document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078498>Question 1078498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this : \r<BR>\n" );
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document.write( "Kepler’s Third Law of planetary motion states that the square of the period T, in years, of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of its average distance d, in millions of km, from the sun.<BR>\n" );
document.write( "(a) Express Kepler’s Third Law as an equation.<BR>\n" );
document.write( "(b) Find the constant of proportionality. Note that the average distance the Earth is from the<BR>\n" );
document.write( "sun is 150 million kilometers, according to Wikipedia. You will also need some of your Earth<BR>\n" );
document.write( "knowledge.<BR>\n" );
document.write( "(c) Neptune is approximately 30 times as far away from the sun as Earth. Does your answer<BR>\n" );
document.write( "correspond with the value from other sources?<BR>\n" );
document.write( "(d) Suppose in another galaxy, planet X is a certain average distance away from its Sun. Another<BR>\n" );
document.write( "planet, Y , is twice the average distance away from the sun as X. In percentage terms, what<BR>\n" );
document.write( "is the period of planet Y in relation to planet X? (You may assume that Kepler’s law applies<BR>\n" );
document.write( "not only in our own galaxy.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692946 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)  T^2 = k * d^3, where k is the constant of proportionality<BR>\n" );
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document.write( "b)  1^2 = k * 150^3<BR>\n" );
document.write( "k = (1 / 3375000)<BR>\n" );
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document.write( "c.  T^2 = (1 / 3375000) * (30 * 150)^3<BR>\n" );
document.write( "T^2 = 27000<BR>\n" );
document.write( "T = 164.3168<BR>\n" );
document.write( "From NASA publication Neptune's period is 165 earth years<BR>\n" );
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document.write( "d.  (T(Y) / T(X)) = (2 * d(X)) / d(X))  = 2 = 200% = twice as long<BR>\n" );
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