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Physics

PCS 181

Margaret Buckby

Summer

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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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