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1361. Kepler and his Laws--lesson plan #18
This is an overview of the story of Tycho Brahe and Johannes Kepler, and of Kepler's laws. Each of Kepler's laws will be studied separately in more detail in later lessons. ... This lesson plan supplements: "Kepler and his Laws," section #10: on disk Skeplaws.htm , on the web . ... The student will confirm Kepler's 3rd law by comparing orbital periods and mean distances for all major planets. ... That is Kepler's first law. ... Yes, Kepler's laws apply to artificial satellites as well as planets. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILkeplaws.htm -- 14.2 Кб -- 22.12.2007
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1362. Kepler's 3rd Law--Lesson Plan #31
Lesson Plan #31 http://www.phy6.org/stargaze/Lkepl3rd.htm . ... It is shown that at least for circular orbits, this calculation leads to Kepler's 3rd law. The velocity required for a low Earth orbit is derived, and a practical formula is obtained for the orbital period in a circular Earth orbit of any radius. ... To prove Kepler's 3rd law for circular orbits . ... Starting the lesson: . ... From Kepler's 3rd law, the orbital period T around Earth in a circular orbit at distance R is . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILkepl3rd.htm -- 15.9 Кб -- 22.12.2007
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1363. Kepler's Second Law--Lesson Plan #21
... This is made evident in two ways: by calculating the ratio of greatest and smallest orbital velocities (in the lesson plan, not given in "Stargazers"), and by invoking the concept of energy. ... Kepler's Second Law Skepl2nd.htm . ... 12a. "More about Kepler's Second Law Skepl2A.htm . ... Get an intuitive understanding for the way orbital velocities vary along each orbit, according to Kepler's second law. Get a first exposure to the concepts of "potential energy" and "kinetic energy." ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILkepl2nd.htm -- 19.1 Кб -- 22.12.2007
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1364. Kepler's First Law--Lesson Plan #20
Here the ellipse is studied in polar coordinates (r,f) , requiring minimal familiarity with the function cos f in the range 0 e . It is also noted that planets actually orbit the center of gravity of the solar system, and that distant planets may be detected by motions of their central star around the centers of gravity of their planetary systems. ... This lesson plan supplements: "Ellipses Kepler's 1st Law," section #11b: on disk Skepl1sto.htm , on the web . ... A circle is also an ellipse. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILkepl1st.htm -- 12.5 Кб -- 22.12.2007
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1365. How Distant is the Moon?--lesson plan #14
This section describes the calculation by which Aristarchus used the duration of a total lunar eclipse to deduce the distance of the Moon. ... This lesson plan supplements: "How Distant is the Moon--1", section #8c: on disk Shipprc2.htm , on the web . ... The shadow of the Earth at the Moon's distance is narrower than the Earth, because the Sun is seen not as a point but as a disk 0.5 degrees wide. ... An eclipse of the Moon is the passage of the Moon through the shadow of the Earth. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILhipprc2.htm -- 9.8 Кб -- 22.12.2007
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1366. Newton's Theory of Universal Gravitation--Lesson Plan #30
Lesson Plan #30 http://www.phy6.org/stargaze/Lgravity.htm . This lesson re-derives Newton's result, that if the force of gravity decreases like the square of the distance from the center of attraction, the same force that causes objects on the Earth"s surface to fall can also be responsible for the motion of the Moon. ... This lesson plan supplements: "Newton's Theory of Universal Gravitation," section #20 http://www.phy6.org/stargaze/Sgravity.htm . ... Starting the lesson: . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILgravity.htm -- 18.6 Кб -- 22.12.2007
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1367. Lesson 34--Frames of Reference: The Centrifugal Force
... Uniformly moving frames of reference experience no new forces. ... If we want to express the equations of motion in their own frame of reference , we must always add "inertial forces" to represent the effects of their acceleration. ... The centrifugal force is needed to describe the same motion, using coordinates, velocities and accelerations of a rotating frame of reference. ... Terms: inertial force, accelerated frame of reference, rotating frame of reference, centrifugal force, bulge of the Earth...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILframes2.htm -- 21.0 Кб -- 22.12.2007
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1368. Lesson 23--Frames of Reference: The Basics
... Velocity and acceleration always need to be measured relative to some fixed benchmarks, which define a "frame of reference. ... This section highlights the simple concept, that two frames of reference moving relative to each other with a constant velocity are completely equivalent, and the same laws of mechanics hold in both. ... Section 22a describes how the motion of the Earth modifies the apparent positions of stars and the arrival direction of the solar wind. ... This lesson plan supplements: . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILframes1.htm -- 19.2 Кб -- 22.12.2007
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1369. Graphs and Ellipses--Lesson Plan #19
An introduction (or refresher) of the concept of graphs in cartesian coordinates, starting with graphs of a straight line and a simple parabola. The implicit relationship x 2 +y 2 = R 2 for a circle is next given, and from that the cartesian equation of an ellipse is developed. ... This lesson plan supplements: "Graphs and Ellipses," section #11a: on disk Sellipse.htm , on the web . ... Learn or re-acquire the use of graphs in cartesian coordinates. ... Focus and major axis of an ellipse. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILellipse.htm -- 16.5 Кб -- 22.12.2007
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1370. The Path of the Sun, the Ecliptic --lesson plan #3
... This lesson plan supplements: "The Path of the Sun, the Ecliptic," section #2: on disk Secliptc.htm , on the web . ... Terms: Zodiac, ecliptic (the line across the celestial sphere),the plane of the ecliptic (flat surface), zodiac, solar eclipse, lunar eclipse [umbra, penumbra]. ... If the Sun and the Earth are in the plane of the ecliptic, the Moon, which is between them, also must be in the plane. (b) In an eclipse of the Moon , the Earth comes between the Moon and the Sun. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILecliptc.htm -- 11.1 Кб -- 22.12.2007
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1371. Coordinates--lesson plan #9
Introduction to ways of labeling points on a plane by (x, y), their cartesian coordinates. Optional--extending this to (x,y,z) coordinates in 3-dimensional space, to (r,?) plane polar coordinates and to 3-dimensional polar coordinates (r,?, ... This lesson plan supplements: "Coordinates," section #5b: on disk Scelcoor.htm , on the web . ... Polar coordinates (r, ?) on the plane (2-dimensions) . ... Can systems of coordinates, other than the cartesian one, be used to label points on a plane? ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/ILcelcoor.htm -- 15.6 Кб -- 22.12.2007
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1372. Clothoid
THE CLOTHOID . ... From this poetic reference the Italian mathematician Ernesto Ces ro, at the beginning of the 20th century, gave the name "Clothoid" to a curve with a double spiral shape, which reminded him of the thread wound around the spindle and the distaff.. ... Actually, if a roller coaster loops around a circle, the entrance to the loop has considerable curvature, imposing a strong centrifugal force on the passengers. ... This remarkable curve has a variable radius along its length. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sclothoid.htm -- 4.8 Кб -- 22.12.2007
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1373. "Get a Straight Answer"
... About asteroids hitting Earth. ... Asymmetry of the Moon's orbit. Measuring distance from the Sun. ... Where do gravity of Earth and Sun balance? ... 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. ... 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). ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/StarFAQ14.htm -- 66.4 Кб -- 22.12.2007
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1374. "Get a Straight Answer"
... The ones included below are either of the sort that keeps coming up again and again, or else the answers make a special point, often going into details which might interest many users. ... About asteroids hitting Earth. ... Asymmetry of the Moon's orbit. Measuring distance from the Sun. ... How Tall Can People Get? ... When a photon from the sun hits the surface of the earth, it may be reflected (in which case its energy goes into making a new photon of the same wavelength) or it may be absorbed. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/StarFAQ13.htm -- 59.4 Кб -- 22.12.2007
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1375. Frying Pan Electrophorus
... 18e. Frying Pan . Electrophorus expt. ... You can easily demonstrate the second approach using mostly equipment found in the kitchen--a flat cutting board or cookie sheet, aluminum foil, saran wrap, adhesive tape, a plastic bag and a flat-bottomed frying pan. ... At this point, with the pan on top of the saran, touching the "switch" foil (but nowhere in contact with the bottom foil, which would short-circuit the cell!), the frying pan is charged by the cell to 1.5 volts. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Selectrph.htm -- 12.7 Кб -- 22.12.2007
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1376. "Get a Straight Answer"
... The ones included below are either of the sort that keeps coming up again and again, or else the answers make a special point, often going into details which might interest many users. ... About asteroids hitting Earth. ... Asymmetry of the Moon's orbit. Measuring distance from the Sun. ... If light speed sets the limit, why fly into space? ... By the way, space launches from near the equator are preferable, because spacecraft then get some (small) help from the rotation of the Earth. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/IstarFAQ8.htm -- 40.2 Кб -- 22.12.2007
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1377. "Get a Straight Answer"
... Who owns the Moon? ... Where do gravity of Earth and Sun balance? ... Do you know at which distance (miles)) and object in space gets attracted or caught by the Earth gravity, and brought down to Earth. ... In particular, the Moon must also be attracted to the Earth--otherwise it would wander off into space. ... To put it more straight forward: IF a shuttle is between the Earth and the sun, at that distance the Earth's gravity acting on it and the sun's gravity acting on it are equal to each other. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/IstarFAQ5.htm -- 51.8 Кб -- 22.12.2007
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1378. "Get a Straight Answer"
... Space Debris . ... However.... you know that the Moon always presents Earth with the same face. ... To answer your second question, let me paste from the glossary of "Exploration of the Earth's Magnetosphere": Sun-synchronous orbit --a near-Earth orbit resembling that of a polar satellite, but inclined to it by a small angle. ... 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? ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/IstarFAQ3.htm -- 84.9 Кб -- 22.12.2007
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1379. "Get a Straight Answer"
... Who owns the Moon? ... Can Earth's rotation reverse, like its magnetic polarity? ... There do indeed exist two "holes" in the Earth's magnetic field, around the MAGNETIC poles, whose magnetic field lines go very far from Earth and afford an easy connection to the solar wind and to interplanetary plasma phenomena. ... Ignoring that step (or starting from a point in earth's solar orbit which is NOT on the earth's surface), I would think that just about any deceleration would allow you to reach the Sun...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/IstarFAQ1.htm -- 47.0 Кб -- 22.12.2007
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1380. "Get a Straight Answer"
... About asteroids hitting Earth. ... Measuring distance from the Sun. ... Why does the Earth rotate? ... Energy from the Earth's Rotation? ... Any time a rotating cloud of matter gets reduced in size--as it did when Earth originated--R gets smaller. ... The picture given in "Seasons of the Year," of the Earth tilted by 23.5 degrees while orbiting the Sun, still describes the situation, except that over the thousands of years, it is slowly rotated in space, relative to the rest of the universe. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/StarFAQ11.htm -- 76.5 Кб -- 22.12.2007
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