document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025920>Question 1025920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time taken for a complete revolution around the sun) is proportional to the cube of its average distance d from the sun<BR>\n" );
document.write( " Neptune is approximately 30 times as far away from the sun as Earth. Without using the speci&#64257;c number of kilometers, what is the period of Neptune? Does your answer correspond with the value from other sources? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641205 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" >= period of a planet<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >= distance from that planet to the sun<BR>\n" );
document.write( "Kepler’s Third Law of planetary motion states that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2=k%2Ad%5E3 ALIGN=MIDDLE  ALT=\"T%5E2=k%2Ad%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let us measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" > values in Earth-years,<BR>\n" );
document.write( "and let us use the subscripts E for Earth and N for Neptune.<BR>\n" );
document.write( "For Neptune,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D%5E2=k%2Ad%5BN%5D%5E3 ALIGN=MIDDLE  ALT=\"T%5BN%5D%5E2=k%2Ad%5BN%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For Earth,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BE%5D%5E2=k%2Ad%5BE%5D%5E3 ALIGN=MIDDLE  ALT=\"T%5BE%5D%5E2=k%2Ad%5BE%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Dividing one equation by the other,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D%5E2%2FT%5BE%5D%5E2=k%2Ad%5BN%5D%5E3%2F%28k%2Ad%5BE%5D%5E3%29 ALIGN=MIDDLE  ALT=\"T%5BN%5D%5E2%2FT%5BE%5D%5E2=k%2Ad%5BN%5D%5E3%2F%28k%2Ad%5BE%5D%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we are measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T ALIGN=MIDDLE  ALT=\"T\"   DISABLED_style= \"max-width:90%; height:auto;\" > values in Earth-years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D%5E2%2F1%5E2=d%5BN%5D%5E3%2Fd%5BE%5D%5E3 ALIGN=MIDDLE  ALT=\"T%5BN%5D%5E2%2F1%5E2=d%5BN%5D%5E3%2Fd%5BE%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D%5E2=%28d%5BN%5D%2Fd%5BE%5D%29%5E3 ALIGN=MIDDLE  ALT=\"T%5BN%5D%5E2=%28d%5BN%5D%2Fd%5BE%5D%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we are told that  Neptune is approximately 30 times as far away from the sun as Earth,<BR>\n" );
document.write( "we can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5BN%5D%2Fd%5BE%5D=30 ALIGN=MIDDLE  ALT=\"d%5BN%5D%2Fd%5BE%5D=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D%5E2=30%5E3 ALIGN=MIDDLE  ALT=\"T%5BN%5D%5E2=30%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D%5E2=27000 ALIGN=MIDDLE  ALT=\"T%5BN%5D%5E2=27000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D=sqrt%2827000%29 ALIGN=MIDDLE  ALT=\"T%5BN%5D=sqrt%2827000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5BN%5D=about164 ALIGN=MIDDLE  ALT=\"T%5BN%5D=about164\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the period of Neptune is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28164%29 ALIGN=MIDDLE  ALT=\"highlight%28164%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Earth-years.<BR>\n" );
document.write( "NASA says Neptune has a period of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=164.8 ALIGN=MIDDLE  ALT=\"164.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Earth-years,<BR>\n" );
document.write( "and that its distance from the sun is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30.07 ALIGN=MIDDLE  ALT=\"30.07\"   DISABLED_style= \"max-width:90%; height:auto;\" > AU,<BR>\n" );
document.write( "so the calculated value is as close as could be expected. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );