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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. Harry Paul Sprain's perpetual Motion Device
  105. Can the plasma that fills space help spaceflight?
  106. Spiral arms of our galaxy
  107. What powers a glider?
  108. UFOs
  109. Maximum speed for propeller-driven airplane?
  110. The speed at which gravity spreads
  111. Layers of the Earth
  112. Why doesn't the sky fall on us?
  113. Imagine a non-rotating Earth
  114. Flying east with a 1° error
  115. US Flag on the Moon
  116. Rope stretched across a long lake...
  117. About studying electronics in the USA
  118. Publish Stargazers as a book?
  119. Charging of Earth by lightning:   +   or   –  ?
  120. If no stars were seen--could Earth's orbital motion be discovered?
  121. Local Solar Time in Iceland
  122. Is orbital motion same as free fall?
  123. Build a straight tower in warped space?

  124. The 2011-2 sunspot maximum
  125. Is Earth adding mass?
  126. Shape of a "bottle rocket"
  127. Fantasy spaceflight vs. reality
  128. Telling a 7-year old about stars "dying"
  129. (1) Why is lightning jagged?     (2) What did Tesla do?
  130. How can the north wall of my house be in sunlight?
  131. Heating the inside of Earth
  132. Dawning of the Age of Aquarius
  133. Why is hydrogen the fuel of choice?
  134. Gamma ray bursts
  135. Counter-clockwise swirling motion in the atmosphere
  136. Leap years on the Jewish calendar
  137. Earth axis tilt and climate (1)
  138. Earth axis tilt and climate (2)
  139. Does the Sun move?
  140. Can the Sun interfere with the visibility of the Big Dipper?
  141. Why can't we feel the Earth's rotation?
  142. Is our galaxy held together by a central black hole?
  143. Why don't gas planets just evaporate?
  144. Source of the Sun's energy
  145. Point of gravity equilibrium
  146. Solar system motion through the Galaxy
  147. Spaceflight by waiting for the Earth to turn?
  148. Does Earth rotation affect size of creatures?
  149. The year 2012
  150. Are our galactic arms winding up or opening up?
  151. Advice to a home-schooling mother
  152. Are all stars we see suns?
  153. 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

153.   Do negative ions make you feel good?

    I attended a session on multiple intelligences at a workshop last week. The presenter stated that we feel better when there is an abundance of negative ions in the air. She said that the wind whips up more positive ions and water produces more negative ions. That is why we feel better around water and the wind tires us out. Has anyone heard of this? Do any of you know of any research to support this? Any help would be appreciated. Sounds kind of questionable to me.


    Sounds questionable, indeed. There always exists a small concentration of ions in air, from radioactivity and cosmic rays, maybe sunlight too. The density of positive and negative ions is essentially the same, for when an electron is torn off an atom, where does it go? It either stays unattached, or attaches itself to some molecule--a negative ion in either case.

    Unbalanced densities create an electric field. A quiet-time electric field does exist in the atmosphere, produced by distant thunderstorms, and the difference over an altitude of (say) 2 meters may be a few hundred volts. That however can only exist because air is a very good insulator. Your body isn't: an electric charge touching it is soon discharged to the ground.

    So, do "we feel better when there is an abundance of negative ions in the air"? Not due to the ions, no. But it could be that a steady electric field requires conditions which are comfortable to the human body, such as low humidity. I wouldn't be able to say.

154.   Shape of the Earth's Orbit

I am a 9th grade Earth Science Teacher. I am trying to find out further information about the Earth's orbit around the sun as determined by Kepler. I would like the students to draw a north orbital view with the earth at aphelion, perihelion, and put dates on the ellipse to correspond with the months, the solstices and equinoxes. I have found lots of information, but much of it conflicts. I am hoping that I can get more information to satisfy myself as to what the correct configuration should be


A perspective view of the Earth's orbit is given in "From Stargazers to Starships" at


and of course it looks rather elliptical, because of the perspective. Equinoxes and solstices are represented by their months, and you can add other details.

    A perpendicular view of the orbit from north won't display any notable ellipticity: I have seen such a graph, and it looks just like a circle. The only visible concession to ellipticity is that the Sun is displaced from the center. The eccentricity e of the Earth's orbit is 0.01673, which means that the distances of aphelion and perihelion have a ratio 1.01673 to 0.98327, so with a diameter of 10 cm, the Sun is displaced by about 0.8 mm from the center, no more.

    An interesting fact, related to the eccentricity of the Earth's orbit, is that spring and fall equinox are NOT exactly half a year apart. That is discussed in section #12A of " ("More on Kepler's 2nd Law") and is related to the fact that we are closest to the Sun around January 4 (sometimes 3 or 5--it varies as the orbit is perturbed). Milutin Milankovich tied this to his theory of ice ages, as described in section #7 on precession.
    Other sections related to Earth sciences are #S-1, S-1A and S-1B dealing with weather and climate, and sections dealing with the Earth's magnetism (also with plate tectonics) in "The Great Magnet, the Earth", home page


especially the sections at the end, marked "Of Special Interest to Science Teachers."  

  • 155.   Questions about the solar corona:
  •                  (1) Why don't its particles separate by weight?
                     (2) What accelerates the solar wind?

        Your Web site is very useful! I'm 45 years old, with an interest in electricity in space, and still learning.

    1.     In the section on The Solar Wind, you mention that "The plasma of the corona is so hot that the Sun's gravity cannot hold it down. Instead, the upper fringes flow away in all directions, in a constant stream of particles known as the solar wind."

        Wouldn't the intense gravitation field of the Sun cause the heavier positively charged particles to fall back to the Sun, resulting in the Solar Wind containing more electrons than protons? Or would any proton falling back, attract an electron along with it?

    2.     I read on a number of Web sites that the Solar Wind accelerates away from the Sun. Is there an explanation? Eg. See




    Dear Ian

        Your first question is quite perceptive. A similar question about the Earth's atmosphere was addressed by Pannekoek in 1922 and by Rosseland in 1924 ("Electrical state of a star", Monthly Notices of Roy. Astron. Soc.84, 720-728, 1924). Here is the idea.

        In an atmosphere consisting of a gas of molecular weight M, the density falls off exponentially, at a rate which depends on M, on the temperature of the gas and on the force of gravity. In the Earth's lower atmosphere, the density falls to one half every 5 kilometers or so (or else, by a factor e = 2.71828.. about every 8 kilometers, a distance known as scale height H). High temperatures and low M increase H and spread out the atmosphere, while strong gravity decreases H and makes the atmosphere more compact. Of course, the Earth's atmosphere is really a mixture of gases, but in the first 100 kilometers, enough collisions occur to create a single scale height, some sort of average among the components.

        Above 100 km collisions quickly become rare, so different gases with different M tend to separate, as has been observed. Pannekoek and Rosseland wondered--what about free electrons in the outer layers of a star (or for Earth, in the ionosphere)? Their mass is so small, that their scale height should be much larger. Their layer should extend to great height, while the heavy oxygen ions (the main positive component) should stay well below them.

        They concluded this was not possible, because even a very slight separation of positive and negative charges would create an "ambipolar" electric field, pulling electrons down and O+ ions up. The field would effectively "add weight" to the electrons and would "buoy up" the O+ ions, until effectively each species senses the same downward force, contributed by both gravity and electric forces. With both species having the same "weight", they also will have the same scale height, and the ionosphere would stay electrically neutral, as is observed.

        The corona of the Sun behaves the same way, although the ambipolar field is probably much stronger, because of the high temperature.
        I am less certain about the second question--the solar wind is really not my field of expertise. In the Earth's lower atmosphere, temperature decreases with height, because heat from sunlight is mainly absorbed by the ground, at the bottom. It is then transported by air flows and by radiation, absorption and re-radiation (by "greenhouse gases") until it gets high enough to be radiated to space, not to return. That height defines the bottom of the stratosphere; other interesting effects occur higher up (e.g. absorption of UV by ozone), but we ignore them now. Because of the upwards flow of heat, the temperature is highest near the ground (where heat comes in) and decreases with height, up to the level where heat is given up.

        Solar physicists expected the same to hold for the Sun, also heated from below, and it is still a mystery, why so much heat is deposited in the corona, making it much hotter than the photosphere below it. Still, once you get to the corona, you would expect the temperature to gradually decrease with height, as one gets away from the source of heat and as the rising gas expands.

        Apparently this cooling is defeated by high heat conduction, because the gas is really an ionized plasma. Thus high layers are reheated from below, and an equilibrium solution, like that in the Earth's atmosphere, is not possible. The only solution Parker found in 1958 is a continued acceleration, until much of the heat is converted to kinetic energy. Mathematically the process has been compared to the acceleration of a rocket jet in the De-Laval nozzle (see
    section on Robert Goddard in "From Stargazers to Starships").

        I always thought the main acceleration took place in the first few solar radii--see Parker's papers. The abstract you cite claims that no, it's above 10 solar radii. I am no good judge of that, but also note that the abstract seems to refer to the solar wind above the Sun's poles, where field lines stick straight out and solar wind velocity is about double what it is near the ecliptic. Maybe the physics there is different.  

    156.   Why does the rising Sun look so big?

    Good day Sir

        I am living in South Africa. I have a 7year old son who has asked me a very interesting question, which I could not answer for him, with regards to astronomy. The question that he put forward to me was this: "Why when the sun is coming up, does it look so big on the horizon?".
            If you could please help me with an answer, it would really be appreciated.


    Dear Kyle

        Your son's question has been asked many times before, usually about the Moon, not the Sun (the Sun is too dazzling to look at, especially when high in the sky). No one is sure of the reason, but it might be an optical illusion--our brain makes us believe objects near the horizon are larger than when they are high in the sky.

    David P. Stern

    157.   Drawing a perpendicular line in rectangular coordinates

    Dear Dr. Stern

        As you said any triangle can be formed by 2 right angle triangles.

        How would a person calculate the exact position along the base line for the perpend to the 3 rd point?
    (I am programming EXCEL using x,y,z coordinates.)


    Hello, Paul

        Let's stick to 2 dimensions (x,y), and say the triangle has a baseline from (x1,y1) to (x2,y2) and the 3rd point is (x3,y3). I hope you meant "every triangle can be DIVIDED into 2 right angle triangles, because two random triangles, with all different sides, cannot be easily combined to one.

        Here is how you do it. Suppose first x1 = x2, so the baseline is parallel to the y-direction. Then the point where the triangles join has the same value of x (say x1) and the line dividing the triangle is parallel to the x-axis, from (x3, y3) to (x1, y3).

        Otherwise, let the baseline have an equation y = Ax + B .
    y1 = Ax1 + B
    y2 = Ax2 + B

    (y2–y1) = A (x2–x1)
    A = (y2–y1) / (x2–x1)
    and once you know A, you can get B = y1 – Ax1

    Now the perpendicular line through (x3,y3) has an equation like
    y = Cx + D

        But if the lines are perpendicular, the equations are related, and the relation is C = –1/A (don't ask me why--study coordinate geometry to find out). I assume A is NOT zero. If it is, that means y1 = y2, the base of the triangle is parallel to the x-axis, and you follow the same steps as before, only with the roles of x and y interchanged. Otherwise the line is

    y = –(1/A)x + D

    and since you know that the 3rd point is on that line

    y3 = –(1/A)x3 + D

    you should be able to derive the value of D. Say now the point on the baseline where both triangles meet is (x4, y4). That point is on BOTH lines and therefore satisfies both equations:

    y4 = Ax4 + B .
    y4 = –(1/A)x4 + D

    Solve the equations for (x4,y4)) and you are home.

    158.   Unequal seasons

    I enjoyed reading your web page on the seasons at:

        I had read that the seasons are of different lengths (i.e., summer, spring, winter, and fall are inherently of different lengths) and was trying to track down the reason for this. I still haven't found that out; any comments on that?


    The seasons are unequal, but the difference is small. That is discussued at the end of section #12a, "More on Kepler's Second law" http://www.phy6.org/stargaze/Skepl2A.htm  

    159.   Is the Big Dipper Visible from Viet-Nam?

    Hi Dr. Stern, I'm a retired teacher (Theatre) from Portland, Oregon. I've finished a book about my experiences in Viet Nam in 1966-67 teaching English to Vietnamese teachers. I'm checking on some points I need to clear up. I've returned to visit two of my closest friends. Once in 2001 and again in 2004. On the first trip back I was in Vung Tau which is south of Ho Chi Minh City. It was October and a crystal clear night.

        I looked for the Big Dipper so I could find the North Star and show my friends. But I could not see the Big Dipper.

        Is the Big Dipper ever visible from Viet Nam? It looks like Viet Nam is about a thousand miles north of the equator. Thanks for your help. I love your web site


    Hello, Brian

        Ho Chi Minh City (aka Saigon) is about 10 degrees north of the equator, so the pole star is about 10 degrees above the horizon. The stars of the Big Dipper circle the pole with radii of 30 to 40 degrees, so they are often below the horizon. (This holds even for much of the continental US, though not for Alaska.)

        Whether you see the constellation depends on the season and on the time of the night. The Big Dipper is on about the same right ascension (same spoke from the pole, if you will) as the constellation of Leo, which is prominent in the evening sky in March and April. At that time your friends should see it in all its glory. Maybe even in December-January, if they look at the sky before sunrise. October is not a good time, however! At such a time it is better to use Cassiopeia for finding the pole star, it is on the opposite side of the pole and should be prominently visible.

    (continuing the exchange, in part)

    Concerning Viet Nam, what is your impression of the books of LeLy Hayslip? I reviewed them at
    http://www.phy6.org/outreach/books/LeLy.htm (For reviews of other books, see http://www.phy6.org/outreach/intbook.htm ).


    "When Heaven & Earth Changed Places" is a wonderful book. Very real. Many touching scenes and several sections that were familiar to me. I did not like the Oliver Stone film at all. Her second book, "Child of War, Woman of Peace" was not as good as far as I was concerned.  

    160.   Holes in a Solar Sail

    I have read with much interest about the application of Solar Sails. However from what I learn Solar Sails will be several kilometers long and incredibly thin. Would the sails be peppered with so many holes from space particles that the sail would be rendered inoperable?

        I urgently await your reply


    Dear Matthew

        I don't know the answer, however, small holes in the sail should not affect its efficiency. In a sailing ship, the sail gathers the wind, which is a fairly dense gas. In a solar sail, everything happens on the atomic scale, and if a hole exists nearby, it will not divert the flow to itself.

        More important is the mechanical integrity of the sail--whether it can transmit forces without tearing. I am sure that before any such sail is flown in space, the material will be extensively tested, for effects of ion flow and also (this may be more damaging) for those of ultra-violet and soft x-ray radiation from the Sun.

    161.   Consequences of no more solar X-rays

        what are your thoughts on this question:
    What would happen to the earth's atmosphere if the sun stopped producing X-rays? In particular, how would the tempereature structure change? Thank you


    Dear Patricia

        Solar x-rays are absorbed very quickly in the high levels of the atmosphere. Thus one would not expect any effects in the troposphere (the lowest level where weather is produced). On the other hand, the ionosphere would be very different, and much thinner. The highest layer, the F layer used in long distance communications, might not exist, or anyway its density will be too small to matter much. Other layers probably will suffer too. Radio amateurs may have a tough time.

        For a better answer, ask someone familiar with long-distance communications and the ionosphere.

    162.   Science Fair Project on the Size of Earth

    I am a 9th grade student. I am having trouble with my science fair project. I would like to measure the size or circumference of the Earth. Do you know any experiments or formulas I can use to get my answer for my project. Thanks for your time I enjoyed your site.


    I hope you have thoroughly read in "From Stargazers to Starships" the sections on Columbus and on the horizon, at


    You also should know what a cosine is: if not, find out from the "Math Refresher" section there.

        Suppose you live on one of the coasts of the US, say in California. Find a friend or relative at the same latitude L, say in Virginia. You should have contact by long distance phone.

        Each of you should plant a stick on open ground, vertical (use a weight on a string to make sure). On the ground, mark the direction of south in a well-defined way, say, by a number of nails stuck into the ground. If you use a compass, make sure you include the appropriate correction, because the magnetic compass deviates a little from north-south. You may use a map and landmarks, if convenient.

        On a day when weather maps suggest no great cloudiness on either coast, set up phone contact. When the Virginia shadow points exactly south, mark your time. Then when the California shadow points south, get in touch again by phone and mark your time again (the time on the other end of the line is governed by time zones, and will probably be different). If the difference is X hours, the Earth has turned by about 360 (X/24) = A degrees. (actually, 4 minutes less than 24 hours, but you can ignore that).

        If you are at latitude L, the circle you make in 24 hours has radius R cos(L). You have gone A degrees of the circle, and the distance you covered--the distance between the stations--can be found from a map (surveyors have derived it already). The rest is up to you.  

    163.   Superposition of waves

    Dear Dr. Stern:

        For two electromagnetic waves of different frequencies (and wavelengths) and amplitude traveling in the same direction, I have noticed they combine their amplitudes when they superimpose. However, I am also noticing an increase in frequency. Am I correct to think that the two frequencies also combine in some manner so that the resulting wave is the combined frequency of the two waves?

        Or am I perhaps misinterpreting observations in that the increased frequency likely has a different cause not necessarily due to the superimposing? I suppose the situation is similar to a radio wave interacting with a visible light wave.


    Your question can be answered at several levels. On the simplest level--two long wave trains of different well-defined frequencies--no, they do not combine, and indeed, can be separated by suitable filters.

        Two waves at SLIGHTLY different frequencies will exhibit beats--a modulation in overall intensity as they slowly get in phase and out of phase again. A freight railroad runs about 2 miles from my home, and I can clearly hear beats when it is pulled by multiple diesel locomotives whose engines run at slightly different speeds. Twin engine airplanes also sometimes sound beats. If your detector smoothes over the rapid variations, it extracts the beat frequency.

        Things get more complicated when wave trains are finite and changing, as in radio waves which carry signals, say music encoded as AM or FM. When such waves are analyzed by frequency (without regard to phase--to where valleys and peaks fall), they always cover a finite "bandwidth" of frequency, around the main one of the carrier signals. Sometimes your radio will receive a mix of two stations, a sign that their bandwidths overlap.

    The question continues:

    Dear Dr. Stern:

        I appreciated your response. I was using a simple copper wire antenna to receive a consistent frequency radio wave, and I was receiving a frequency slightly higher at periodic times, when I was introducing a different frequency electromagnetic wave.

        Initially I thought that the waves may be combining, but based on your e-mail, could I conclude superposition instead? In other words, the antenna was receiving both frequencies simultaneously, which appeared as one larger frequency on the oscilloscope.

        Is my conclusion correct? Is it possible for the antenna to receive different frequencies from different types of electromagnetic waves simultaneously resulting in a larger frequency reading? I used a radio receiver antenna in place of the oscilloscope antenna, and at the periodic times I could hear choppiness or pulses with the earpiece that coincided with amplitude increases on an oscilloscope attached to the radio receiver. Could the pulses be the beats to which you were referring in that possibly what I was observing was two radio waves of slightly different frequencies? Thus, the oscilloscope attached to the simple copper antenna was giving me the readings of the radio waves and the other electromagnetic wave was not being recorded.


    Dear Chris

        Your questions go somewhat beyond my experience. I suggest you look up "The Radio Amateur Handbook" which most amateurs (and some libraries) have, and perhaps discuss them with a knowledgeable amateur.

        In general, superposing signals of one frequency does not generate a higher frequency stable enough to be observed on an oscilloscope. The sidebands I mentioned give irregular wave trains, to which a filter can respond, but not a 'scope.

        Beats occur between very close frequencies. If one diesel train engine emits a low growl at 100 cycles/sec and one next to it gives 101 cycles, the combined intensity will rise and fall with a 1-second period. I believe however you can get beats if a radio wave from a transmitter reaches you by two different paths, and the path difference slowly changes (ionosphere rising, say). That may explain the "choppiness" you observe.

    164.   The Sun and Seasons

        After looking at the page on
    "#1. Stargazers and Sunwatchers" I have a question related the sun's position on the horizon. The page talks about how the sun sets at different places on the horizon depending on the time of year, and my question is about the statement that "during the Winter Solstice the sun is as far to the south as it can be" at any one location.

        I'm assuming that this means that at different locations the sun can set further to the south or closer to west. If this is what was implied, then do you have an understanding on the relative direction the sun can set on the horizon at the equator or the poles or about mid-way between the two? And most importantly, what is the cause for this?


    Dear Jason

        You should read on! Your question is answered in section #2 "The Path of the Sun, the Ecliptic" and section #3, "Seasons of the Year." Right in front in section #2 you will see a schematic view of the path of the Sun at the summer solstice, at equinox and at the winter solstice.

        Why the different paths? You must understand that because of the rotation of the Earth, all objects of the sky seem embedded in a huge "celestial sphere" which seems to rotate around us, in a tad under 24 hours (that is discussed in section #1a). Some objects seem to migrate slowly around that sphere: the Sun, the Moon and the planets. Most stars don't migrate, however, and form the same patterns night after night, the "constellations" of the sky.

        The Sun seems to move in a huge circle, one circuit per year. If that circle were the celestial equator--halfway between the "poles" of the sky, the points around which the sphere seems to turn--then day after day the Sun would follow the same path, of which exactly 180 degrees are visible (during the other half, at night, it is below the horizon), and all days would be 12 hours long.

        Actually, the circle it follows is inclined to the equator by 23.5 degrees, because the axis of the Earth is not perpendicular to the plane of its orbit around the Sun ("the plane of the ecliptic"), but is 23.5 degrees off that perpendicular. So the Sun is half the year south of the ecliptic, and half the year north of it. When it is north of it, it is summer--each day (in the US) it covers more than 180 degrees, and days are longer than 12 hours. When it is south of it, its daily path above the horizon is less than 180 degrees long, and days are shorter than 12 hours, as they are now in December.

        The location of sunrise and sunset on the horizon varies over the year, but the ANGLE between the path of the Sun and the horizon depends on your latitude. On the equator it is 90 degrees, and sunrise wanders south or north in the same way as it does in the US. At the north pole, on the other hand, the angle is ZERO. At this location, the celestial equator is along the horizon. In half the year when the Sun is north of the equator, you will see it 24 hours a day, and it NEVER SETS. That is the long polar day, and a sun-observing telescope at the South Pole Research Station has taken advantage of this. If the Sun is south of the equator, in the part of the sky you do not see, it NEVER RISES and you have the famous polar night, lasting nearly half a year. Regions near the pole have similar seasons.  

    165.   If the Earth's Rotation would Stop... (1)

    Theoretically, what would happen if the world would stop spinning, and I mean a total standstill, for a period of let's say one month?


    Questions like yours were asked before--see

        It would take a miracle, of course--and therefore, it isn't certain that events following afterwards obeyed familiar physics. It would take a miracle because the spinning Earth has so much angular momentum, and so much energy, that if something suddenly caused the spin to stop, then following Newton's laws, that "something" would itself have to absorb a huge amount of energy and angular momentum. No such object lends itself to the task. A massive colliding object could in principle end the rotation, but it would smash earth to bits in the process.

        But a miracle... H.G. Wells once wrote a delightful fantasy tale "The man who could work miracles," (you can find the text one the web, and a description on Wikipedia). In that story, during an argument while drinking beer in a tavern, an ordinary working Englishman discovers he has miraculous powers, any wish of his is immediately fulfilled. All sorts of funny things follow, and in the end he is challenged to do what Joshua did--stop the moon and Sun from moving across the sky. His request granted, he immediately finds himself flying head over heels through the air, because what he has really done is stopped the rotation of the Earth, while HE HIMSELF keeps going at his previous speed. That part of the story is included in "Stargazers" here.

        But suppose a non-violent miracle accomplished what you asked for-- making one side of Earth keep facing the Sun, the other stay dark (the planet Mercury does something close to this--but not exactly). The sunny side will heat up considerably, the other will chill down. I expect the weather will get quite violent, because much of the heat received on the sunny side escapes by winds going to the dark side. I wonder which place on Earth would be most hospitable to life!

    Further question

    Wow, you really caught me by surprise. All the references you sent and the variety of subjects you have written about; you probably are never bored.

        Your answer that one side of the globe would be very warm (sunny side) and the other side that would be freezing, I must agree. How about in between?


        If the Earth somehow miraculously stopped spinning, the boundary between the roasting dayside and the freezing night side would probably be very, very windy, though the temperature may not be extreme.

        The factor driving weather and climate on Earth is the need to balance the input of solar heat and the loss of heat radiated to space, as described in sections S-1, S-1A and S-1B of "Stargazers." Several factors are important. One, incoming sunlight is mostly in the visible range, to which the atmosphere is transparent (or completely reflective, with clouds), but the radiation returned to space is infra-red and therefore strongly absorbed by water vapor, carbon dioxide and other molecules. That is the infamous "greenhouse effect" which actually, without being made extra-strong by human activities, is quite beneficial. That means only the top layers can radiate to space, and vertical motions (aka weather) must transport heat up and down.

        Secondly, heating is greatest at the equator, and this drives winds which spread warm air to higher latitudes, allowing a greater part of the globe to participate in the return of heat to space. That drives climate, whose complex system is also influenced by land/water distribution and by energy taken up by water vapor and released by its condensation.

        If the Earth did not rotate, such processes would drive warm air from the sunlit side towards the dark one, where it would cool more effectively and return at different latitudes or altitudes. Hard to predict the pattern (except maybe by computer simulation), because on the actual Earth, the rotation of the globe has a huge effect on it (see above web pages).

        The situation may be similar to what happens in the upper atmosphere of Venus, which indeed has powerful winds. Venus rotates very slowly--in a funny way, so that every time it is closest to Earth, it presents us with the same face. It's hard to believe the gravity of the Earth could have such a profound effect and maybe it's an accident, though at one time it frustrated radar astronomers trying to map Venus by radar (later on satellites around Venus did a much, much better and thorough job). But it's slow enough to approximate your suggested scenario. The bottom of the Venus atmosphere probably moves little, because it is quite dense and therefore heavy.  

    166.   If the Earth's Rotation would Change... (2)

    I am a fourth year geophysics student and I have been taking some physics courses concerning the effects of the rotation of the earth. I was wondering if it was possible to change the flow of a river by increasing or decreasing the rotation of the earth. For example, right now the Mississippi flows to the South, would it be possible to make it flow North just by changing the earth's rotation?


    It would take a major miracle to change the rotation of the Earth (see preceding Q&A!)--too much energy and angular momentum are needed.

        However, even if it were possible, I don't think flows of rivers would change. Suppose you did by some miracle manage to slow down the Earth by 10%, or speed it up by that much--what would happen? The equilibrium shape of the Earth would change, as discussed in section 24a of "Stargazers"


    and that would cause major earthquakes on land and huge sloshing of the oceans. But when all this would have ended, if the slope of the land in the US remained the same (i.e. elevations above sea level remained the same, even though "seal level" re-adjusted), then the Mississippi would still flow south, draining its sources in the north.

        Look at it this way. If any new force is added to make the Mississippi flow north, it will also make ocean water flow towards the poles. Initially, that may happen--if the equatorial radius of the Earth shrinks by half a mile (rotation slowing down), water at the equator will find itself half a mile higher than its final equilibrium position, and will flow away. But it will be strictly a one-time event, and once it ends, no additional energy is available to make the water flow any more  

    167.   What if the Earth stopped in its orbit?

    Hi! I'm 14 and I live in a small town in Ohio. I have some questions.....
      Is it possible for Earth to crash into the Sun if it's orbit has stopped? If the orbit did stop how long would this take?


        Nothing happens in nature without a proper cause.

        Yes, if Earth suddenly stopped in its orbit, it would fall into the Sun: but what could make it stop? There is a huge amount of kinetic energy involved, and I for one cannot think of anything forceful enough to stop this motion. Yes, if a planet the size of the Earth and moving in the opposite direction collided with us head-one--it would stop the motion, and the fragments of that collision (both planets would be smashed to little bits) would fall sunward. But nothing remotely resembling such a planet ever been seen, so you can sleep easy.

        By the way, there have been suggestions we should get rid of nuclear waste by rocketing it into the Sun. Not a good idea! Nothing in the solar system is as hard to hit as the Sun itself, even leaving the system completely takes less thrust. To hit the Sun, our spaceship would first have to get free of Earth (velocity needed, 11.3 km/sec) and then add a velocity of 30 km/sec to cancel the orbital velocity around the Sun. That would take enormous thrust, more than any space mission I know.

    About the time it takes... use Kepler's 3rd law:

    T2 = k a3

    Where T is the orbital period of a planet and a its semi-major axis, half the width of its orbit (k is some number, depending on the units we use). For Earth, T = 365 days, a = 150 million kilometers, a number we indicate by the letter A. So

    3652 = k (A3)

    A very skinny orbital ellipse, one end at Earth and the other at the Sun, has length A, half length A/2. If the period of that ellipse is denoted "t", we get

    t2 = k (A/2)3
        = k (A3/23)
        = k (A3) /8
        = 3652/8

    Working out "t", it comes to 129 days. A one-way trip from Earth to the Sun will take half the orbital period or 64.5 days, so that is your answer.

    168.   Fast Trip to Mars     (1)

        I am trying to create a trajectory to Mars for a science experiment. I understand the Hohmann Transfer Orbit and can do these calculations, but I would like to reduce the time spent in transfer orbit. I understand that if I would like to achieve a higher orbit (say a transfer orbit to Jupiter, overshooting Mars), I would need a higher Delta-V to escape the sun. So, if I apply more thrust, I should be able to go faster. Then it would be a matter of determining where the spacecraft would meet the orbit of Mars and setting the launch opportunity accordingly. This should shorten the time spent in transfer orbit, correct? Is this actually possible?


        You certainly can choose any point on the Mars orbit as final destination, head for it and calculate the time it takes. That will determine where Earth should be at the time you launch.

        Once you arrive at Mars, you will need to match velocities with the planet, using your thrust. You might be able to aim at the atmosphere of Mars and use if for braking your motion.

        My guess is that any deviation from the Hohmann ellipse would cost you plenty in terms of extra thrust. If you have a serious interest, go to a university astronomy department and get advice from someone who knows orbits, then look up the literature. You may also need a suitable computer code to experiment with various orbits.

    169.   Fast Trip to Mars     (2)

    I am a junior in the mechanical engineering department at Vanderbilt University in Nashville, TN. This semester I have been researching a project I was given. The project involves designing a fission fragment rocket engine that would be capable of traveling from Earth to Mars in two weeks.

        The reason I am writing this letter is because I have been having a great deal of trouble calculating the flight path of our rocket. I have learned a great deal from your website, especially about the Hohmann transfer orbit, but I have been unsuccessful in finding an appropriate orbit for so quick a flight.


        A flight to Mars in two weeks would almost follow a straight line, and would definitely not resemble a Hohmann ellipse (still, two weeks seems rather fast). What you would do is launch a very fast spacecraft to intercept Mars somewhere in its orbit, and on arrival (it will most likely be a one-way trip!) use the thin Martian atmosphere to brake your flight. Without this trick , you will need an enormous reverse thrust to match velocities with Mars. Failing either of these, your spacecraft will whiz by Mars and leave the solar system.

        The question is, in what direction to the Earth's motion should you launch to get away with the smallest initial velocity and initial thrust. If you launch parallel to the Earth's orbit you get the advantage of the Earth's orbital velocity of 30 km/s, but the distance is greater, so you need a greater average velocity to cover it in two weeks. If the Earth's orbit is a circle with radius R1 = 1 AU circle and that of Mars has R2 = 1.52 AU, your distance is approximately 1.14 AU (square root of the difference of squares). If you go out radially, away from the Sun, your distance is only 0.52 AU but you also need cancel those 30 km/s. My guess is, write a short code and calculate the mean velocity at 5 degree increments of the angle of the initial velocity to the Earth orbit, but the result is almost certainly close to radial.

        That gives you the variation of he MEAN velocity with angle. However, the motions are actually in a 1/r potential--the spacecraft starts faster than the mean and ends slower. Modify your code to derive the initial velocity. Then interpolate to find the angle which gives you the trip with smallest initial velocity. All these motions are in straight lines, not ellipses, but for a rough engineering estimate, that's probably good enough.

        The trick, of course, is to design a nuclear engine which is reliable, safe and won't contaminate the environment. If you read my web page on nuclear pace flight, you probably saw that Carlo Rubbia proposed a fast Mars trip like yours--see "Nature", vol 397, page 374, 4 February 1999. I vaguely recall he proposed using an Americium isotope as fuel.

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

    Last updated 9-17-2004   Edited 1 November 2016