Locus of points where difference in gravitational forces is constant - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T07:16:14Z http://mathoverflow.net/feeds/question/87586 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87586/locus-of-points-where-difference-in-gravitational-forces-is-constant Locus of points where difference in gravitational forces is constant Jennifer Gao 2012-02-05T14:27:55Z 2012-02-19T15:22:12Z <p>Is there a name for the curve in the plane defined by</p> <p>$a/\|x - p\|^2 - b/\|x - q\|^2=\mathrm{constant}$</p> <p>where $a$ and $b$ are fixed numbers and $p$ and $q$ are fixed points? How about if I don't square the denominators? How about if $a$ and $b$ are both $1$?</p> http://mathoverflow.net/questions/87586/locus-of-points-where-difference-in-gravitational-forces-is-constant/87589#87589 Answer by Joseph O'Rourke for Locus of points where difference in gravitational forces is constant Joseph O'Rourke 2012-02-05T14:59:25Z 2012-02-05T14:59:25Z <p>I cannot offer names for your functions, but I was interested to see what they look like. Here is the function with the denominators unsquared, i.e., just the distances $||p-a||$ and $||q-b||$: <br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <img src="http://cs.smith.edu/~orourke/MathOverflow/ContourPlot.jpg" alt="Contour Plot"> <br /> You might look at <em>power Voronoi diagrams</em>, which have a similar flavor (for multiple sites $p$, $q$).</p>