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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)

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

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

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

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

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

Thank you for any answer you might offer!

Reply

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

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

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

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

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

219. Gravity at the Earth's center

No idea if you're still updating your site, but noticed a possible mistake. at http://www.phy6.org/stargaze/StarFAQ11.htm#q180. You were asked there

What is the gravitational field at the mass centroid of the earth? and replied:

The answer is zero. No gravity at the center!

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

Reply

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

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

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

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

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

Reply

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

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

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

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

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

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

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

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

You have a very clear way of explaining complex issues.

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

Reply

Interesting question, interesting answers.

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

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

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

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

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

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

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

226. Does precession affect the time of summer?

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

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

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

Reply

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

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

Follow-up question about other variations of Earth orbit

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

Reply

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

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

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

227. Newton's law or Bernoulli's?

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

Reply

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

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

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

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

228 Does the universe have an axis?

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

Reply

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

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

229. Frictional electricity

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

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

Reply

Being a physicist does not make one an expert on everything! Certainly, not on the matters you ask about. I do know however that the effect is called "triboelectricity" and you can use that term to search for appropriate items on "Google," as I have done. Here are three relevant locations:

http://en.wikipedia.org/wiki/Triboelectricity
http://www.regentsprep.org/Regents/physics/phys03/atribo/default.htm

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

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

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

230. Syllabus for catching up on physics

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

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

Reply

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

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

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

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

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

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

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

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

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

Good luck in your kind efforts!

231. Parabolic reflector

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

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

Reply

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

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

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

232. At what distance does Earth start looking spherical?

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

Reply

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

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

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

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

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

233. Is the Sun on fire?

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

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

Reply

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

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

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

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

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

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

234. Confusion about the "Big Bang"

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

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

Reply

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

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

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

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

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

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

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

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

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

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

I hope that clarifies matters to you!

235. How did Tycho calibrate his instruments?

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

Reply

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

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

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

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Author and Curator: Dr. David P. Stern
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Last updated 10 May 2005 Edited 1 November 2016

Get a Straight Answer

Please note!

Items covered:

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

Reply

219. Gravity at the Earth's center

Reply

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

Reply

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

Reply

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

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223. What determines the quality of a telescope?

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224. Why design maps around curved lines?

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

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226. Does precession affect the time of summer?

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Follow-up question about other variations of Earth orbit

Reply

227. Newton's law or Bernoulli's?

Reply

228 Does the universe have an axis?

Reply

229. Frictional electricity

Reply

230. Syllabus for catching up on physics

Reply

231. Parabolic reflector

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232. At what distance does Earth start looking spherical?

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233. Is the Sun on fire?

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234. Confusion about the "Big Bang"

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235. How did Tycho calibrate his instruments?

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