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1721. Navigation
... And a star to steer her by . ... Longitude . ... One had to use the Sun and the stars. Imagine yourself standing at night at point P on Earth and observing the pole star (or better, the position of the north celestial pole, near that star), at an elevation angle h above the horizon. ... As with the pole star, rather than measuring the angle a from the zenith--which is not marked in the sky!--it is simpler to measure the angle ( 90?-a ) from the horizon, which at sea is usually sharply defined. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Snavigat.htm -- 19.9 Кб -- 22.12.2007
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1722. Comparing Masses Without Use of Gravity
... Mass . 17a. Measuring Mass . ... A medium-size (1.25 inch wide) binder clip, as is used in offices to hold papers together--the type made of flat blue steel, with two wire handles. ... The theory predicts that the oscillation period should be proportional to the square root of the oscillating mass, including the mass of the clip. Note that gravity plays no part here: the oscillation period would be the same on the Moon or in zero-g. Denoting square root by SQRT, we have . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Smasscom.htm -- 8.9 Кб -- 22.12.2007
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1723. The HARP Project and the Martlet
... The SHARP cannon . ... HARP Gun (Photo by Peter . ... HARP, for High Altitude Research Project, was a study of the upper atmosphere by instruments shot from a cannon. ... The cannon which propelled the Martlet to the high atmosphere was the creation of Gerald Bull, a Canadian engineer who specialized in the design of cannon. ... Like Gerald Bull, the German designers started with a big cannon designed for a battleship, but then they inserted in it a narrower barrel, of caliber 210 mm or about 9". ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Smartlet.htm -- 8.4 Кб -- 22.12.2007
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1724. Latitude and Longitude
... Longitude . ... All points on the same line of longitude experienced noon (and any other hour) at the same time and were therefore said to be on the same "meridian line", which became "meridian" for short . ... As the Earth rotates around its axis, at any moment one line of longitude--" the noon meridian "--faces the Sun, and at that moment, it will be noon everywhere on it. ... On Earth , the equator is divided into 360 degrees, with the zero meridian passing Greenwich and with the longitude angle ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Slatlong.htm -- 19.2 Кб -- 22.12.2007
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1725. The Lagrangian Points L4 and L5--alternative derivation
... 34a. L1 Lagrangian pt. #34b. L2 pt. ... The following derivation of the L4 and L5 points follows "When Trojans and Greeks Collide" by I. Vorobyov, "Quantum," p. 16-19, Sept-Oct. ... Suppose we have 3 point-like masses (m 1 , m 2 , m 3 ) orbiting under their mutual attraction. The three form a triangle ABC with sides masses (R 1 , R 2 , R 3 ) where R 1 is the side across from m 1 , R 2 is across from m 2 and R 3 is across from m 3 (Figure 1). ... If we denoted the total mass by M . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Slagrng3.htm -- 15.2 Кб -- 22.12.2007
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1726. The Lagrangian Points L4 and L5
... As noted, two points exist on the Sun-Earth line, the Lagrangian points L1 and L2, where (if only the gravity of these two bodies is considered) a spacecraft will maintain its position relative to the Sun and Earth. ... sin ? ... cos ? ... Even the general "restricted three body problem" where one of the bodies is very small--e.g. Earth, Moon and spacecraft--is insoluble, although specific solutions exist, like the ones in which the spacecraft is positioned at one of the Lagrangian points. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Slagrng2.htm -- 22.6 Кб -- 22.12.2007
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1727. The Lagrangian Point L1
... By using the tools of sections (20) and (21), the mathematics of approximate solutions developed in (M-5), and assuming all orbits are circles, it is a relatively straightforward job to calculate the distance to the Lagrangian L1 point (or to L2). ... Let the gravitational constant be denoted by G , the mass of the Sun by M , that of Earth by m , the Earth's distance from the Sun by r and its velocity in its orbit by v . ... GMm / r 2 = mv 2 / r . and multiplying both sides by r / m . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Slagrang.htm -- 12.4 Кб -- 22.12.2007
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1728. Kepler and His Laws
... 9a. Earth orbits Sun? . ... Kepler's Laws . ... and First Law . ... Tycho was a Danish nobleman interested in astronomy. ... He even measured and took into account the very slight shift of star positions near the horizon, due to the bending of light in the Earth's atmosphere, similar to its bending in glass or water. ... Not only were Kepler's laws confirmed and explained by later scientists, but they apply to any orbital system of two bodies--even artificial satellites in orbit around the Earth. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Skeplaws.htm -- 19.1 Кб -- 22.12.2007
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1729. Kepler's Second Law
... Kepler's Laws . ... Second Law . ... Energy . ... In many ways, a planet around the Sun , or of a scientific satellite around Earth, moves like that, too , although the equations are different. ... Kepler's law states: . ... For a satellite of mass m orbiting Earth (or for a planet around the Sun) at a distance of r meters, a similar formula exists: . ... Kepler's second law tells us everything about this variation and should allow us to obtain a formula that gives the way f varies with time t . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Skepl2nd.htm -- 15.2 Кб -- 22.12.2007
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1730. Kepler's First Law of Planetary Motion
... 9a. Earth orbits Sun? . ... Kepler's Laws . ... and First Law . ... Such " polar coordinates " ( drawing on the left, below) are the ones best suited for describing planetary motion. ... All planetary orbits resemble ellipses, each with its own value of e or eccentricity : the smaller e is, the closer the shape to a circle. ... We can now state Kepler's law more precisely as "the square of the orbital period T is proportional to the cube of the semi-major axis a of its orbit around the Sun." ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Skepl1st.htm -- 18.4 Кб -- 22.12.2007
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1731. The Jewish Calender
... The Calendar . 6a. Jewish Calendar . ... 8c. Moon dist. (1) . ... In the Jewish calendar, today is the 6th day of the month of Adar --and in this year, that is the "first Adar" or "Adar Aleph", because this is a leap year. ... Of course, you realize that the Jewish calendar follows the Moon: "Rosh Chodesh," the beginning of the month, is always supposed to fall on the new Moon --the time when the Moon's position in the sky passes that of the Sun. ... When does the Jewish year begin? ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sjewcale.htm -- 15.7 Кб -- 22.12.2007
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1732. Ion Rockets
... Orbits in Space . ... The ion rocket is another means of providing thrust, more gradually but also more efficiently than a conventional rocket. ... As in the nuclear rocket, the energy which propels the xenon jet comes from a different source; here it is electrical energy from solar cells. ... The XIPS ("zips") ion engine developed by the Hughes corporation was tested in the laboratory and then aboard a Russian spacecraft, launched 6 October 1997; it is the one shown on top of this page. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sionrock.htm -- 8.0 Кб -- 22.12.2007
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1733. Distance to the Horizon
... The Round Earth . 8a. The Horizon . ... 9a. Earth orbits Sun? . ... What is the distance D to the horizon? ... Your line of sight to the horizon is a tangent to the Earth--a line which touches the sphere of the Earth at just one point, marked B in the drawing here. ... From the top of Mauna Kea on Hawaii, an extinct volcano about 4 km high (also the site of important astronomical observatories), the horizon should be about twice as distant, 226 km. ... One more: Distance to the horizon on Mars . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Shorizon.htm -- 9.0 Кб -- 22.12.2007
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1734. Estimating the Moon's Distance
... The Round Earth . ... Aristarchus around 270 BC derived the Moon's distance from the duration of a lunar eclipse (Hipparchus later found an independent method). ... Let R be the radius of that circle and T the time it takes the Moon to go around once, about one month. ... Viewed from Earth, a "new Moon" (occuring between the time a thin crescent is last seen before sunrise and the time one is seen shortly after sunset) happens when the Moon in its apparent motion around the sky overtakes the Sun. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Shipprc2.htm -- 10.6 Кб -- 22.12.2007
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1735. How distant is the Moon?
... Eclipse over Romania . ... The Round Earth . ... 9a. Earth orbits Sun? . ... That eclipse was total at the Hellespont--the Dardanelles, part of the narrow strait that separates the European and Asian parts of Turkey--but only 4 / 5 of the Sun were covered in Alexandria of Egypt, further to the south. ... Hipparchus concentrated on point E at the edge of the Moon (drawing), which during totality, when viewed from the Hellespont (point B) just overlapped point D on the edge of the Sun. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Shipparc.htm -- 17.6 Кб -- 22.12.2007
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1736. Newton's theory of "Universal Gravitation"
... Newton's 2nd Law . ... The Moon orbits around the Earth. ... If a mass m on Earth is pulled by a force mg , and if Newton's "inverse square law" holds, then the pull on the same mass at the Moon's distance would be 60 2 = 3600 times weaker and would equal . ... He proposed that a "universal" force of gravitation F existed between any two masses m and M , directed from each to the other, proportional to each of them and inversely proportional to the square of their separation distance r . ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sgravity.htm -- 19.0 Кб -- 22.12.2007
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1737. Robert Goddard and His Rockets
... Rocket History . ... Another was a young American, Robert Hutchins Goddard (1882-1945). ... Plurality" was Goddard's term for multiple rocket stages, and the patents also covered expansion nozzles and liquid fuel, although Goddard did not experiment with them until 1915 and 1922, respectively . ... A rocket is essentially a heat engine, a device for converting the energy of heat (obtained from the chemical energy of the fuel) into mechanical energy--here the kinetic energy mv 2 / 2 of its exhaust...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sgoddard.htm -- 19.9 Кб -- 22.12.2007
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1738. Frames of Reference: The Centrifugal force
... 22.Reference Frames . ... Inertial Forces . 23a. The Centrifugal Force . ... When calculating the motions of the oceans and the atmosphere, it is much easier to use reference points on the rotating Earth and add a centrifugal force to all equations. ... The rest arises because the Earth is not a perfect sphere: the centrifugal force of its rotation causes its equator to bulge out , making the surface there more distant from the Earth s center and thus weakening the gravitational pull. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sframes3.htm -- 12.9 Кб -- 22.12.2007
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1739. Accelerated Frames of Reference
... 22.Reference Frames . ... Inertial Forces . 23a. The Centrifugal Force . ... The other case of a moving frame of reference studied here is an accelerated frame of reference. ... The roller-coaster car, however, is undergoing various accelerations, and as a rule, when we try to apply the laws of motion inside an accelerated frame of reference, extra forces enter the picture, known as inertial forces. ... That is the inertial force acting in the frame of the accelerating airplane. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sframes2.htm -- 13.3 Кб -- 22.12.2007
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1740. Airplane Flight: How High? How Fast?
... Lesson plan (flight) . ... Optional unit on the principles of airplane flight) . ... An airplane stays aloft because of the flow of air above and below its wing. ... Here L is the lift in (say) Newtons, d the air density (about 1.3 kg/meter 3 at sea level) and v may be in meter/sec, mph or km per hour--whatever one prefers. ... Any closer to the speed of sound (1200 km/h = 746 mph, varies with temperature) and the air flow above the wing creates shock fronts which increase drag and reduce lift. ...
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Ссылки http://www.cosmos.ru/mirrors/stern/stargaze/Sflight2.htm -- 16.5 Кб -- 22.12.2007
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