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Basic Physics.docx

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Department
Physics
Course
PCS 181
Professor
Margaret Buckby
Semester
Summer

Description
Basic Physics In the sixteenth and seventeenth centuries, scientists discovered the laws of the motion of material objects. These laws help scientists to explain and predict the motions of celestial bodies. Kepler's Three Laws of Planetary Motion Johannes Kepler formulated three laws to approximate the behavior of planets in their orbits. To understand Kepler's First Law of Planetary Motion ( Law of Ellipses), one must first be familiar with the properties and components of anellipse. An ellipse is the path of a point that moves so that the sum of its distances from two fixed points (the foci) is constant. An ellipse has two axes of symmetry. The longer one is called the major axis, and the shorter one is called the minor axis. The two axes intersect at the center of the ellipse. Kepler's First Law states that the orbit of a planet is an ellipse with the Sun at one focus (see Figure 1 ). The size of an ellipse is given by the length of the semi-major axis (half of the major axis), which is also equal to the average distance of the planet to the Sun as it travels about the Sun in its orbit. The shape of an ellipse is measured by theeccentricity, or a measure of how much an ellipse deviates from the shape of a circle (e = CF/a = (1 – b /a )2 1/). Therefore, a circle would have an eccentricity of 0, while a line would have an eccentricity of 1. The closest approach of a planet to the Sun is known as the perihelion, a distance equal to a(1 – e). The greatest distance between a planet and the Sun is the aphelion equal to a(1 + e) (see Figure 2 ). Figure 1 An ellipse. The shape of the ellipse is determined by the ratio of the distance between the two foci (F) to the length of the major axis (the eccentricity). If the foci are closer together, the ellipse will have a smaller eccentricity and will more closely resemble a circle. If the foci are farther apart, they will have a greater eccentricity and will more closely resemble a straight line. Figure 2 The elliptical orbit of a planet around the Sun (ellipticity is greatly exaggerated; most orbits are nearly circular). Kepler's Second Law of Planetary Motion ( Law of Areas) states that a line connecting the planet with the Sun sweeps over an area at a constant rate. In other words, if the time for an object to move from position A to position B is the same as the time to move from C to D, the areas swept out are also equal. This law is actually an alternative statement of the physical principle of the conservation of angular momentum: In the absence of an outside force, angular momentum = mass × orbital radius × the tangential velocity (that is, the velocity perpendicular to the radius) does not change. In consequence, when a planet moves closer to the Sun, its orbital velocity must increase, and vice versa. Kepler's Third Law of Planetary Motion ( Harmonic Law) details an explicit mathematical relationship between a planet's orbital period and the size of its orbit, a correlation noted by Copernicus. Specifically, the square of a planet's period (P) of revolution about the Sun is proportional to the cube of its average distance (a)from the Sun. For 2 3 example, P = constant a . If P is expressed in years and the semi-major axis a in astronomical units, the constant of proportionality is 1 yr /AU , 3 and the proportionality becomes the equation P = a .2 3 Although Kepler's Laws were deduced explicitly from study of planets, their description of orbital properties also applies to satellites moving about planets and to situations in which two stars, or even two galaxies, move about each other. The Third Law, in the form as proposed by Kepler, however, applies only to planets whose masses are negligible in comparison to that of the Sun. Newton's Three Laws of Motion and a Law of Gravitation Newton's First Law of Motion ( Law of Inertia) states that an object continues moving at the same rate unless acted upon by an outside (external) force. If no external force interferes, a moving object keeps moving at a constant velocity(that is, both speed and direction remain the same). Similarly, an object at rest stays at rest. This tendency of matter to remain at rest if at rest, or, if moving, to keep moving in the same direction at the same speed is called inertia. Mass is what gives an object inertia. Mass is a measure of the quantity of material in an object, not its weight, which is a measure of the gravitational force exerted on an object. Newton's First Law is a statement of the modern principle of Conservation of Momentum, where momentum (p) is an object's mass (m) times its velocity (v). Momentum stays constant if the outside force is zero. As in any mathematical expression of a physical law, each term has a precise definition and meaning. Both velocity and momentum are vector quantities; that is, each has both a size and a direction. Thus, p = mv involves both the magnitudes of the quantitie
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