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Get a Straight Answer



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 complete list, including earlier questions not listed below, 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>


218.   Any limits to Newton's 2nd Law?

I am a Science teacher working in Sweden. I teach 9th grade Physics and we have begun with Newton's three laws of motion.

    The question I have concerns the second law... F = ma

    I am wondering about acceleration. If acceleration is meters per second per second, then if we put a force of 1N on a 1kg object in space we should see it accelerate at 1meter per second each second. BUT...

    Question is... WILL IT ACCELERATE INDEFINITELY? (Going faster and faster from only one Newton of force?) Provided that there is nothing to stop it (If we remove all gravitational forces, particle resistance; all other forces)?

    Thank you for any answer you might offer!

Reply

    You ask: " WILL IT ACCELERATE INDEFINITELY?" Yes, it will. As you approach the velocity of light, the increase in velocity gets smaller and smaller--but I think the growth of the energy remains the same. You just have to use the formula from the theory of relativity.

    However... it is not easy to maintain a steady force for a very long time. On a rocket, the force moving it forward is produced by throwing material backwards. As explained at the end of
section #25 of "Stargazers", if the velocity at which the material is thrown back is comparable to the forward velocity, you need to start with a fuel supply much, much bigger than your final payload. That is the case for "chemical" rockets used in most of spaceflight.

    An ion rocket (section #33) throws out matter at very great velocity, and so (with plentiful energy from the Sun, or from a nuclear reactor) it can sustain a small acceleration over a very long time--even months--reaching high speed quite "cheaply." Of course, it must already be in orbit in space: to lift it from the ground to its starting orbit you still need a chemical rocket.

    A solar sail can also in principle produce a small steady acceleration over a long time, but with the further advantage that it needs no material thrown back. All you need is a very powerful laser on Earth or somewhere in the solar system, kept shining at the solar sail (which must be quite big). Section 32 on solar sails tells of some such plans; right now they all belong to science fiction.

    Supposedly Archimedes once said that he could move the Earth with his lever, if only he could get a firm spot to anchor it. That's the trouble, there always remains some small detail which interferes with one's great plans!  

219.   Gravity at the Earth's center

    No idea if you're still updating your site, but noticed a possible mistake. at
http://www.phy6.org/stargaze/StarFAQ11.htm#q180. You were asked there
    What is the gravitational field at the mass centroid of the earth?
and replied:
    The answer is zero. No gravity at the center!


    But what about the sun, the moon, Jupiter? They're still there, and they have no effect on the location of the mass centroid of earth. Agreed, there is a point that has zero gravity, but it's not quite at the mass centroid

Reply

    The web site is continuously updated, but still, I would rather not change anything. First of all, I don't think the questioner (on the file you cite) intended to include those small forces, and secondly, explaining the effect may add to the confusion.

    Take a similar question--what is the gravity force on you where you are? Obviously, you need consider the pull of the Earth, towards its center. But should you also include the pull of the Sun?

    Yes--and no. The gravity of the Sun is certainly present, but you also move with the Earth in its orbit, and the centrifugal force of that motion balances the Sun's pull. Or, looking at it in a different way--your orbital motion with the Earth already amounts to free fall in the Sun's gravitational field, so the pull of the Sun adds no extra new force.

    Another example: is an astronaut in orbit subject to the Earth's gravity? Yes,--but he or she is also weightless, and the pull of gravity has no effect, because of the orbital motion.

    As the saying goes--I'd rather let sleeping dogs lie!  

220.   Does the Earth follow a "squiggly" orbit?

I was watching a NOVA program about Isaac Newton and I started thinking. Is the elliptical orbit of the Earth around the Sun, as usually drawn, an "average" orbit?

    By this I mean, does the movement of the Moon around the Earth pull it faster, slower, inward and outward depending on the moon's position? In that case, if the actual orbit could be rendered, wouldn't it be (to a minute extent) a squiggly line?

Reply

    Yes, the orbit would be "squiggly," though the squiggles would be rather small. By the laws of celestial mechanics, what actually moves around the Sun in a (relatively) smooth ellipse is the center of gravity of the Earth-Moon system.

    The Earth is about 81 times heavier than the Moon, and their combined center of gravity is on the Earth-Moon line, 1/82 of the Moon-Earth distance from the center of Earth and 81/82 of that distance from the center of the Moon. Since the Earth-Moon distance is about 60 Earth radii, it follows that this point is always inside the solid Earth--about a quarter of the distance in.

    As the Moon orbits the Earth, the center of the Earth will move back and forth, from 3/4 radius sunwards of the orbit when the Moon is full, to 3/4 of the radius nightwards of the orbit when the Moon is new.

    The average distance of the Sun is about 23500 Earth radii, so if you draw the Earth's orbit on a sheet of paper, that squiggle will be (on the same scale) much thinner than the line of your drawing--as you wrote, "minute." But it should still exist.
 

221.   Third grader asks: how far to zero gravity?

    My son Bradley asked how far away from the earth would one have to travel to no longer be effected by gravity? I thought I would be able to find a quick answer but have not and we would appreciate your expertise, as would his third grade classmates in Fishers, Indiana.

Reply

The formulas of gravity put no limit on how far it extends--it just gets weaker and weaker.     At the distance of the Moon it is still strong enough to keep the Moon from running away. That was what gave Newton the idea that gravity was "universal"--that the same force which drops apples from a tree to the ground also holds the Moon in its orbit.

    The Moon is about 60 times as far from the center of the Earth as we on the surface are. Newton figured everything was pulled towards the center of Earth--and also that the force of gravity got weaker like the intensity of light when you move away from a lamp. At 60 times the distance, light gets 60 times 60 = 3600 times weaker, so Newton wondered--would a force equal to 1/3600 the gravity we feel be enough to hold the Moon in its observed orbit? He did the calculation, and it came out just right. That was how gravity was discovered!

    At about 236 times the distance from the center--about 4 times the distance of the Moon--there is a point between Earth and Sun where a spacecraft can stay balanced between the pull of the Earth and the Sun. NASA puts spacecraft there, or near that point (putting it right in front of the Sun makes tracking difficult). I guess that is about the limit of space dominated by Earth's gravity. The pull extends much further, but other sources of gravity are more important there.

    Astronauts in orbit are "weightless", but that is because the force of gravity is compensated by the orbital motion. Gravity is still around there!
 

222.   "How does inertia affect a rolling ball"?

I go to a school called Morning Star Academy online. I am in 7-th grade and have questions I myself can not answer and would like help!

How does inertia affect a rolling ball?

Reply

    Handling rolling objects takes more math than you have. Let me explain a little. Suppose you have a solid cylinder rolling down a slope (a cylinder is easier to handle than a ball): how fast will it accelerate?

    If energy is conserved, after it has descended 1 meter, it will have gained the same amount of energy as an object of the same weight falling from the height of one meter.

    If it were just SLIDING down smoothly, with no friction, that cylinder would indeed have the same speed v as an object falling from that height. But if it rolls, some of the energy also goes to the motion of rotation around the axis of the cylinder. As a result the forward motion is slower than v, it gets only part of the energy.

    Calculating the energy of a solid cylinder of radius (say) R, rotating around its axis with (say) 1 revolution per second, is not easy. Different parts move at different speeds--those on the edge are fastest, with some velocity we can call V, while the middle does not move at all. What we need is find some average velocity V', equal to some fraction of V, so we can use the formula for kinetic energy (1/2)m V'2 (one half mass times velocity V' squared).

    Calculating that average takes a branch of mathematics called integral calculus, and involves a mechanical property known as "moment of inertia." It's the same with a rolling sphere--only more complicated, since now the averaging involves also the third dimension, parallel to the axis. With a cylinder you need not worry about the 3rd dimension--if you chop up the cylinder into narrow slices (like a stack of coins), V' will be the same in each slice.

All calculations of rolling inertia involve integral calculus and moments of inertia. You will have to wait!
 

223.   What determines the quality of a telescope?

    I have been interested in amateur astronomy since I ground and polished a mirror for a 6" telescope when I was 11 years old, 60 years ago. An uncle gave me a mysterious box as a birthday gift. It contained two discs of glass (one Pyrex), assorted abrasives, rouge and a block of pitch. A book by Ingalls with instructions accompanied it. The telescope functioned for many years with its rudimentary mount made of plumbing pipefittings.

    Grinding the 6" mirror as a youngster was an unforgettable experience and the thrill of seeing common sights, e.g. Jupiter's moons or Saturn's rings through a device I made was indescribable. I was also intrigued by the simplicity and cleverness of Foucault testing and being able to see the contour of the mirror blank as the work progressed as described in the book.

    I understand that a mirror gathers light. This explains why star images are brighter but does not explain why they are larger. Is this magnification solely a function of the eyepiece?

Reply

The quality of a telescope depends on many factors. Yes, of course, a larger mirror collects more light and can see dimmer stars. The magnification indeed depends very much on the eyepiece--if I remember right, in the simplest case on the ratio between focal lengths of the front mirror or lens and the eyepiece.

    But there are more things to consider. Light is a propagating wave, and the magnification of a telescope is also limited by the wave nature of light, a limit which depends on the ratio between the wavelength and the size of the collecting mirror (or lens); increasing magnification beyond this limit gives you a bigger blur, but not any more detail. So a bigger mirror is better--up to about 12 inches. Bigger mirrors may hit another limit, due to the turbulence of the atmosphere: you overcome this by carefully choosing the location of the telescope (high altitude and cold air help, as does luck) and recently clever telescopes have been built with can actively bend their mirrors by slight amounts, to minimize atmospheric effects.

Actually, some radio telescopes may have by far the best resolution of all telescopes.

    Remember, the limit is set by the ratio between the dimensions of the telescope and the wavelength of the light, or whatever radiation is used. You may think, because radio wavelengths are so long, that ratio will not be too big: however, one can combine radio signals between different dishes, and then the dimensions of the array are what counts.

    In the southwestern USA there exist arrays tens of miles wide! You can even record the signals on tape and compare later, and that way combine radio-telescopes across the ocean. Right now the limit is set by the size of the Earth--and with dishes in space and on the Moon, who knows how far future radio-astronomers will go!

    And magnification is not the only problem. You want a wide field of view (avoid the equivalent of looking down a narrow tube!) and all colors should focus together. If you are really interested in all that, I recommend the recent book "Stargazer" by Fred Watson, as Australian astronomer who has traced the history of the telescope with many interesting stories.
 

224.   Why design maps around curved lines?

    When lines of latitude and longitude were first conceived, why was the decision made to have longitude lines converge at the poles. Why not have them as parallel "slices" similar to latitude? An advantage would be that a degree of longitude would be of equal number of miles regardless of its distance from the equator.

Reply

    We live on a sphere (or near-sphere) and a sphere cannot be ruled using a square grid. You may start with a square grid, but as you get far from where you began, your squares grow unequal in dimensions, or collapse into lozenges.

    Besides, latitude and longitude are most easily derived for purposes of navigation: see the section
http://www.phy6.org/stargaze/Snavigat.htm

    Before latitude and longitude were defined, astronomers probably defined declination and right ascension on the heavenly sphere. It makse sense there--it's relatively easy to measure how far a star is from a pole, and the angle of rotation gives the second coordinate. I think that's how Hipparchus catalogued his stars.

    It's true, you need some calculation to figure out distances in miles. There exist ways, not too hard (at least, for short distances). You can also project the Earth on a flat paper with a rectangular grid, e.g. the famous Mercator projection, but it is obviously distorted.

    Any way of trying to project the surface of a sphere on a flat paper will create distortion: maps try to reduce it, but it cannot be eliminated. For instance, a map on a cone can be unrolled onto flat paper, so you can imagine starting with a cone put on top of the globe of the Earth, like a conical hat. To map any point on Earth onto that cone, find the radius to it from the center of the Earth, then continue the radius until you reach the cone, and mark that point. In other words--you "project" the point, as if a light existed at the center, the globe was transparent and the point was casting its shadow on the cone. Do so for all surface points. The map of the surface is then mapped onto the cone, and if you then unroll the cone you get a usable map.

    The mapping is only accurate on the circle where the cone touches the sphere. If however you let the cone cut through the sphere, your mapping is accurate along two circles, the boundary between where the cone goes "underground." Such maps also exist, and between those circles the error is not too bad. Some more complicated mappings exist, too.

But you'll never get an exact mapping onto a rectangular grid!  

225.   "Drag" by the Sun on the Earth's motion

You have a very clear way of explaining complex issues.

    This is a very simple question -- Does solar flux interact with the Earth's magnetosphere to produce rotational drag? If so, would we expect the day to become longer, and the distance between Earth and Sun to increase?

Reply

Interesting question, interesting answers.

    First of all, the length of the day is mainly governed by the equatorial bulge of the Earth, pulled by the Sun and Moon, leading to tides. The tides dissipate energy, which comes from the Earth's rotation--so yes, days are slowly getting longer. The Moon is the main culprit (and grows more distant in the process), but the Sun is an accomplice too.

    As for orbital motion around the Sun--any "drag" which opposes the Earth's motion will make it come closer to the Sun, and therefore, move faster, a result which also agrees with Kepler's 3rd law. If this seems puzzling to you, you are not alone, but that's physics.

    Look at it this way: to launch a rocket from Earth, you need give it extra energy. To raise a spacecraft from low Earth orbit to synchronous orbit, you need add still more energy. And similarly, to get further away from the Sun, you need add energy. If instead you lose energy, you are pulled closer. Motion in the distant orbit is slower than in the near orbit, which means less kinetic energy--but the gain in potential energy outweighs it.

    (Some of this is discussed in
http://www.phy6.org/stargaze/Smars2.htm , especially the section in the yellow box).

    So, does drag exist? Yes, but it won't much affect the motion of the Earth. The so-called Poynting-Robertson effect causes sunlight to exert a drag on any orbiting object. However, it is mainly effective on small particles. It may help clear the solar system of dust particles from comets--the ones large enough not to be blown away by sunlight pressure.

    In addition, the solar wind will also exert a drag. The reason is that as sensed by Earth, it does not come straight from the Sun (in which case momentum absorbed from it by the Earth would only modify the attraction of the Sun). Because the motion of the Earth at 30 km/sec is vectorially combined with the radial motion of the solar wind at about 400 km/s, that wind appears to us to come from a direction displaced about 4 degrees from the direction of sunlight. The momentum absorbed from the solar wind as it encounters the magnetosphere therefore produces a certain drag, but it is too small to significantly affect the Earth's orbital motion. The force is transmitted through the magnetic field.

    You wrote "this is a very simple question." Questions may be simple, but their answers may easily turn out complicated!  

226.   Does precession affect the time of summer?

    I am a meteorologist, recently retired from the National Weather Service. I am planning to volunteer at a Science Center, and wanted to do a presentation about seasons, and also talk about the precession of the earth's axis. It is my understanding that because of the precession of the earth's axis, the axis will be slanting in the opposite direction in about 13000 years. According to one source from the internet, that meant that the northern hemisphere will be facing towards the sun in December, and facing away from the sun in June.

    But according to one of the previous questions directed to you about precession (question 173), you stated that this change in the axis is relative to the background stars, and would not affect the timing of the seasons. That was because one year was defined from solstice to solstice (winter solstice to winter solstice, for example).

    But, if we define one year from being Jan 1st to Dec 31st, would not the day of the solstices and equinoxes change over the years due to precession?

Reply

The way we define the length of a year is up to us: is it from solstice to solstice, or is it from the time the Sun passes a certain position relative to the stars, a certain celestial longitude (aka right ascension), until it passes it again? The two choices for the length of the year are slightly different, because while the Sun goes around its orbit, the position of solstice relative to the stars moves just a wee bit, due to precession.

    Our years are reckoned using the first choice. If the second were used, yes, mid-summer and mid-winter would have slowly migrated.

        Follow-up question about other variations of Earth orbit

    One more question, this one concerning aphelion and perihelion, as I seem to be getting somewhat conflicting information from sources in the internet (or am interpreting the information wrongly). I know the dates of the aphelion and perihelion will vary slightly over the next 20 years or so (from information I got from the internet), but how much of a variation will occur by the next, say, 20,000 years or so? Will these dates ever vary significantly from the dates now?

Reply

    You have to ask a professional astronomer: I would not be surprised if the long-term effect is zero, except for small fluctuations. Note that a shift of perihelion or aphelion date of less than a week makes very little difference in the Sun-Earth distance (compared to assuming that date being constant), because at times when distance is maximal or minimal, changes in it are very small.

    The size of the orbit (semimajor axis) is essentially constant: it is a measure of the energy of the orbital motion, and since all external perturbations are periodic, the energy may fluctuate a little, but not really change.

    The distance to perihelion and aphelion does change, because the eccentricity of the orbit changes. See illustration in
        http://www2.ocean.washington.edu/oc540/lec01-23/
 

227.   Newton's law or Bernoulli's?

I was telling my science teacher about what you said and he wanted me to ask you what affected flight more--Newton's 3rd law or the Bernoulli principle?

Reply

    Presumably you are writing about the forces on an airplane wing. The two principles are not contradictory, and it would be fair to say both apply.

    Bernoulli's principle--increased velocity goes with lower pressure (if friction at boundaries can be neglected)--is mostly a consequence of Newton's 2nd law. It shows how faster air flow over the top of a wing creates a lifting force or "lift."

    However, Newton's 3rd law must also hold. If any force pushes the wing upwards, an equal and opposite force must push "something" downwards. That "something" is the "downwash," a downward flow of air. You note it most visibly below a helicopter, whose whirling rotors (which are really narrow wings) cause air to be forcibly pushed down--as is very evident in pictures of helicopters landing or taking off, especially above grass or water.

    The downwash is less evident in an ordinary airplane, which flies so fast that the downflow of air from its wings is spread over a much larger area, stretched along the path of the airplane. You also notice it behind a propeller-driven airplane ("prop wash") because again, a propeller is really a set of small whirling wings.
 

228   Does the universe have an axis?

    I seem to recall reading a newspaper article some years back where a NASA scientist confirmed that outer space actually possesses a north-south axis. Is my memory correct here? If so, could you explain?

Reply

Sorry, I'd have to see that article. "Outer space"--on what scale? The magnetosphere around Earth reflects the north-south axis of the Earth's magnetism, the solar system of course is centered on one plane (approximately, the ecliptic), and its north-south perpendicular direction enforces a certain north-south symmetry.

    But beyond that, north-south does not mean much. Our galaxy has an axis of course, but it is perpendicular to the Milky Way, with no north-south preference. Other galaxies have axes in all sorts of directions--we see some head-on, some edge-on and some at a slant. And the universe, as far as I know, is completely symmetric, with just small irregularities here and there, as shown by the cosmic microwave background, measured by the COBE spacecraft.
 

229.   Frictional electricity

    I came across your neat article "
Frying Pan Electrophorus" whilst looking for an explanation of the phenomena of charging by rubbing. If you could point me to a fairly detailed, satisfying discussion of this effect I would be most grateful.

In particular, which material becomes positively charged ? What is the charging when 2 pieces of the same material are used?

Reply

    Being a physicist does not make one an expert on everything! Certainly, not on the matters you ask about. I do know however that the effect is called "triboelectricity" and you can use that term to search for appropriate items on "Google," as I have done. Here are three relevant locations:
    http://en.wikipedia.org/wiki/Triboelectricity
    http://www.regentsprep.org/Regents/physics/phys03/atribo/default.htm
    http://www.physics.umd.edu/lecdem/services/demos/demosj1/j1-01.htm


    Of course, when you rub substance A against substance B, you only separate charges, not generate new ones: the (say) positive charge on A equals the negative charge on B. The second reference (and others too) lists substances in order of the ease with which they acquire charges of one sign or the other (I would guess rubbing two substances of the same kind has no effect). The third one claims that charging is a quantum tunneling effect, causes by intimate contact.

You might look at some of my other web pages for related physics:

    http://www.phy6.org/stargaze/Svandgrf.htm
about electric charging in Van de Graaff generators, Xerox copiers and thunderstorm clouds; and
    http://www.phy6.org/stargaze/Q8.htm
about quantum tunneling  

230.   Syllabus for catching up on physics

    We are a school in India dedicated to the rehabilitation of children with learning disabilities, and are not very happy with the way we now teach science. The problem is that when our students arrive they are emotionally and behaviorally maladjusted, and their language skills (both mother tongue and second language–English) are at the "letter level." We take more then 1-2 years to bring their language up to a reasonable standard. After that they still have language deficiencies, but we can start teaching them science in a way they can comprehend.

    If we have to adjust a child 15-16 years of age to a 10th grade syllabus, and if the child can comprehend orally but cannot read and write for the first 1-2 years, yet still has the ability to comprehend conceptually–how should we start teaching science to such a child?. This under the condition that the first two years are presented without reading and writing, but only transferring scientific concepts orally.

Reply

    I do not know why you contacted me, of all people, since I teach rather advanced science. You have a very difficult job! Usually, before trying to teach science, one teaches reading and writing. After that come numbers--addition, subtraction, multiplication and division. Only after a child understands those, can you start with science.

    When I was a child, science in school started with measuring: the length of a table, the width--then the area, perhaps. Learn what a meter is--the story makes students aware of the spherical shape of the Earth.

    We also learned about weight, and how to weigh objects. We learned of different substances--wood, plastic, stone, aluminum, iron, copper, lead--and listed their densities, perhaps calculated some, by measuring a block of metal, weighing and dividing. Using the density--if you know the length, width and thickness of a board of wood, and the density, you can estimate how much it weighs, and then check with scales.

(I don't know if the students can handle mathematics, especially multiplication. Calculators will help and may even give some understanding of the volume of a cylinder or sphere.)

    It works for liquids, too; they too have densities, and oil floats on top of water. You learn about liters, and about what floats and what does not

    If you are well equipped, you can tie a piece of stone to a spring scale and weigh it, then lift a pot of water around the stone and see how much less weight is registered, because some of the weight is supported by water. In a floating object, all the weight is supported. That brings you to the story of Archimedes and of his principle. Students can learn about pumps (water pistols are pumps, and I understand kids in India play with them when celebrating Holi).

    They can also learn about levers, mechanical advantage, and pulleys. From that comes the idea of energy--you lift a heavy weight a short distance or a light one a long way, but the work you do is always the same.

    How much science like this can be given your students, I do not know. You should have good science teachers in India to help you.

    And about teaching reading (and numbers) you may look at my web site on teaching our own children to read, when they were very young
           
http://www.phy6.org/outreach/misc/ilana.htm
Maybe some of the tricks we used may help your students, too.

Good luck in your kind efforts!  

231.   Parabolic reflector

    I am working in a project of constructing a solar waterpump using collectors (troughs) as the solar cells are too expensive and delicate for the use in African Sahara where the temperature reaches about 45° in shadow. My question is:

    What is the equation (formula) of the optimal parabola to use? I got the formula: Y=X2/4P from a physicist and the formula: Y= X2 /16P from another. Please help me with the right answer.

Reply

    Any advice I can give you is minimal, because I have no idea what you want. If you want to pump water, just producing heat is probably not enough. Parabolic reflectors can heat water, and their light is concentrated at the focus (x,y) = (0,P), where the first equation is the one to use, that is Y= X2/4P . You will find the derivation at
http://www.phy6.org/stargaze/StarFAQ6.htm#q109.

    But it is not so simple. The light focuses onto that point only when the y-axis is pointed at the Sun. Since the Sun moves across the sky in the course of a day, you may have to move the mirror by some machine, or else accept some defocusing--e.g. with a mirror having the cross section of a parabola in the north-south direction, but stretched out in the east-west direction with the same cross section along its entire length, and facing up, tilted slightly south. To get temperatures high enough to (say) run a steam turbine is not easy.

    Solar cells can be made quite robust: my daughter had one on her sailboat, going around the Caribbean, and sailboats on the ocean encounter pretty rough conditions--maybe no dust, but a lots of spray and corrosion. But her solar array was also fairly expensive, so in the desert, guarding against theft is a problem. I have read that in the last decade, Japanese industry had managed to cut the cost of solar cells by about one half, so maybe you should inquire about it. In any case, ask experts in this field--I am NOT one! Good luck  

232.   At what distance does Earth start looking spherical?

Dr Stern: How high must an astronaut be to view the Earth as a sphere??

Reply

    It's up to the viewer to decide! If you are about 2500 km high, the Earth subtends about 90°, so you can see all of it in your field of view, and I guess it seems spherical.

    At 1000 km, your field of view is about 120°, you can still encompass it all by waggling your head. Still a sphere?

    At the space shuttle altitude, say 300 km, you can't see the whole Earth with one look. But the horizon seems curved, not straight. Does that define a sphere?

    Finally, on the bridge of a ship, the horizon seems flat, but you know ships disappear behind it. Approaching a tall mountain, you may see its top first, the rest only later. Is that enough for you?

In short, you are asking about perception, not science. In perception, everyone formulates personal rules.
 

233.   Is the Sun on fire?

    I have just recently come across your web page. It is a great contribution to us in need to know. I do not know if you are still taking questions, but I have one.

    At my home, the fire needs air to breathe, and substance to burn in the fireplace. Does our Sun draw any air, or substance to it as it burns? Does the suns gravity, pull air, or molecules of any type or substance like the fires in our fireplace does? I would like to have an answer, very much.

Reply

    I don't know your age or where you attended (or attend) school, but you still have a lot of science to learn. The good news is--it's interesting and can even be fun.

    Fire in a fireplace is a chemical reaction. Combining atoms of oxygen with those of the fuel releases energy, which turns to various forms of heat.

    The heat of the Sun does not come from such chemical combinations. For one thing, the Sun is much hotter than any ordinary fire (we know that by studying its color), maybe 8 times hotter than what's in your fireplace. The colors of the Sun (its "spectrum", see
section S-4 in "Stargazers") also tell about its contents--mostly hydrogen, with some helium, and only token amounts of oxygen and carbon, which is what fuels your fire.

    Instead, the Sun's heat comes from the combination of atomic nuclei--mainly hydrogen turning into helium (see section S-7, though you will need study other parts first--such as #15, which tells you about energy). That can generate tremendous heat--much hotter than the Sun's surface. What you see on the Sun is just the final form of that heat, after a long journey from the inner core of the Sun outwards.

    Physicists in our laboratories cannot (yet?) tap this source of energy, because no material we have can stand the tremendous heat and pressure it produces. Some have worked on this up to 50 years, holding the hydrogen by magnetic forces: they have had some success, but still cannot release enough "fusion energy" in a practical way. The inner core of the Sun can hold such hot high-pressure gas, because of the enormous weight piled on top of it, held by the Sun's gravity.

I hope this answers your question. For more--go study!  

234.   Confusion about the "Big Bang"

Kudos to you. It is a treat for us physical Universe nuts to read the information on this web site!!

    Is it the general opinion with the Big Bang theory, that the Big Bang was the Milky Way's birth, not the birth of many galaxies or the birth of our current Solar System? That just this galaxy of ours the Milky Way originated by a big bang or implosion?

Reply

    The "Big Bang" marked the beginning of the ENTIRE universe, not just our galaxy. Let me explain, as well as I can remember here, sitting at the keyboard.

    Early stargazers observed the Milky Way, a whitish strip around the sky--I think the Greeks named it "galaxy", from the Greek word for milk. They had a legend that a mother goddess spilled her milk around the heavens.

    Galileo, with the first astronomical telescope (1609) saw that this whitish cloud was just a collection of many dim stars, probably very distant. Herschel and Laplace, over a century later, guessed that what he saw was a wheel-shaped collection of stars, to which our Sun and all stars we see with the eye belonged (well, almost all). It was probably rotating slowly, which explained its wheel-like shape. They still called it "the galaxy."

    But in addition to stars, the night sky also contained glowing clouds or "nebulae." No one knew what they were, or how far they were located. A Frenchman named Messier listed them (his list is still used), not because they were of interest, but to make sure they were not confused with comets, for which astronomers were searching. Comets moved, nebulae stayed put. Better telescopes showed that one big spiral nebula, in the constellation of Andromeda, had stars in it, and so did two "Magellanic clouds" in the southern sky, discovered by Ferdinand Magellan. On the other hand, a big nebula in the "sword" of Orion (to the unaided eye it just looks like a star) seemed shapeless.

    In the 20th century, especially thanks to Edwin Hubble, a new method was introduced: bright "Cepheid Stars" were noted to periodically get brighter and dimmer, with a period which related very well with their actual brightness (the brightness they would have if all were placed at the same distance). The periodicity of such Cepheid stars told how bright those stars were, and their actually observed brightness gave their distances.

    Similar stars also seemed to exist in Andromeda and other nebulae, but there they were quite dim, suggesting those nebulae were very, very far away--"island universes" like our galaxy, but outside it. Astronomers guessed those were star collections resembling our galaxy, and began talking about "galaxies" in the multiple. Not all nebulae turned out to be galaxies: the one in Orion was a cloud inside our galaxy. But many seemed to be galaxies like ours.

    After that it turned out that the colors of such very distant nebulae were shifted. One can expect that colors emitted by elements are shifted to red if the source moves away from the observer, to blue if it is approaching. (This is the Doppler effect, the same reason why the tone of a train's whistle drops as it passes by us). It turned out that the light of very distant galaxies was appreciably red-shifted--the more distant, the greater was their shift. Galaxies were moving away from each other!

    Today, using "type 1 supernovae" whose brightness also can be calibrated precisely (but are much brighter than Cepheid stars) we can extend the scale of the observed expansion and say pretty confidently, that all stars started expanding from a small region, some 13.7 billion years ago. THAT WAS THE BIG BANG.

    It was not an explosion into empty space, but space itself began expanding (both it and time started at the Big Bang). Galaxies always filled all the space available, it's just that this space itself has been steadily growing. You would think that the expansion would slow down, because stars and galaxies attract each other, and overcoming the attraction requires energy. To keep the expansion going at a fixed rate, something has to pump energy into the universe, or else we might see the expansion slow down, maybe even reverse.

    The latest observations suggest that indeed, something IS adding energy all the time--"dark energy" is a popular name--because the expansion, far from slowing down, seems to have gradually speeded up over those 13.7 billion years. Stay tuned--we still don't understand everything.

I hope that clarifies matters to you!
 

235.   How did Tycho calibrate his instruments?

    In my Honors class we were discussing about Tycho Brahe and the fact that he was one of the first scientists to consider instrument calibration as an important component of any observation. A student asked how he calibrated his instruments. I said I did not know but I suggested he might have used Polaris for calibration. Can you point me out to a source that addresses exactly how he performed his calibration?

Reply

    Tycho Brahe had no telescope, and all his observations concerned angles. You can always set up double targets on the ground at accurately measured distances, forming a known triangle with the observer. Angles can then be derived from
trigonometry, and measuring the angles with your instrument than gives calibration.

    Tycho's calibration was so good that he could measure the shift in a star's position near the horizon, due to atmospheric refraction. See http://www.phy6.org/stargaze/StarFAQ6.htm#q99

    About Tycho--I highly recommend the book "Tycho and Kepler" by Kitty Ferguson. See http://www.phy6.org/outreach/books/Tycho.htm


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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