Calculations Using Kepler

# Calculations Using Kepler - is which is exactly the...

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Calculations Using Kepler's Third Law A convenient unit of measurement for periods is in Earth years, and a convenient unit of measurement for distances is the average separation of the Earth from the Sun, which is termed an astronomical unit and is abbreviated as AU. If these units are used in Kepler's 3rd Law, the denominators in the preceding equation are numerically equal to unity and it may be written in the simple form This equation may then be solved for the period P of the planet, given the length of the semimajor axis, or for the length of the semimajor axis, given the period of the planet, As an example of using Kepler's 3rd Law, let's calculate the "radius" of the orbit of Mars (that is, the length of the semimajor axis of the orbit) from the orbital period. The time for Mars to orbit the Sun is observed to be 1.88 Earth years. Thus, by Kepler's 3rd Law the length of the semimajor axis for the Martian orbit

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Unformatted text preview: is which is exactly the measured average distance of Mars from the Sun. As a second example, let us calculate the orbital period for Pluto, given that its observed average separation from the Sun is 39.44 astronomical units. From Kepler's 3rd Law which is indeed the observed orbital period for the planet Pluto. Here is a Kepler's Laws Calculator that allows you to make simple calculations for periods, separations, and masses for Keplers' laws as modified by Newton (see subsequent section) to include the effect of the center of mass. ( Caution: this applet is written under Java 1.1, which is only supported by the most recent browsers. It should work on Windows systems under Netscape 4.06 or the most recent version of Internet Explorer 4.0, but may not yet work on Mac or Unix systems or earlier Windows browsers.)...
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## This note was uploaded on 12/04/2011 for the course ANT ANT2000 taught by Professor Monicaoyola during the Fall '10 term at Broward College.

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Calculations Using Kepler - is which is exactly the...

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