Cannon Westfall

Quick! The empire needs your help! It’s time for you to prove your allegiance and help take down those rebel scums.
The second Death Star (DS2), the planet destroying superweapon, needs to take out the rebel base on the forest moon of Endor, and is currently in orbit. The empire faces a problem, however, in that they don’t know when the Death star will be in proper position to blast those rebels away! Using calculus with the givens that the orbit about Endor is circular and the DS2’s orbit is elliptical, try to see if you can find out when the Death Star will be in proper position to squelch the rebel resistance! The Death Star will be able to fire when the line normal to the tangent line has an undefined slope.

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In order to find each occurrence where the line normal to the tangent’s slope is undefined, one must first find where the derivative of the equation is equal to zero. Ellipses will have derivatives equal to zero at every 90 degrees (90,180, 270, 360, etc.). This means the slope of the line tangent to the ellipse will be a slope of zero, giving the line normal to the tangent, meaning perpendicular to, undefined, giving the Death Star a perfect orientation to fire its superlaser at the rebel base. Let’s just hope we don’t lose another Death Star.

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