document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141722>Question 1141722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "I am having trouble with a problem regarding Newton's Synthesis. I am giving the following equations and I have to solve for \"G\" and I am somewhat confused. \r<BR>\n" );
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document.write( "Force of Gravity is G*Mm/r^2<BR>\n" );
document.write( "Centripetal Force is mv^2/r\r<BR>\n" );
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document.write( "How would I solve for \"G\"\r<BR>\n" );
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document.write( "Thank you!  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762326 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are you saying  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+mv%5E2%2Fr+=+GMm%2Fr%5E2+ ALIGN=MIDDLE  ALT=\"+mv%5E2%2Fr+=+GMm%2Fr%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you need to solve for G?<br>\r<BR>\n" );
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document.write( "It matters very little anyway, so I will just say this: if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F+=+GMm%2Fr%5E2+ ALIGN=MIDDLE  ALT=\"+F+=+GMm%2Fr%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can solve for G by the following steps:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F+=+GMm%2Fr%5E2+ ALIGN=MIDDLE  ALT=\"+F+=+GMm%2Fr%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Re-writing, so G will end up on the left:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+GMm%2Fr%5E2+=+F+ ALIGN=MIDDLE  ALT=\"+GMm%2Fr%5E2+=+F+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Multiply both sides by r^2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+GMm+=+F%2Ar%5E2+ ALIGN=MIDDLE  ALT=\"+GMm+=+F%2Ar%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Divide both sides by mM:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G+=+F%2Ar%5E2%2F%28Mm%29+ ALIGN=MIDDLE  ALT=\"+G+=+F%2Ar%5E2%2F%28Mm%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Now you can replace F with some other expression and you will likely get some cancellation of some variables, for example, if you say F = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+mv%5E2%2Fr+ ALIGN=MIDDLE  ALT=\"+mv%5E2%2Fr+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G+=+%28mv%5E2%2Fr%29%2Ar%5E2+%2F+%28Mm%29++=+%28cross%28m%29v%5E2%2Fcross%28r%29%29%2Across%28r%29%2Ar+%2F+%28M%2Across%28m%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G+=+v%5E2%2Ar%2FM+ ALIGN=MIDDLE  ALT=\"+G+=+v%5E2%2Ar%2FM+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "To the student:  the answer to your question is yes.   Sorry, just noticed you had asked for additional detail.  \r<BR>\n" );
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