# Fisica

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CHAPTER 3

GRAVITATION

CONTENT
3.1 KEPLER’S LAW
3.2 UNIVERSAL GRAVITATION LAW
3.3 GRAVITATION CONSTANT
3.4 GRAVITATION ATTRACTION FORCE OF OBJECTS NEAR THE EARTH’S SURFACE
3.5 GRAVITATION ATTRACTION FORCE EFFECT TO MAINTAIN AN ARTIFICIAL SATELLITE IN ORBIT

The curiosity and need of humans to know about the phenomena’s that surround them have always been present and the comprehensionof the behavior of objects that are part of the universe near mankind maintained Tycho Brahe, observing and studying the paths of these objects, that Johannes Kepler explained empirically the paths and time of planets around the Sun.
Isaac Newton announced a law of attraction between planets and satellites as a property of the mass and he explained why the Earth and the Moon, all solar system andgalaxies are maintained together.
We will consider Newton’s Universal Law of Gravitation (to understand the motion of the planets, Newton use as the starting point the Moon’s motion), that describes this fundamental force, and analyze the motion of planets in terms of certain fundamental laws called Kelpler’s Law.
3.1 KEPLER’S LAW
Objective: to know the laws of motion of planets around theSun
Our ancestors considered the Earth as the center of the Universe, and that remained static and the stars were in a crystal sphere, and spin around the Earth. The planets were placed in spheres that described a more complicated motion this proposal is known as the Geocentric Theory of the Universe and Aristotle was responsible for this proposal and was improved by Ptolomeo. In the XV century,Copernicus discovered that the motion of the planets was described in a simple way, it was considered that they spin around the Sun in circular orbits, this proposal is known as the Heliocentric Universal Theory. These two theories were debated in the XVI century from a philosophical view, where man was considered the center of the creation and the Earth as the center of the Universe.
The Danishastronomer Tycho Brehe, dedicated to observe the motion of the planets and stars, registering their paths and exact position during more than twenty years. He improved the existing astronomical equipment, having a great precision in registering his notes, which are still used in our days. Brahe gave his notes to the German Kepler.
Kepler studied and analyzed this notes of the planets, trying toadjust in perfect circular orbits, which was impossible. After living this idea the planets move in circular orbits he found that they described an elliptical orbits. From the previous we can state what is known as the First Kepler’s Law.
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“ All planets move in elliptical orbits, with the Sun as one of its focus”

This is, all planets movedescribing elliptical orbits with the common focus, the Sun. besides that the planet’s orbits were elliptical, Kepler found out that nearer to the Sun, a planet would increase its speed and farther from the Sun its speed would decrease. This indicated Kepler that the motion wasn’t uniform. Because motion varied according to the Sun’s distance. After analyzing these observations made by Brahe, Keplerestablished his Second Law:
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“When a planet moves in its orbit, the line that joins the planet and the Sun covers equal areas on the same time”.

Kepler searches some relation between the sizes of the orbits of the planets and their periods. From Brahe’s data, he found he found what is known as Kepler’s Third Law:-------------------------------------------------
“The square of the periods (T) of the planets is directly proportional to the cubes of its average distance (r) from the Sun”
T2=Kr3
With K= T2/r3
What Kepler found was the ratio T2/r3 was always the same for all the planets.
Therefore that constant K was the same value for all planets which is 300.46x10-21 s2/m3. An easy way to calculate is to use the known data of...