Galileo

Galileo was right about many things, like contradicting Aristotle on the motion of different size bodies in free fall. They all fall equally fast. He was totally wrong in others. In a dispute with Kepler he argued that tidal motion was due to the rotation of the earth, rather than the moon s dominion over the waters .  

Galileo formulated some mechanical principles that enabled Newton to establish the physical basis of Kepler s laws. By noticing that a ball which rolls on a plane that slopes downward is accelerated and one on a plane that slopes upward is retarted, he argued that motion along horizontal planes should be uniform and perpetual. This view represents an important advance 

Galileo s Acceleration Formula The acceleration (a) represents the velocity increase in unit time. The total increase over a period t is therefore given by at. Hence the final velocity is w = w -f- at, where u is the initial velocity. A graph of the acceleration is given by the straight line AB, on axes of velocity vs time. The distance traversed at uniform velocity u over a period t is given, by definition, as s = ut, which corresponds to the area of the shaded rectangle. The total area OABC represents the distance traversed in the accelerated motion, i.e. 

By equating uniform and circular motion it is natural for the earth to move in a circle, not an ellipse, but without a law of gravitation Galileo could never present a coherent discussion of centrifugal effects. Objects kept on flying away from the rotating earth as from a potter s wheel. 

It seems that Galileo distanced himself from Kepler to demonstrate his respect for traditional dogma, but, by denying the difference between heaven and earth, this concession was not enough to protect himself against the Inquisition. 

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A. Balkrishnan, W. Nicolet, S. Sandhu, and J. Dodson, Galileo Probe Thermal Protection Entry Heating Environments and Spallation Experiment Design,... 

Fig. 10. The 800 x 800 pixel scientific CCD specifically designed for the Galileo mission to Jupiter. The devices are shown in wafer form after initial...

The LHS of this expression contains a dimensionless group known as the Galileo number, defined as Ga = gdVv. ... 

The ratio Ap/p can be replaced by AT/T. Ar relates the influence of velocity and temperature of a jet when discharged into an environment of a different temperature. In some instances the Froude number, Galileo number, or Grashof number may replace the Archimedes number. 

Galilei, Galileo, 1638, Genuan in Ostwalds Klassiker, Discorsi. 11, 106-109. 

However, this simple model of a periodic motion occupied the central position in the theory of oscillations from its very beginning (Galileo) up to the time of Poincar6, when it was replaced by the new model—the limit cycle. 

In the old (Galileo) theory of oscillations the pattern of a periodic motion was assumed to be the closed trajectory around a center. As is well known a trajectory of this kind is determined by its initial conditions—a point (x0, y0) in the phase plane. If the initial conditions are changed, there will be another closed trajectory and so on. One has, thus, a continuous family of dosed trajectories, each of which can be realized by means of proper initial conditions. 

On Galileo Ar PiPs p)gd3 P2 Gravitational settling of particle in fluid... 

The pressure of the atmosphere can be measured with a barometer, an instrument invented in the seventeenth century by Evangelista Torricelli, a student of Galileo. Torricelli (whose name coincidentally means little tower in Italian) formed a little tower of liquid mercury. He sealed a long glass tube at one end, filled it with mercury, and inverted it into a beaker (Fig. 4.4). The column of mercury fell until the pressure that it exerted at its base matched the pressure exerted by the atmosphere. To interpret measurements with a barometer, we need to find how the height of the column of mercury depends on the atmospheric pressure. 

Abstract A brief review of major milestones of the historical race to large telescopes is given, from the Galileo s refractor to the 4-6m class telescopes. 

The invention of the telescope arguably constitutes an essential milestone in the history of science. Galileo s turning to the sky an instrument - a very modest one by today s standard- would not only change radically our understanding of the universe, it would eventually shatter the foundations of science, philosophy, and faith. 

The refracting telescope predated Galileo devices able "to bring far objects closer than they appear" were known well before his time, and their first origin... 

The idea to produce a converging objective from a reflecting, concave surface, instead of a refractive lens, was recognised by Galileo himself, and tried by Zucchi in 1616 (Fig. 4). Such arrangement, however, does not deliver acceptable image quality as a spherical surface used off-axis produces strong aberrations, and Zucchi s attempt was doomed for reasons he could not know. 

The structural adaptation of the skeleton is one of the most fascinating problems in the history of science. Galileo observed in 1638 that longer bones had to be thicker than shorter ones to have the same structural... 

Gatti, Hilary. Giordano Bruno s "Ash Wednesday supper" and Galileo s "Dialogue of the two major world systems". Bruniana Campanelliana 3 (1997) 283-300. 

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