396B Posssibility of Asteroid Hitting Earth (2)
If you have a relevant question of your own, you can send it to
68. Two questions, one answer
Someone I know maintains that we never actually landed on the moon. It was
all a Hollywood production. This person claims that if you look at it from
a physics perspective things do not add up. I really haven't paid much
attention to this but it came up again today with this person. I was
wondering if anyone had heard of this before and what the arguments are for
both sides of the picture. I really do not want to get into a large debate
over this and these days my time is really limited. I would appreciate any
information on this issue.
(b) Was Moon landing a hoax?I came across a website that is marketing a video that supposedly proves that the US never landed on the moon. It claims that the Apollo 11 & 12 missions were staged for political reasons. In an effort to prove his point, the director makes these statements about the "dangers" of the Van Allen Radiation Belts. I was wondering if you would give your opinion as to the accuracy of the director's statements:
"The only time in history that an astronaut, Soviet or American, is said to have left the relative safety of Earth orbit and ventured through the Van Allen Radiation Belts, a twenty-five thousand mile thick band of intense radiation which surrounds the Earth beginning at an altitude of about one thousand miles, is going to the moon. The Soviets, with a five-to-one advantage in the early part of the space race, never once sent a human through the radiation belts to even orbit the moon.
If you wish to see the website, it's http://www.moonmovie.com.
Reply (to both questions)I get many e-mail messages, and now and again someone asks whether the moon landing was staged on Earth and actually never occurred. The idea is not new. A fairly good film ("Capricorn One," 1978) was shown in movie houses some years back, involving a faked landing on Mars, but of course it was a work of fiction. I have answered related questions in
and especially the 2nd question there is relevant.
I have not seen the film you referred to, but looked at the web site you mentioned. Its producer sounds a rather shrill note, a single tone repeated again and again. Too much evidence points to the Moon landing being real. Besides the testimony of participants (including New Mexico's senator Harrison Schmidt), we have the famous video of feather and hammer dropped in vacuum, the reflected laser beam experiment (a dim memory tells me it was by Prof. Alley of the University of Maryland), scientists' analysis of moon rocks and much more. Of course, having worked as a scientist for NASA for 40 years (but nowhere close to project Apollo or manned space flight), I also know a thing or two about the competency of the agency, and can confidently say that a hoax like that is way beyond its capabilities.
The Soviets indeed never sent a manned space flight beyond the radiation belt, but it was not for want of trying. Their rockets kept blowing up, and their space program was badly overextended before it shrank back.
As for flashes of light seen by astronauts, I have never heard about that before. Flashes HAVE been seen on Earth, due to cosmic ray particles (muons) whose speed is close to that of light in vacuum. As I understand it (a dim memory of an article in "Nature", I believe) such particles pass through the eyeball fluid, where their speed is greater than the local velocity of light, which decreases in transparent media. That produces a flash of light, the "Cherenkov effect," which has been likened to the shock produced by a supersonic airplane or missile. I believe the subject of the experiment sat in a dark room and particle counters verified the path of the particle.
It is highly unlikely shuttle astronauts would see such flashes. Anyway, inner radiation belt protons (the main radiation hazard) are too slow to produce Cherenkov light. I am not sure about fluorescent scintillations, though--you might have to ask someone. Cancer of the eye may perhaps be treated by radiation, and if so, there should exist experience from there.
69. Clockwise or counter-clockwise?(From Fort McMurray, Alberta)
We are sitting around a bunch of us at work (EMS) and we got on the topic about the rotation of the earth on its axis and its rotation around the sun. So...are we correct??? We think that the earth rotates counter clockwise on its axis and clockwise around the sun. Seems like a question everyone would know the answer to, but we've checked so many sites and can't find the answer anywhere.
ReplyOn a whim I looked up Fort McMurray in an atlas: boy, are you up there in the frozen north--icy winters, tar sands, bloodthirsty mosquitos in the summer--and are you in the permafrost belt yet? At least you can watch the polar aurora. I have studied a lot about it and wouldn't mind enjoying it more often.
As for the rotation of the Earth... you should first of all realize that "clockwise" and "counter clockwise" are not absolute properties, but depend on your point of view. Imagine a clock with a transparent face, with you watching it from the rear. The number 12 is still on top and 6 still on the bottom, but now 3 is on the left and 9 on the right. So when the clock hand moves from 12 to 3, it moves ... counterclockwise!
To define rotations with no ambiguity, we can stipulate they are always observed from the NORTH, from some point far above the north pole of the Earth.
I live on the Eastern seaboard of the US, while my son lives in California. I would not think of phoning him in the early morning--it may be day here, but the Sun has not yet risen where he lives, before that happens the Earth has to rotate an extra distance towards the Sun. To do that, the Earth must rotate COUNTERCLOCKWISE, as you have proposed.
The motion of the Earth around the Sun is harder. Let us start with the APPARENT motion of the Sun around the celestial sphere. You go out in the early evening in winter and see Orion in the sky. By early springtime Orion has moved west and now it is the constellation of Leo the lion that is in full view in the evening sky. Look on a star chart: Leo is east of Orion.
So the evening constellations open up eastward: you could not see Leo in the winter, because the Sun occupied that part of the sky, but now the Sun has moved eastward and opened up for viewing a new patch of the heavens. To move across the celestial sphere from west to east, the Sun has to go around the pole (as viewed from north) COUNTERCLOCKWISE.
However... that is the apparent motion of the Sun. If the Sun SEEMS to move around the Earth counterclockwise, but actually the Earth is the one moving around the Sun, is the Earth's motion clockwise or counterclockwise? You need a sheet of paper to solve this problem, which is also problem #1 among the ones listed in "Stargazers." But I won't keep you in suspense: it is ALSO a counterclockwise motion.
So your second guess was incorrect. In fact all orbits in the solar system are counterclockwise, even of the larger satellites (except for one of Neptune, suggesting a captured asteroid). The common explanation is that all planets and their satellites condensed from a swirling cloud of gas and dust, and their rotations reproduce that of the cloud ("conservation of angular momentum").
70. Isotopes in Center of Earth(from France)
I'm a student. Could you tell me what kind of isotopes are disintegrating in center of the earth?
ReplyMany, many unstable isotopes can exist. However, the Earth is billions of years old--4.7 billion is the latest estimate I heard--so only isotopes which disintegrate over a scale of billions of years are expected to exist in nature. All others (except for some rare types) would have finished disintegrating long ago.
That leaves mainly three: uranium, thorium, and potassium 40 (K40, with atomic weight 40). I do not know the numbers, but they all make important contributions to the heat inside the Earth. Uranium and thorium disintegrate in steps, creating intermediate elements such as radium, and these also contribute heat, but the ultimate source are these two elements. The end product is lead--as well as helium, ejected from unstable nuclei as fast alpha-particles. The helium we use to fill balloons comes almost entirely from this source: natural helium (e.g. of the Sun) has a certain percentage of helium with atomic weight 3, but the gas we get from underground sources is practically all helium with atomic weight 4. Potassium decays to argon, a gas which forms close to 1% of our atmosphere.
The heat-producing isotopes seem to be mainly concentrated in the crust of the Earth. Evidence on the interior suggests that the temperature rises quickly as one goes down in the crust, but rises only slowly deeper down.
71. Density of the Sun's corona and the "Scale Height"(from Turkey)
I am curious science teacher and I wonder "What is the coronal pressure? I mean for example 10 000 km of the photosphere."
ReplyDear Science Teacher
Questions are easy, answers are difficult. I do not know the correct presure "off the top of my head" although I know the number is small. The encyclopaedia on the web says the density of the sun's photosphere is about 1/1000 that of the atmosphere on the ground, and even allowing for a 20 times larger absolute temperature, this is still quite rarefied. At 10,000 kilometers you are in the lower corona, and the answer is harder still.
Since you are a teacher, I will go here into some more detail, maybe your class will be interested. The Sun is not my field, but I should know enough to explain.
Why is the Earth's atmosphere near the ground under pressure? Because it is supporting the weight of all the air above it! You go up 10 kilometers and the pressure is down to 25%, because only 25% of the air is above that level, 75% is below it. In the atmosphere near the ground, pressure goes down by a factor 2 about each 5 kilometers (or by a factor e=2.71828... every 8 kilometers--that is called the "scale height"). The number depends on temperature, so it may go up and down a bit, but you can see it decreases very fast. Above about 100 kilometers the air is so rarefied that molecules and atoms rise up and fall like thrown stones, rather than colliding constantly, and then different rules hold and the decrease is slower.
If the air were 20 times hotter (as in the photosphere of the Sun, 6000 degrees absolute against 300) the pressure would still be the same, because the weight above remains the same. The difference would be that the atmosphere would expand 20 times--"the halving distance" would rise to 100 km--while the density of the air would be only 1/20th. So with density dropping 20 times and temperature rising, the pressure SHOULD be the same.
The same rules hold in the photosphere of the Sun.
The gas is indeed has about 20 times hotter, trying to make the "scale height" 20 times larger than ours. However, gravity near the surface of the Sun (or what to the eye looks like one, it's really all gas) is about 28 times the gravity at the surface of the Earth, and that more than counterbalances the higher temperature. Most important, perhaps, is that the photosphere is mostly atomic hydrogen, about 1/30 times lighter than atmospheric molecules, and the scale height is larger by a corresponding factor. If you put all this together (and ignore temperature changes in the photosphere) you get a scale height of the order of 150 km and a "halving distance" of about 100 km.
That is larger than in our atmosphere--but the Sun is much bigger too, and you realize that by the time you reach 10,000 km, something HAS had to change. As a matter of fact, the photosphere is only about 400 km thick. For the next 5000 kilometers you are in the chromosphere--hotter and very uneven, but still decreasing fast in density, and at 10,000 kilometers you are in the lower corona, temperature of about 1.3 million degrees, and who knows what pressure and density!
I have looked for some references and found on the web an article
which claims to observe at 1.03 RS (solar radii; that is, at about 20,000 km above the surface) a density of 180 million electrons per cc (and if that is the density of atoms, that is more rarefied than any laboratory vacuum!) and a "nonthermal" velocity of 33 km/sec. Let me try and check it. Earth is about 200 RS from the Sun and is immersed in the solar wind, density about 10 per cc and velocity about 400 km/sec.
If the flow is the same in all directions, in each second, the flow fills a spherical shell of radius 200 RS and thickness 40 million cm, containing
10 . (12.56 [200 RS]2) . (40 000 000) atoms
= 10 . (12.56 . 40000 RS2) . (40 000 000) atoms
The atoms are of course ionized, and we should really express RS in centimeters, but as will be seen, that is not needed. If the flow is continuous, and the 33 km/s refers to a radial outflow, the same amount of material leaves each second a spherical shell of thickness 33 km near the Sun, with a radius near 1 RS. If D atoms/cc is the density in that shell , then
10 . (12.56 . 40000 RS2) . (40 000 000) = D . (12.56 . RS2) 3 300 000
Canceling 12.56 . RS2 . 1000 000 (which is why the exact size of RS was not needed!)
16 000 000 = 3.3 D
Your message was titled "coronal plumes." If you have not yet seen the 1999 eclipse photograph of the corona, look at
72. Did Tesla extract free energy from thin air?This may be a dumb question.....Nikolai Tesla supposedly powered a electric car with a set of vacuum tubes and a antennae set up, which he claimed tapped power from the "aether ." Do you think he actually accomplished such a feat with this kind of set up ? It would seem logical that the massive energy from our planet / universe could be tapped in some way.
ReplyLong ago our post office had a sign in its display window: "If something seems to be too good to be true, it probably is."
I do not know too much about Tesla, but he had eccentric ideas, and one of them, I vaguely recall, was to tap energy from the atmospheric electric field. There exist relatively large vertical voltage differences across the atmosphere, the residual effect of atmospheric electric processes in distant storms, the same as are responsible for lightning.
The reason they can persist is that the atmosphere is a very, very good insulator. Electric power companies string their cables in the air and never worry about any leaking away! To get any useful power from that voltage (as Tesla may have wanted) you need a closed circuit, part of which runs in the atmosphere, and the air would not allow it to flow there.
I never heard about an electric car being run from this source. And although, when you stand, the voltage of the air around your head may be (say) 300 volts above the one at the ground, you never feel anything, because the tiny electric charge involved is immediately drained away by your conducting body, essentially short-circuiting the voltage to zero.
73. What does "lapse rate" mean?(excerpt from a message from Turkey)
What are adiabatic lapse rates?
'Adiabatic' means internal change.
ReplyA "lapse rate" is the rate at which the atmosphere cools with growing height above sea level (in degrees per kilometer). Air cools with increasing altitude, because heat deposited by the sun on the ground or ocean is escaping out to space, and the way heat is transferred is by rising currents of warm air, which later radiate their heat to space.
The higher those air currents get, the less air remains above them. The weight of that air is what compresses them, so the higher the air rises, the lower the pressure of the air. As it rises the lower pressure makes it expand, and the expansion cools it. That is why high mountains can have snow, even in regions where the climate is warm at sea level.
If the air is dry, the cooling rate is that of adiabatic expansion--the rate air cools when it cannot take heat from another source (or lose it to another source). The formula for adiabatic expansion--temperature against pressure--then gives the adiabatic lapse rate, which is rather fast. Actual air usually contains water in the form of humidity, and as that water condenses to liquid--in clouds or rain--it slows down the rate of cooling. Depending on humidity, the actual lapse rate is usually lower, sometimes down to about half that of dry air.
74. Motion of the Sun through spaceHello Mr. Stern, I was wondering if you could tell me who made the discovery (and when the discovery was made) relative to the fact that the sun has its own eliptical path? Up until just a few minutes ago I had always believed the sun to be stationary. Was this a fairly recent discovery or did I miss that day in science class?
ReplyYou did not give details about the discovery YOU made just before sending the message below, so I am unsure about the elliptical path you have in mind.
The Sun does move slightly because, in the solar system, only the overall center of mass (aka "center of gravity" or c.g.) is at rest. (That is, before we consider the motion of the entire system relative to other stars.) For instance, Jupiter has about 1/1000 the mass of the Sun and is about 1000 solar radii away. Therefore their mutual c.g. is near the visible surface of the Sun, and if no other planets interfered, the Sun (and Jupiter) would move in ellipses around that point. The existence of planets shifts the c.g. somewhat, but not by much.
This effects helps locate planets around other stars: see "Refining the First Law" in
The entire solar system moves among the stars at about 20 km/sec, in a direction first estimated by William Herschel in 1783, about the time he discovered the planet Uranus. I don't know if that is elliptic motion around the center of the galaxy or (more likely) residual motion relative to other stars which share such a motion.
75. Teaching about tides(From site devoted to communication among physics teachers)
I am looking for any ideas for activities or models that will help teach a group of 30 3rd-5th grade students about how tides work. Since I am in Colorado most students are not familiar with tides or tide charts. Any ideas would be greatly appreciated. Thanks.
ReplyNot easy, at this level, especially in Colorado. However, even kids who have not seen the ocean know the Moon always presents the same face. Why? Because the Moon is deformed, a bit like a melon, elongated along the Earth-Moon line. The extension on the side facing the Earth is pulled a bit stronger than the symmetric one on the far side, because it is closer to Earth. Therefore that side is locked into facing the Earth.
This demonstrates tidal forces and is explained in the second part of
The Earth is a bit different, because it has an ocean. The water on the side facing the Moon is closest to the Moon, so you get a tide there. The water on the far side is most distant, and therefore the Earth is pulled away from it, producing a tide there as well. So at any time you get two tides. And since the Earth rotates around its axis, those tides progress around the Earth, creating a traveling wave. Coast lines channel that wave, so in some places the tides are small, in others (Bay of Fundy, northern France) they get quite big.
Take it from here.
76. Distance to the HorizonI'm very sorry to bother you, but I picked up your email address at the following web site: http://www-istp.gsfc.nasa.gov/stargaze/Shorizon.htm.
The reason that I'm emailing you is that my father and his friend have a bet as to the distance you can see off of the coast of Manhattan on a clear day. They are building something 7 miles off of the shore, and my father thinks that you wouldn't be able to see it.
Since I haven't use the math side of my brain in a
That would put the distance you can see at: D = 112.88 * 0.031622 so D would be about 3.57 km or 2.22 miles?
Thank you so much for your time, and sorry about the intrusion.
No need to apologize, I receive many messages and since I'm retired, I try to reply to the more serious ones. Your calculation is correct, but.... how tall is that "something" being built 7 miles off shore? You certainly won't be able to see an oil slick, but suppose it's a lighthouse 16 meters high. Someone standing on top of the lighthouse can see YOU from there, even your feet (same formula gives a horizon 4 times more distant), so by inverting the light path, YOU should be able to see the top of that lighthouse. If the lighthouse lantern is placed at that height, its light would reach you.
(By the way, this also explains why lighthouses are often tall towers, or else are placed on top of a cliff or mountain: the higher the lantern, the further can its light be seen.)
77. "Can geocentrist theory still be possible?"Hi ,
I have a few questions on the solar system I hope you have the time to answer. You see, I have a friend who started believing in this geocentrism stuff. Now, I am no scientist, but is this not kooky stuff??? That is why I am contacting you. Or can there be some sort of legitimacy of a geocentrist view??? I mean, can the geocentrist theory still be possible at all??? Or is the thing thoroughly refuted in favor of heliocentrism??? Can you recommend some good books then proving heliocentrism???
Thanks and I await your response,
ReplySince you had my e-mail address, you must have visited my web site "From Stargazers to Starships," with home page http://www.phy6.org/stargaze/Sintro.htm (or the alternate NASA site). In the first part, devoted to astronomy, you and your friend will find more than enough. Let me sketch out the steps by which heliocentrism arose, and you can read the details in the appropriate astronomy sections. Dates are on the timeline of the same site.
The ancients, of course, assumed the Earth was the center of the universe and everything--Sun, Moon and stars--revolved around it. The unnamed authors of the Book of Psalms thought so and wrote so in the bible, causing great grief to poor Galileo 2000 years later. A Greek scientist, Aristarchus of Samos, seemed to support it by estimating the distance of the Moon, a result confirmed by Hipparchus some 150 years later, by a different method.
Aristarchus went on to cleverly estimate the distance and size of the Sun: his conclusion was that the Sun was 20 times more distant than the Moon. He also found the Sun was 10 times bigger (in diameter; both were bad underestimates) than Earth, and he then proposed that the Sun, not Earth, was probably the center. However Hipparchus and Ptolemy objected. If the Earth went every year around such an ENORMOUS circle (we now know it is actually 20 times wider than what Aristarchus proposed!) wouldn't the stars appear shifted when viewed from the opposite side of that circle? Since they did not seem to shift ("exhibit parallax"), they concluded the Earth did not move, and their view prevailed for 1500 years. Their argument was sound--they just did not realize how enormously distant the stars were!
Now except for the motion of the Moon (which Aristarchus essentially explained) there exist two sets of motions in the sky. The planets and the Sun change their position among the stars on the scale of years, and all celestial objects, stars included, rise, set and move across the sky with a period of about 24 hours. Today we explain the first by orbits around the Sun and the second by the rotation of the Earth around its axis, as Copernicus proposed in his book (1543). Yet it took many years to sink in.
The motion of the planets around the Sun was easily reconciled, because the bible made no pronouncements about it and the old method by Hipparchus and Ptolemy, representing the orbits of planets by "circles around circles" in the sky, was cumbersome and inaccurate. But the rotation of the Earth met resistance, because of those verses in Psalms. Tycho de Brahe around 1600 proposed a compromise, that all planets rotated around the Sun, but the Sun rotated around Earth every 24 hours--and the stars every 23 hours 56 minutes, causing the Sun's position to migrate around them once a year.
Then came Galileo's telescope, showing that Venus could be a crescent like the Moon, meaning it orbited the Sun, and that Jupiter was the center of a disk of little moons, the way Copernicus visualized all planets, even Earth, to orbit the Sun. That convinced most people. Then came Newton and derived his law of gravitation, using the Moon (see section #20). His law suggested that if the Sun and other bodies rotated around the Earth, the gravity of the Earth was far too weak to hold them (plus other objections). That was the clincher: the laws of Newton's mechanics (which we still use) did not allow geocentrism. Since then of course much more evidence arrived--satellites, Earth observations from the Moon, etc.
I don't know if either you or your friend attended college, but most probably you did graduate from high school, where you may have first heard about heliocentrism. Your questions upset me: they suggest that your science teachers have done a rather superficial job, memorization rather than instruction. If I were king I would decree that no student would graduate from high school without the realization--backed by many, many examples, not by say-so dogma--that when scientists (finally) conclude this or that can be taken as proven, they do so on the weight of evidence, which has left them no other choice.
78. Can Earth's rotation reverse, like its magnetic polarity?Dear Dr. Stern,
I have seen the answers you have posted at
concerning polar reversal, but still need to clarify a few points for a book I'm writing. It looks at science from a philosophical perspective.
Over how long a period of time does a polar reversal on earth take place?
Will it have any effect on the behavior of electricity, electric appliances, computers, etc.? How about physiologically?
Will it have any effect on the rotation of the earth?
It is my understanding that rotation was established during the formation of the solar system as the planets cooled. Is this so?
Is there anything that could cause the earth's rotation to reverse?
This last question may seem especially strange, but there are prophecies currently circulating that this will actually take place. I will greatly appreciate your answers since I want to make sure that what I've said in my book concerning all of this is correct.
Let me start with rotation. A consequence of the Newton's laws of motion is the conservation law of a quantity called angular momentum. Given a collection of objects which only interact among themselves, the law says that the sum-total of their angular momenta cannot change.
This law explains why a spinning ice-skater greatly speeds up his or her rotation by just pulling in the arms. It explains Kepler's second law and the stability of the bicycle, and it is also the reason why the rotation of the Earth is not likely to reverse or change much. It was established not when the planets cooled but before that, a relic of the swirling of the cloud of gas and dust from which the solar system (and the Sun) formed.
In principle, the rotation of the Earth could reverse by the intervention of an outside force, e.g. collision with some moving object of comparable size. No such object is known (planetary motion is constrained), and any such collision is likely to break up the Earth. Otherwise, it would take a miracle to stop the rotation; about that, see "The Man Who Could Work Miracles" by H.G. Wells.
Concerning the length and effects of reversals--none has been observed, so we can only guess. Computer simulations and magnetic records of relatively recent "geomagnetic excursions" (big changes short of reversals) suggest they can be as fast as a number of centuries. Still, electromagnetic effects would be too small to detect. And physiologically, our body is unaware of magnetic fields. No on traveling to Australia notices that the magnetic field there is reversed!
79. Why is the Earth round?Dear Dr. Stern
Why is the Earth round (planets and the sun, too)?
ReplyIt's the gravity, of course.
Imagine Earth were liquid--consisting, say, only of water. Gravity would of course pull that water towards the center, and if any could flow closer to the center, it would do so.
Therefore, if such an Earth were not a sphere--if some points were higher than the average--their water would quickly flow down. Water would also flow into any valley deeper than the average and fill it up. The final shape MUST be a sphere. Only then does every point on the surface have the same distance from the center.
Gas planets like Jupiter, Saturn, Uranus and Neptune behave the same way, since gas flows like a fluid. The Sun is gas, too, so it must be spherical. But Earth? The Moon? Why should a planet composed of solid rock have the same shape as one composed of water?
Because, dear friend, once you descend a few hundred miles (or kilometers), rocks flow like a fluid, too. A rock 300 miles underground bears the weight of a 300-mile layer of rock, and under such pressure even solid material will gradually yield, more so because of the intense heat there. Hence the rocky Earth is close to a sphere.
Mountains may stick up 30000 feet, but not much more, otherwise the ground will slowly sink under their weight. Olympus Mons on Mars can reach 80000, but the weaker gravity of Mars makes it possible. Asteroids 100 miles across may still be potato-shaped (not enough gravity to give the outer layers enough weight), but by the time you reach 300 miles, round is the rule.
Round ... but not always completely round. Earth bulges a little at the equator, because rotation flings matter outwards, weakening gravity there by a fraction of 1%. Jupiter spins faster than Earth--just under 10 hours--and bulges much more: telescope pictures of Jupiter show it visibly fatter at the equator. And our Moon--why do you think it always presents the same face to the Earth? Yes, it is lightly longer in that direction, and the pull on the part sticking out towards Earth keeps it aligned that way (see " The Moon: The Distant View").
80. The De Laval NozzleDear Mr. Stern,
I am a middle school student writing a short report on the De Laval nozzle. I found your site "(26) Robert Goddard and His Rockets" "(26) Robert Goddard and His Rockets" useful. I wasn't able to access the page specifically on De Laval nozzles from the table of contents (http://www-istp.gsfc.nasa.gov/stargaze/Sgoddard.htm).
One of the things I need for the report is primary sources. I figured that you might have some first hand experience with the De Laval
My questions concerning the nozzle are:
Tough questions! I do not know how De Laval calculated the flow speed in the nozzle (De is part of his family name--I think his first names were Gustav Patrick). I suspect there exist formulas which give the steam velocity in a pipe, given the initial steam pressure, the initial diameter of the exit pipe and its final diameter. The calculation of the complete nozzle flow involves fluid dynamics, thermodynamics and calculus.
Before the nozzle was introduced by Goddard for rockets, it was used in steam turbines. The trouble there was that the steam jet was very fast, and to effectively gain energy from it, the vanes of the turbine wheel had to rotate at something like half its speed, in practice, the speed of sound or faster. That creates big stresses, and the rotation of the shaft must be geared down a lot to turn ordinary machinery, creating wear and energy loss.
What happens here is that while the nozzle is very efficient in converting heat to kinetic energy of the jet, converting that to useful mechanical energy is hard. In modern steam turbines heat is converted gradually to mechanical energy as the steam flows through the turbine wheel. In a rocket, of course, the jet is what we use.
I do not know the ratio of the dimensions of the convergent-divergent flows--you may estimate it from pictures, like the photo on my web site. And about the 2% efficiency--you guessed correctly.
Now a suggestion to you, if this subject interests you. Have you read "October Sky" by Homer Hickam? It was also made into a very good movie, but the story of the nozzle is in the book only (movies cannot hold all the details). It is the true story of the boyhood of a NASA engineer, now retired, growing up in poor coal-mining country in West Virginia. Homer was attending school when Sputnik, the first artificial satellite, was launched by the Russians--in October 1957. The date may be one reason for the title of the book, although it is also an anagram of its original title, "Rocket Boys." With friends and help he built a series of rockets, cooking their fuel according to various formulas, and they flew higher and higher--when they explode or fly erratically. However, they never reached any serious altitudes until he discovered the De-Laval nozzle. Read it, you will enjoy it.
Reply to the above, by the correspondent:Dear Dr. Stern,
Thank you so much for your prompt and useful answer. Ironically I am reading "October Sky" right now and this is the project that my teachers assigned to go along with it. I have already read the book and seen the movie before and found it quite enjoyable.
81. Why 23.5 degrees?Hello. I came across your site rather by accident and have been enjoying it tremendously. Actually, I was hunting for an explanation involving the Earth's orientation in space. I know this is basic but I can't seem to see how the earth's 23.5 degree tilt is related to the earth's orbital plane. Am I correct to imagine that if I define the plane of the earth's orbit around the sun as zero degrees then the polar axis of the earth is inclined to this plane at 23.5 degrees? If so, does this mean that if this angle were zero degrees instead of 23.5 degrees, the apparent motion of the sun (the way we draw the ecliptic) would always be perpendicular to the horizon at sunrise and sunset? And at the poles, the sun would appear to hug the horizon like a race car going around a track? Would the celestial equator and the ecliptic coincide at all points?
I'm going to be teaching an elementary astronomy course next year (high school) and have always managed to confuse myself on the relationship of the equator and 23.5 degree polar axis, the ecliptic, and the plane of revolution of the earth about the sun and the "horizon." Hope this "question" isn't a hopeless ramble.
ReplyYour understanding of the tilt of the Earth's rotation axis is correct, as is your understanding of how the Sun would appear moving across the sky, if that angle were not 23.5 degrees but zero. I encourage you to go through the first part of "Stargazers" where these matters are further discussed.
But you wanted to know WHY. That I do not know, but can hazard a guess. All planets (except for Pluto, the runt) seem to orbit pretty much in the same plane (the plane of the ecliptic is a convenient reference plane for the others), in the same direction (counter-clockwise when seen from north), and the planets usually spin in the same sense, as does the Sun. Astronomers see that as evidence that all these objects started as a cloud of gas and dust, swirling in that direction, and conservation of angular momentum ensured that whatever they produced would swirl in the same direction.
However, while the orbital planes are close to each other, the inclinations of the spin axes vary. The one of Mars is as much inclined as the Earth's, while that of Uranus is almost in the ecliptic. (More about that in the section "Tilt" of the we page http://www.phy6.org/Education/wotherms.htm ; the magnetic configuration drawn there is one I derived and published before the Voyager encounter). Perhaps that is because by far most of the angular momentum is in the orbital motion. The planes of planetary motions (e.g. the ecliptic) are thus very close to the average plane of the swirling of the original solar nebula.
On the other hand, when the planets themselves were assembled, from the collisions of smaller chunks, these were usually not head-on collisions, and transferred some of the angular momentum to the rotation of the combined mass, around its center of gravity. The orbital motion changed by only a little, but the impact was sufficient to shift the spin axis. Perhaps different processes interfered close to the Sun, because Venus hardly spins, while Mercury spins slowly in a funny locked mode. Note that while the tilt angle of the rotation axis varies only slowly (and not by much), the direction of the spin axis moves around a cone. That is discussed in section #7 on precession.
82. What is Gravitational Collapse?What is gravitational contraction (from the fundamentals) and thermonuclear reaction? How do these result into production of energy in stars?
Your article, (s-7) has impressed me a lot. I am doing a project on the production of energy in stars. This is not university work, not an assignment, just one of my personal hobbies!
(letter from Zambia)
ReplyAnd I thought my web site gave all required information! In brief, about gravitational contraction: if brick falls down from a high place, it releases energy. If a heavy building collapses, it releases MORE energy. If an entire star collapses to a smaller size, it releases A LOT of energy. THAT is gravitational collapse.
The Sun does not collapse, because nuclear fusion in its core creates heat, which keeps it puffed up (like a hot air balloon, the Sun is all gas). But it slowly uses up its fuel source, In 5 or 10 billion years it will run out of fuel, and will collapse to something smaller, ending probably as a small "white dwarf" which cools more gradually. Ultimately it will go dark.
The brick is attracted to the center of the Earth; going part of the distance (when it falls) releases part of its energy. Two protons (hydrogen nuclei) are also attracted, by the nuclear force, and if they could stick together, they too would release energy. That is nuclear fusion. On Earth hydrogen does not undergo fusion, because its protons are all electrically positive, and the repulsion of their electric charge prevents them from getting close enough for the nuclear force to prevail. In the core of the Sun, temperature is high enough to allow this to happen, and the weight of all overlying layers keeps the extremely hot hydrogen trapped.
83. Can Earth capture a Second Moon?Dear Dr. Stern,
If a large asteroid came close enough to Earth's magnetosphere, at the precise moment the Sun had a massive solar eruption aimed at Earth, would it be possible for the asteroid to get caught in Earth's gravitational force and become a secondary moon?
ReplyThe answer is no, for several reasons, and I hope you did not plan to write a science fiction story around this. The momentum of an asteroid is much too big, and it is concentrated in a small object. The momentum of the matter ejected in a solar eruption is probably smaller, and in any case, it is spread out over a huge volume. To act on the asteroid it would have to hit its body. Magnetic forces are again much too weak and asteroids we know about are probably not too magnetic.
However, it is theoretically possible that an asteroid could be injected into a trapped orbit by the gravity of the Moon (and also by the combination of gravities Earth-Sun). In section #35 of "From Stargazers to Starships" you can read about "gravity assist" (or "swingby") maneuvers of spacecraft encountering a moving planet like Jupiter, or our own Moon. If the two come from opposite directions (like ping-pong ball and paddle in the example there), the spacecraft gains energy; if it overtakes (like the water jet in a Pelton turbine, section #35a) is loses energy. It is possible that an asteroid overtaking the Moon loses energy and ends up trapped around the Earth. Something like that apparently happened to Comet Shoemaker Levy, whose fragment crashed onto Jupiter 8 years ago, in July 1994. The capture itself was never observed, the comet was only discovered afterwards.
Of course, an asteroid coming close enough to Earth to become captured would be a definite collision hazard. Not likely, but not impossible, either.
Further message:Thank you for your reply. However, I wonder why you would hope that I am not writing a science fiction book or screen play about the effects on humans, ... planet Earth, tides, real estate, animals, weather... after our planet does in fact acquire a secondary moon. The last bit of polishing to the story is to present a possible and/or feasible way in which we do acquire a second moon, which occurs at the onset of the story.
I have done research, (perhaps not enough) and have found no other novels or works of literature in which Earth gets or has two moons. Do you know of any? if so, please inform me.
ReplyMy comment about a science fiction story was meant as a joke, and I did not realize it scored a hit. A story is OK, but the science better be plausible, or at least hard to disprove. A solar eruption if too far out.
You wondered about effects on humans. If I wrote such a story, the main emotion would be sheer terror, since an asteroid approaching us so close could well hit Earth. Even if it went into an orbit around Earth, that orbit would most likely be very eccentric (like that of Shoemaker Levy) and chances would be high of it hitting later (again, like Shoemaker Levy), after the orbit had undergone perturbations. The second moon would be a clear and present danger and humanity's main concern would be probably getting rid of it.
Have you read "The Star" by H.G. Wells? Its premise is somewhat similar. See
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Author and Curator: Dr. David P. Stern
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Last updated 9-17-04