO2, blimps with much heavier gasses could be used. I would expect hydrogen, oxygen, and nitrogen blimps to be common, since these three gasses are highly useful commodities in their own right on a world with little water, and no breathable atmosphere.

Reply

    Flying a balloon on Mars is not easy. The ground-level atmosphere is (I believe) 1/140 times as dense as ours, and even with 1/3 of the gravity, it may be equivalent to flying a balloon at 25,000 meters on Earth or at 80,000 feet. It can be done, but takes a big balloon. With the fierce storms of Mars, one also wonders how long such a balloon would last.

    About the lifting power--it equals to the weight of the displaced atmosphere, minus the weight of the gas inside the balloon, required to keep it inflated. Whether that is hydrogen or helium should make little difference, because either gas weighs much less than the air (or on Mars, carbon dioxide) which is displaces. Hydrogen should be available on Mars, if only a little water can be extracted there, which seems likely. Hydrogen was of course used in all the Zeppelins in WW-I and with proper caution is quite usable.

    Oxygen and nitrogen are rather heavy, cutting the lifting power by a factor of about 4: considering how marginal any balloon is on Mars, they are clearly unsuitable..

    Scientific high-altitude ballooners on Earth prefer helium because of the way its temperature changes as the balloon rises and the gas inside expands, but on Mars a balloon probably won't rise far. Rubber balloons launched to probe the weather are filled with hydrogen, which is much cheaper: they rise quickly and explode at their maximum altitude, but by then all required data have been transmitted by radio.
 

194.   Planet Mars "huge" in the sky, in August 2005?

Is there a terrestrial phenomenon occurring this month with Mars? I've heard form a few "wannabe" astrologers that the planet Mars will be "huge" is the sky and look as big as the moon with the naked eye. This is an event that has happened every 5000 years or so. Mars is to come within 34,649,589 miles to Earth. I have not seen any television reports on this (maybe due to the recent NASA landing). Could you expound upon this for me ? Thanks,

Reply

    [Note: The above turned out to be a false rumor, which had quite wide circulation. The reply below was written before the news media reported on it.]


    Beats me. The average Mars-Earth separation is 0.5237 AU, and with 1 AU equal approximately to 150,000,000 km or 93,000,000 miles, this comes to 48.8 million miles. The actual closest approach may be larger or smaller, because of the ellipticity of the orbits (mainly the one of Mars),

    In any case, Mars seen by the unaided eye is never as big as the Moon. It is true, though, that viewed through a telescope, Mars appears to be about as big as the Moon seen by the unaided eye (although, unless seeing conditions are very good, the image may shimmer and distort).

    After writing the above I looked up Google for some more precise facts--see
          http://www.imcce.fr/en/observateur/support/opposition_mars/index.php.

The next closest approach is October 30, 2005, and will bring us within 43,000,000 miles of Mars. The closest approach your friend mentions happened 2 years ago and was indeed unusually close.
 

195.   Astronomy and telescopes for ones' own children

Having looked at the elementary school texts my children have been assigned, I have been disappointed. Some of the most enthusiasm they have shown recently toward learning more about the physical world and doing a bit of thinking, is during a recent discussion of "how to point a telescope." But they do not get those kind of examples, or anything that seems remotely stimulating from their textbooks. Unfortunately, that kind of motivation seems only to come from strictly extracurricular activities.

    If they do continue to show interest more than a few days in the telescope project, then I hope to help them build (instead of buy) a set of telescope drive controls. So far their enthusiasm has not waned, and they are asking a lot of questions about how to find objects in the sky and point the scope. My experience doing some controls engineering will help, but I want to let them do some of the programming to make the telescope follow the right target. My challenge will be to keep their challenges at the right level.

    Your pages provide a nice balance. Appropriate examples, and reasonable approximations that make some of the fundamental calculations of motion of celestial objects trackable. I think if I can learn that art of finding and sharing simple examples, then the telescope project will generate several fun and useful lessons. Otherwise, it will become just another project.

Thanks for your contributions in making physics, astronomy and earth sciences fun for non-scientists.

Reply

I do not know your children--what ages, what interests, what school. Nor do I know the limits of your budget.

Textbooks are generally uninspiring--they are produced to sell, not to inspire, and are often the result of committee work. If your kids would like to know about the universe, here are two books they may like
          "Seeing in the Dark" by Timothy Ferris
          "A short History of Nearly Everything" by Bill Bryson.
I reviewed the 2nd of these in an article later picked up by "Eos", on
         
http://www.phy6.org/outreach/books/creation.htm

    As for telescopes, I might have a different philosophy here--give the kids an instrument with minimal hassles, to let them go right away and observe. For our son's birthday (32nd, I think) we gave him a Meade 3.5" telescope. We scrimped and did not buy the computer controlled model, and that was a mistake--I think he would have used it more if he had the one with built-in star catalog. On advice we also bought for it a 90-degree elbow eyepiece (easier to look at objects high in the sky), a better eyepiece and a subscription for "Sky and Telescope" (he had a tripod already, and he crafted his own camera attachment).

    If your kids are not yet in that league, they have plenty to read in my web pages. I can also send you solutions to the problems, if you want to teach them that way. They should keep in mind, though, that no one will care as much about their own education as they themselves. If they want it, it's theirs for the taking.  

196.   Does the solar wind have escape velocity?

Your site claims the particles in the solar wind are leaving the Sun at about 400 km/s. This is less than the escape velocity which is about 600 km/s. Does it mean many of these particles will eventually fall back to the Sun? Is there any evidence of such as behaviour?

    Also, what are the leading "hot" topics on Solar Physics now?

Reply

    The solar wind starts not from the Sun's surface, but from the corona, and is accelerated somewhat gradually. Obviously, it has to overcome solar gravity, which I suspect is one of the conditions needed for accelerating the solar wind--maybe like a lid on a pressure cooker, holding down the hot corona until it can just barely escape.

You might want to look up
http://www.phy6/org/ Education/FAQs6.html#q82

    Incidentally. NASA has been toying for years with the idea of a solar probe, approaching the Sun within 4 solar radii--following boost from a "hairpin" orbit around Jupiter (mentioned briefly here and in the page following it). It would be shielded from the Sun's intense heat by an "umbrella" of tungsten or similar material, and would study the solar wind in its source region. How can it do so with a metal barrier between it and the Sun? Simple: at closest approach is moves at about 300 km/s, perpendicular to the line to the Sun, so in its own frame of reference, solar wind particles (unlike sunlight) would seem to arrive from the side, at an angle. They would seem to have the vector sum of their own velocity and that of the corona relative to the fast-moving probe.

    "The leading hot topics"? I am only slightly involved in solar research, but the big question there seems to be what happens beneath the surface--where do sunspots originate and how, what are they, and what creates the uneven rotation of the Sun (which drives sunspots and magnetic fields). When I got into the space research, it was proposed all these were shallow phenomena, in the outermost layers of the Sun, but current study suggests they actually extend to appreciable depth. If you have a science library nearby, try to find

Parker, E.N., The physics of the Sun and the gateway to the stars, Physics Today, 53, p. 26-31, June 2000  

197.   Astronomy for cliff-dwellers of New York City

I live in NYC (have all my life) and I became a lunatic (yes, I know the prefered term is lunarian..but ..) because you could see the moon.(I was an adult before I was any place dark enough to see the milkyway--NYC is not a good place for astronomers.

    'I've read, and taken advantage of places like the Hayden planetarium, and I have made (and continue to make) my own observations.

    I am blessed now to live in a high rise, with a clear south and west view.--more or less.. (I live close to Flushing Meadow park,)

    My observation is: at the winter solstices, the sun sets in Brooklyn.. and by now, its getting close to down town Brooklyn. soon it will set in Manhattan. and by summer, it sets in midtown.. (certain building of the NY skyline are my personal stonehenge!)

    But the moon, oh , the fickle moon.. there must be a pattern.. but in the 18 months I have lived here, I haven't worked it out..

    Sometimes it sets in downtown, some times in midtown.. but it doesn't seem to move in a smooth pattern, (a sine wave say) but its all over the map! I can't tell from one month to the next were the moon will set.

    I am sure information about the moons patterns and movements (or perceived movements) must be documented. I 1 read about the sun's movements and began as a child to note were it set (and more often where it rose, since my childhood home had clear eastly views.) observation and reading have brought me a clear sense of the movement.

    But the moon.. can you suggest some reading?

Reply

    I loved your e-mail message! You are truly observant. I don't know what you do for a living, what your age or education are, ... but you have the soul of a good scientist. Brings to mind what a friend ones said: The most powerful phrase in scientific discovery is not "Eureka, I found it" but "Hmmm ... that's funny!" (He did not known who had said it, but I cited it anyway.)

    The Moon is not fickle, just a bit harder to predict. To understand, you should know what the ecliptic is--"Stargazers" has
a section about it--the plane of the orbit of Earth around the Sun.

    The ecliptic cuts our visible sky in two halves (half the stars are north of it, half, south of it), and the dividing line (also called "the ecliptic") is where the Sun is in the sky, it goes once around the ecliptic in one year. The constellations along the ecliptic are "the zodiac," so dear to astrologers.

    The ecliptic is inclined to the plane of the equator by 23.5 degrees, because the rotation axis of the Earth does not point perpendicular to the ecliptic, it is off by 23.5 degrees. Actually, it nowadays points almost exactly towards a fairly bright star, the pole star Polaris (there's a section on that, too). Because of that inclination, the Sun is further north (up to 23.5 degrees closer to the pole star) in the summer, and more distant (up to 23.5 degrees) in the winter. That tells why now in January the Sun is lower in the sky and days shorter (that is on the web site, too), while around midsummer, it's the other way around. And why the apparent motion of the Sun at sunrise or sunset migrates north and south in a yearly cycle, as you have noted (and ancient astronomers have before you).

    Still with me?

    Now the solar system is flat. Other planets all orbit the Sun in planes rather close to the ecliptic, and our Moon does too (about 5 degrees off, I think, and we'll ignore that). That means that the imaginary line around the sky where the Sun makes its path is also the only place where we are likely to see the planets (when close to each other, they are clearly strung out in a row), and the Moon too.

    Think about it: the path of the Sun around the sky is also (almost) the path of the Moon around the sky. With one big difference: the Sun makes its circuit in one YEAR, while the Moon does so in each MONTH. They both follow the same path (almost), so that yearly north-south dance of the sunrise (Brooklyn-Manhattan-midtown and back), the Moon completes it in one month. No wonder you find it irregular!

    But if you track only the full Moon you might see the reverse of the Sun's cycle--north in winter, south in summer, because the full Moon is always opposite the Sun. It better be REALLY full, because the Moon shifts its position across the sky 12 times faster.

    That's as far as you can go. Let me add that the actual motion of the Moon, to the precision astronomers need, is rather complicated. In the nautical almanac, "low precision formulas for the position of the Moon" take about 50 terms (each with its sine or cosine; I had to use them once), while precise ones take many more. That complexity arises because many factors disturb the Moon's orbit--the Sun, the equatorial bulge of the Earth, maybe Jupiter too is important enough. In the 1800s the French astronomer DeLauney spent 20 years calculating the orbit of the Moon, yielding a formula so long it filled an entire book. In modern times this was checked by a computer, which only needed minutes, and it found everything was correct, except for 3 small errors which did not change anything important.

    Enjoy your Stonehenge! Alas, two big menhirs it used to have are now gone.

Response--with a bit of personal confession

I am not in modern way of thinking a scientist (having a piece of paper), but yes, I think of myself as one.. (I like too, to think of myself as a polymath.. but truth is, I lie somewhere between a dilletante and polymath.) and my piece of paper says I have mastered the art of business administration (is that really an art?).

    I am getting to be 'of a certain age'-- that is, I admit to being 47, but don't discuss how long I have been 47! 47 is a prime number, and well, I am in my prime.

    Now that I have an idea of the motion, I will begin a more studied observation of the moon.

    I had great fun last year, and the year before stopping neighbors and passersby and insisting the look at the lunar eclipse--and on a language board I frequent, when the word camera came up, I was the one of a few who know the origins of that words, (alas, I do not really know Latin.. just a smattering of words, no real declensions,) -- I remember making camera obscura's to watch a solar eclipse as child.. (and again in 1990's -- I watched that eclipses in Times Square--on an extended lunch hour)

    NY skyline as a Stonehenge has some limits.. (geology is the underlying factor, ha) I would have only been able to see the very tops of the towers from my current vantage point (there are some tall building close by that block some of my skyline view) -- I moved here, after 2001 and never saw them from here. I worked close to them in Manhattan in 2001, (close enough to be evacuated) , and unlike many NYer's I had been to the top several times.

    I have no trouble with the math in your explanation, -- I was blessed as child, and went to an all-girl school, with well educated nuns, who had no truck with math phobias. In elementary school, I was introduced to the geometry of classical curves. It was great fun, and occasional, when watching the coverage of those early space flights, I could actually understand some of the 'formula's'--they were the same ellipses, parabola, hyperbolas and circles we were plotting for math homework. I also learned octal and binary in elementary school-- as an adult I have picked up hex. I taught all three systems to my kids, it took with my son, and since he had an immediate use for the knowledge.(we had a home computer in the early 1980's--a 16 bit one that used hex)--for me, these numbering systems were stupid number games. He has far surpassed me --I can do simple math in binary, he can think in binary! I do still read math and science for fun--which puts me definitely into the nerd category, but I think "nerd" is a rather complimentary term!

    My knowledge of the world, is miles wide, and microns thin, with an occasional pot hole and one or two sink holes! and being a child (and adult) raised on concrete, tides and nautical tables are an area where my knowledge is stretched to vapor thinness.

    I do have a parochial view,--I KNOW NYC*-- and have learned a bit about the tides, (rule of 12) because the tides, while they are rather small (only about 4 foot on average between high tide and low), they do interesting things in parts of the estuary. especially were they 'meet' in the Harlem "river' at Sputendival, and in the east 'river' at Hellgate.

    [*My knowledge of geology is rather specific.. I know NY geology well, and geology in general less well, same with botany, I know NYC botany quite well, but trees and plants of the tropics.. hardly at all, and so on for must subjects.. I am lucky that I live in an area with interesting geology and diverse plant (and animal) life, and great building, and wonders of engineering, and museums and other cultural institutions!]

    But now, thanks to your kindness, and pointers of where to look and why, in another year or two, I'll have a new pothole full of knowledge about the movement of the moon.

    Thank you, thank you, thank you!

Reply

    I enjoyed reading your letter. Maybe your "piece of paper" is an MBA, but you are not among those yahoos who pride themselves on never having understood science, or cared for it. Gone are the days when no one was accepted as well educated who did not at least have some understanding of nature!

    If I may direct you to some of my web pages... a very good book (OK, with some errors, but it's still great fun) is Bill Bryson's "A Short History of Nearly Everything," whose paperback version has been on the top 10 list of The Washington Post for about 6 weeks. I reviewed it among others at
    http://www.phy6.org/outreach/intbook.htm
The above is a link to the entire list, because you might like other books listed there, too, Another collection is
    http://www.phy6.org/outreach/intedu.htm
from which your son may find that the Romans made use of the binary system, even though they were not aware of it.
    And a highly recommended book on astronomy is "Seeing in the Dark" by Timothy Ferris.

Have fun with any or all of these.

David  

198.   Portable star finder

    I am looking for a hand held display which, when held facing north, can help an individual locate visually the different constellations, stars, & planets, visible with the naked eye at that time of year in the northern, mid-western sky. I intend to use it to help youngsters & new observers locate the wonders of the sky. I hope what I am seeking exists.

Reply

    What you want is a map of the sky. I typed "Sky map" into Google and got a long list, starting with
    http://www.fourmilab.ch/yoursky/
Give it your location and it will give you a map of the sky for tonight's date. Click on any point on the map and get a magnified view of the sky around it. You enter your location and get a sky map for today's date. I guess you can print the page and use it outdoors.

    A useful trick which someone told me requires fast-drying "whiteout" paint used by typists to blot out mistaken letters or words, which are then overtyped correctly. Draw the stars in the constellations which you want to watch on a fairly large sheet of paper, put on top of it a sheet of saran wrap from the kitchen, and with the white-out brush mark on it the stars you want to identify--bigger marks for brighter stars.

    Then take a wire-hanger used for clothes, pull it apart to a square, wrap the edges of the saran sheet around the wire and maybe secure them with tape. You now have a transparent star map you can take outdoors and hold against the sky.
 

199.   What if the Moon was closer?     (A)

My name is Korey and I am a high school student looking for an answer to the question of my project: If the Moon was to get closer to the earth what would happen to the tides?

Reply

The tides would of course be higher.

    In fact, the Moon WAS closer to Earth in the past, and is even now gradually receding. This is a side-effect of the tides, which may be viewed as a world-wide system of waves, losing energy as it hits continents and islands. This takes away energy from the Earth's rotation, which slows down (days get longer, but at a very slow rate). Because of conservation of angular momentum in the Earth-Moon system, this causes the distance of the Moon to gradually increase.

    How close was the Moon originally? The answer depends on the way the Moon originated--was it formed with the Earth, captured by the Earth or somehow torn off the Earth? George Darwin, son of Charles Darwin

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Darwin.html

who was a well-known scientist in his time, believed in the last possibility. He claimed that originally the Earth rotated too fast to be stable, a bulge formed, and it was torn off by the rotation, to form the Moon. In this view the Moon was originally "within touching distance", but the action of the tides (which initially must have been huge) caused it to recede to where it is now.

    More careful studies showed Darwin's theory cannot hold. I think most astronomers feel the Moon and Earth were created together, as a double planet, though other views persist--see "The Big Splat", a book by Dana MacKenzie. If you can find the old book "Biography of the Earth" by George Gamow (written about 50 years ago) you will find he still supported Darwin's theory. It's a delightful book, even though not everything in it has stood the test of time.

What if the Moon was closer?     (B)

Today in physics class, my teacher talked about the moon. He said that the moon is moving away from Earth each year by a certain distance. Can you tell me the actual annual movement of the moon away from Earth? Thanks

Reply

The average rate at which the moon recedes is 3.8 cm per year, about an inch and a half. See
    http://www.talkorigins.org/indexcc/CE/CE110.html

    This happens (and your teacher might have said so already) because of the tides in the oceans. The moon pulls the water into a wave which tries to remain pointing at the moon; the moon also pulls the entire Earth, leaving behind a second crest of the tide-wave on the opposite side of the Earth.

    The two crests try to line up with the Earth-Moon direction, but the rotation of the Earth under them causes them to collide with shorelines. Such collisions slow down the rotation of the Earth and give up energy, whose ultimate source of that energy is the rotation of the Earth and the motion of the Moon.

    However, by Newton's 3rd law, if the Moon produces a force on the ocean tides, those tide-waves must also produce an equal and opposite force on the Moon. The result may be best explained using the conservation of angular momentum. The total angular momentum of the Earth-Moon system must be conserved, so if the Earth loses some, the Moon must gain some, and it does so by moving further out.
 

200.   Why doesn't the Moon have an atmosphere?

Dear Doctor, I was wondering if you could answer a question of mine. If the moon's gravitational pull is strong enough to affect water movement here on earth (by creating tides), how can it not be strong enough to hold on to its own atmosphere. I know this question might sound dumb so forgive me.

Reply

The two problems are quite different. If the Moon were big enough to hold an atmosphere but (say) 3 times as distant, tides might have still been as big: one effect does not inform about the other.

    How exactly are atmospheres held? By gravity of course, but note that the density of the atmosphere decreases with altitude. With Earth, it drops to one half about every 5 kilometers in altitude (temperature can modify this). If you rise 5 kilometers, only half the atmosphere is above you, with only half its weight compressing the air, so density and pressure are down to 50%. Rise to 10 km, and it's only 25%, and so on. At 100 kilometers you are down to about one part in million, and collisions between molecules become more rare, so that they rise and fall like stones tossed upwards.

    The "halving distance" could be more than 5 kilometers, or less. If gravity were smaller (as it is on the Moon) and temperature higher (as happens at high altitudes), it would be larger--and the atmosphere would rise higher. The somewhat early loss of the space station "Skylab" in 1977 was helped by higher sunspot activity, which caused the upper atmosphere to heat up and expand (from more solar X-rays), with more air resistance in low orbit.

    Also, above 100 kilometers, sunlight may break up molecules (e.g.) of water, and the atmosphere is no longer evenly mixed, in constant proportions. Lighter atoms (e.g. hydrogen) then rise higher than heavy ones (e.g. oxygen), because their velocity is larger, at the same temperature.

    The velocity is still much less than escape velocity--but in a hot gas, a spread of velocity exists (a "Maxwellian" spread, named for James Clerk Maxwell who first derived it) and a few atoms or molecules always move fast enough to escape. On Earth, over geological time spans, all the helium has escaped (the helium we get from natural gas was produced as alpha particles by radioactive elements such as uranium). As the attached graph shows, on the Moon all common gases are expected to be gone.

The graph is from
    http://abyss.uoregon.edu/~js/ast221/lectures/lec14.html

    Hope this answers your question. If a comet rich in water were to hit the moon (as may happen--a small comet may have hit Siberia in 1908), the Moon would have a watery atmosphere for a thousand or maybe a million years, but it won't last.
 

201.  Telling a 3-year old about the atmosphere     (A)

Hi-- My three year old daughter, Sarah, would like to know . Any help you can provide would be appreciated

Reply

Hmmm. Questions have come from all ages, and from all over the world. Some 8-year olds have asked quite profound ones--but Sarah is probably the youngest yet. I'll try to answer, but YOU are the one who has to make it clear to her.

    First of all, it is a GOOD THING there is no air in outer space! Outer space is SO BIG, if our air could spread out over all of it, almost nothing would be left for us to breathe.

    Luckily, air has WEIGHT. (You don't feel it, but the air in a room weighs more than Sarah).

    Without weight, everything would FLOAT FREE, like astronauts in a spaceship (I hope Sarah has seen pictures). Weight is what keeps tables, chairs, people, cats, dogs, cars and so on standing on the ground, also keeps down the water in oceans and lakes. And it also keeps our air from floating away.

    Weight tries to keep everything as LOW DOWN as possible. Water flows downhill. In the winter, sleds slide down a hill by themselves, but need to be pulled back. Weight also keeps air attached to the ground.

    Weight is caused by GRAVITY--the pull which any piece of matter has on any other. The pull is very weak: any two stones pull each other, but so weakly, you can never feel it. But the EARTH is such a BIG piece of rock, that it has enough pull to keep all of us, and all things around us, safely on the ground.

    It even has enough pull to keep the MOON from running away. As well as all the satellites NASA and others have launched, which like little moons go around the Earth..

    Please let me know if the above is good enough for a 3-year old!

Telling a 3-year old about the atmosphere     (b)

Thanks so much! This answer did seem to satisfy her (mostly, anyway). Now she just wants to know where the air came from in the first place Thanks again for such a thoughtful and speedy response--it was really helpful!

Reply

It is probably hopeless to try keep up with the questions of a 3 year old! On the long run, it may be easier to teach her to read (as we have done--see

http://www.phy6.org/outreach/misc/ilana.htm

and then let her find answers in the library.

    Let me still try answer this one. Where did air come from? Hard to say. I guess it came with the Earth. There exist other "worlds" in space, a little like ours (some smaller, some bigger), called "planets." They look like stars in the night sky, though stars are different (stars stay in fixed groups, planets move among them). Some planets have "air", others (like the Moon, still another "world") came without it.

    OUR air is different, however: we can breathe it! Air on other planets is too hot (if they are closer to the Sun), too freezing cold, if more far away. But in addition, hot or cold, we COULD NOT breathe it, we would choke. It would be the wrong kind.

    For breathing, air needs to contain something we call OXYGEN. That is the part of the air which we breathe, the rest just goes in and out. Sick people in hospitals, who can't breathe well, sometimes get oxygen from special metal bottles.

    Our planet at first had "bad air", too. It has oxygen only because we HAVE GREEN PLANTS. Trees, grass, green leaves everywhere, with the help of sunlight, change air we cannot breathe, and make oxygen out of parts of it. If our world stopped growing trees or grass, our air would slowly become bad. So we should thank plants for our good air!  

202   Three-Color Vision

    I have heard somewhere that three colors are not enough to reproduce ALL colors which the eye can see. Is that true?

    (Adapted from question asked on Physhare, a list server of physics teachers)

Reply

    It is true.

    I have looked up this question in the writings of the true master, Richard Feynman, who dealt with color vision in chapters 35 and 36 of "The Feynman Lectures", volume 1. It is remarkable how far his interests have ranged, how few were the topics he did NOT look into. My own field of magnetospheric physics is unfortunately one of those few, and that only because his sister Joan (who is still with us) worked in it. When her brother showed interest, she told him to butt out, leave something for her to do. He did, and now we are stuck with all sorts of unresolved problems.

    You should read Feynman's exposition, in particular chapter 35, which I tried to flesh out a bit here. Feynman is so much more articulate than I can ever be, and what I wrote below is anyway my own interpretation, not necessarily the same thing.

    The important thing to do is to pose the proper question: what exactly do we want to claim? There is no question that the normal eye has 3 kinds of receptors, which we may designate (R,G.B) for (red,green,blue), although each is sensitive to a wide spectral range beyond the "pure" rainbow colors of red, green and blue.

    When we look at some colored object, with some standard brightness (I choose here a standard brightness for all colors, so that only relative intensity matters), if the (R,G,B) sensors detect intensities (a,b,c), we will see SOME color, and that color will be characterized by the 3 numbers (a,b,c). The range of values for (a,b,c)--say, from 0 to 1 for each, after we have standardized intensities--covers ALL colors the eye can see. There exists nothing more.

    The real question to ask is--is it always possible to "fake out" the color (a,b,c) by presenting the eye with a superposition of 3 colored sources, of three standard colors (U,V,W). These can be pure spectral colors, or not. (Red, Green, Blue) are a good choice, though, because each stimulates primarily one kind of receptor. Therefore, by twiddling with their intensities, we can make each type of receptor receive an EQUAL intensity, and the result registers in our mind as white. Let this be an assumed restriction on the choice of "primary" colors, requiring that we CAN get white; three different hues of green may never be able to do so.

    Let the color U create responses (a1, b1, c1) in the 3 receptors of the eye. Similarly:
        --the color V creates responses (a2, b2, c2), and
        --the color W creates responses (a3, b3, c3)

    These numbers (a1 . . . c3) are all COMPLETELY determined by our choice of reference colors (U,V,W).

    Suppose we want to illuminate a white surface with a combination (a', b', c') of the 3 sources, in such a way that the eye will be made believe that it sees a GIVEN color (a,b,c). Then

    a  =   a1 a'  +   a2 b'   +   a3 c'
    b  =   b1 a'  +   b2 b'  +   b3 c'
    c  =   c1 a'   +   c2 b'   +   c3 c'


    It is now necessary to invert the equations: (a,b,c) are given, (a', b', c') are to be determined. (You can write it in matrix notation if you wish, and you then need invert some matrix). There always exists a solution (unless the equations are dependent--e.g. the 3rd is the sum of the first two), so it SHOULD be possible.

    Having reached that point, Feynman raises a warning. A solution exists, but do we have a guarantee that (a', b', c') are all positive? They have to be if we add light from three sources--we cannot subtract (except maybe by using a colored screen, something he briefly discusses).

    If we choose (U,V,W) wisely, the coefficients will be positive for a wide range of color combinations (a,b,c), all of which can be represented by combinations of our reference colors. But there may exist some oddball combinations (a,b,c) where the solution gives some negative coefficient. NO combination of (U,V,B) can then fool the eye to believe that it sees that color. Feynman claims that there will always exist such colors, and at this point I tend to believe him.

Unless there is some flaw here, you may pass all this to your class. Let them see Feynman's book, too!


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Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   stargaze("at" symbol)phy6.org .

Last updated 10 May 2005