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Angle between ecliptic and Milky Way

(Continuation)--About the year 2012

396A Posssibility of Asteroid Hitting Earth (1)
396B Posssibility of Asteroid Hitting Earth (2)

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

Reply

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

http://www.phy6.org/stargaze/Sseason.htm

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.
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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

http://www.phy6.org/earthmag/demagint.htm

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

http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1994kofu.symp..401T

Ian

Reply

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.
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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.

Reply

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.

Sincerely
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.)

Reply

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 .
Then y₁ = Ax₁ + B
y₂ = Ax₂ + B subtract

(y₂–y₁) = A (x₂–x₁) so 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: http://www.phy6.org/stargaze/Sseason.htm

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?

Reply

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

Reply

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 ).

Reply:

"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

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

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

Reply

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.

Reply

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

http://www.phy6.org/stargaze/Scolumb.htm
and
http://www.phy6.org/stargaze/Shorizon.htm

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.

Reply

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.

Reply

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?

Reply

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?

Reply

Questions like yours were asked before--see

http://www.phy6.org/stargaze/StarFAQ6.htm#q108

http://www.phy6.org/stargaze/StarFAQ6.htm#q78

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?

Reply

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?

Reply

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"

http://www.phy6.org/stargaze/Srotfram1.htm

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