Get a Straight Answer

    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!

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I was watching a NOVA program about Isaac Newton and I started thinking.

Is the elliptical orbit of the Earth around the Sun, as usually drawn, an "average" orbit?

    By this I mean, does the movement of the Moon around the Earth pull it faster, slower, inward and outward depending on the moon's position? In that case, if the actual orbit could be rendered, wouldn't it be (to a minute extent) a squiggly line?

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    The Earth is about 81 times heavier than the Moon, and their combined center of gravity is on the Earth-Moon line, 1/82 of the Moon-Earth distance from the center of Earth and 81/82 of that distance from the center of the Moon. Since the Earth-Moon distance is about 60 Earth radii, it follows that this point is always inside the solid Earth--about a quarter of the distance in.

    As the Moon orbits the Earth, the center of the Earth will move back and forth, from 3/4 radius sunwards of the orbit when the Moon is full, to 3/4 of the radius nightwards of the orbit when the Moon is new.

    The average distance of the Sun is about 23500 Earth radii, so if you draw the Earth's orbit on a sheet of paper, that squiggle will be (on the same scale) much thinner than the line of your drawing--as you wrote, "minute." But it should still exist.

    At the distance of the Moon it is still strong enough to keep the Moon from running away. That was what gave Newton the idea that gravity was "universal"--that the same force which drops apples from a tree to the ground also holds the Moon in its orbit.

    The Moon is about 60 times as far from the center of the Earth as we on the surface are. Newton figured everything was pulled towards the center of Earth--and also that the force of gravity got weaker like the intensity of light when you move away from a lamp. At 60 times the distance, light gets 60 times 60 = 3600 times weaker, so Newton wondered--would a force equal to 1/3600 the gravity we feel be enough to hold the Moon in its observed orbit? He did the calculation, and it came out just right. That was how gravity was discovered!

    At about 236 times the distance from the center--about 4 times the distance of the Moon--there is a point between Earth and Sun where a spacecraft can stay balanced between the pull of the Earth and the Sun. NASA puts spacecraft there, or near that point (putting it right in front of the Sun makes tracking difficult). I guess that is about the limit of space dominated by Earth's gravity. The pull extends much further, but other sources of gravity are more important there.

    Astronauts in orbit are "weightless", but that is because the force of gravity is compensated by the orbital motion. Gravity is still around there!

How does inertia affect a rolling ball?

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    Handling rolling objects takes more math than you have. Let me explain a little. Suppose you have a solid cylinder rolling down a slope (a cylinder is easier to handle than a ball): how fast will it accelerate?

    If energy is conserved, after it has descended 1 meter, it will have gained the same amount of energy as an object of the same weight falling from the height of one meter.

    If it were just SLIDING down smoothly, with no friction, that cylinder would indeed have the same speed v as an object falling from that height. But if it rolls, some of the energy also goes to the motion of rotation around the axis of the cylinder. As a result the forward motion is slower than v, it gets only part of the energy.

    Calculating the energy of a solid cylinder of radius (say) R, rotating around its axis with (say) 1 revolution per second, is not easy. Different parts move at different speeds--those on the edge are fastest, with some velocity we can call V, while the middle does not move at all. What we need is find some average velocity V', equal to some fraction of V, so we can use the formula for kinetic energy (1/2)m V'² (one half mass times velocity V' squared).

    Calculating that average takes a branch of mathematics called integral calculus, and involves a mechanical property known as "moment of inertia." It's the same with a rolling sphere--only more complicated, since now the averaging involves also the third dimension, parallel to the axis. With a cylinder you need not worry about the 3rd dimension--if you chop up the cylinder into narrow slices (like a stack of coins), V' will be the same in each slice.

All calculations of rolling inertia involve integral calculus and moments of inertia. You will have to wait!

    Grinding the 6" mirror as a youngster was an unforgettable experience and the thrill of seeing common sights, e.g. Jupiter's moons or Saturn's rings through a device I made was indescribable. I was also intrigued by the simplicity and cleverness of Foucault testing and being able to see the contour of the mirror blank as the work progressed as described in the book.

    I understand that a mirror gathers light. This explains why star images are brighter but does not explain why they are larger. Is this magnification solely a function of the eyepiece?

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    But there are more things to consider. Light is a propagating wave, and the magnification of a telescope is also limited by the wave nature of light, a limit which depends on the ratio between the wavelength and the size of the collecting mirror (or lens); increasing magnification beyond this limit gives you a bigger blur, but not any more detail. So a bigger mirror is better--up to about 12 inches. Bigger mirrors may hit another limit, due to the turbulence of the atmosphere: you overcome this by carefully choosing the location of the telescope (high altitude and cold air help, as does luck) and recently clever telescopes have been built with can actively bend their mirrors by slight amounts, to minimize atmospheric effects.

Actually, some radio telescopes may have by far the best resolution of all telescopes.

    Remember, the limit is set by the ratio between the dimensions of the telescope and the wavelength of the light, or whatever radiation is used. You may think, because radio wavelengths are so long, that ratio will not be too big: however, one can combine radio signals between different dishes, and then the dimensions of the array are what counts.

    In the southwestern USA there exist arrays tens of miles wide! You can even record the signals on tape and compare later, and that way combine radio-telescopes across the ocean. Right now the limit is set by the size of the Earth--and with dishes in space and on the Moon, who knows how far future radio-astronomers will go!

    And magnification is not the only problem. You want a wide field of view (avoid the equivalent of looking down a narrow tube!) and all colors should focus together. If you are really interested in all that, I recommend the recent book "Stargazer" by Fred Watson, as Australian astronomer who has traced the history of the telescope with many interesting stories.

    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.

    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?

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    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.

    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?

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    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

    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/

    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.

    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.

    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 transfering scientific concepts orally.

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    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.

    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.

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    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.

    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.

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    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.

    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?

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    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.