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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 an index file listing questions by topic, click here.

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°?
  129. "Constellation" or "Asterism"?
  130. "Position of the Stars when I was Born"
  131. Rotation of the Earth's Core"
  132. How hot is the Sun?
  133. How much weaker is gravity higher up?
  134. The Big Bang
  135. Eclipse of Venus?
  136. The Big Bang

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

  153. Do Negative Ions make you Feel Good?
  154. Shape of the Earth's Orbit
  155. Questions about the Solar Corona:
                        (1) Why don't its particles separate by weight?
                        (2) What accelerates the solar wind?
  156. Why does the rising Sun look so big?
  157. Drawing a Perpendicular Line in Rectangular Coordinates
  158. Unequal Seasons
  159. Is the Big Dipper visible from Viet Nam?
  160. Holes in a Solar Sail
  161. Consequences of no more solar X-rays
  162. Science Fair Project on the Size of the Earth
  163. Superposition of Waves
  164. The Sun and Seasons

If you have a relevant question of your own, you can send it to audavstern("at" symbol)erols.com
Before you do, though, please read the instructions


  1.   Do negative ions make you feel good?
  2.     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. --------------------  

  3.   Shape of the Earth's Orbit
  4. 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."  

  5.   Questions about the solar corona:
  6.                  (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.  

  7.   Why does the rising Sun look so big?
  8. 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.

        Show your son the web site "Why Does the Moon Look So Big on the Horizon?" by Kathy Wollard, at:

    David P. Stern

  9.   Drawing a perpendicular line in rectangular coordinates
  10. 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.

  11.   Unequal seasons
  12. 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  

  13.   Is the Big Dipper Visible from Viet-Nam?
  14. 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.  

  15.   Holes in a Solar Sail
  16. 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.  

  17.   Consequences of no more solar X-rays
  18. Hi,
        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.  

  19.   Science Fair Project on the Size of Earth
  20. 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.  

  21.   Superposition of waves
  22. 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.  

  23.   The Sun and Seasons
  24.     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.

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Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   audavstern("at" symbol)erols.com .

Last updated 9-17-2004