Unformatted text preview: c and a in the diagram above. From this equation we can calculate that c must be equal to: The distance between the two thumbtacks is: String Length – Let’s calculate the exact string length needed (and then we can add a little bit to tie a knot). We can think of this in terms of the triangle shown above and add up the lengths of the three sides. We already know the bottom side. To get the other two sides we need to: 1) Note that the triangle above is an isosceles triangle since our pencil is at the end of the semi-minor axis b. Therefore, the two unknown sides are equal. 2) Remember the definition of an ellipse – the sum of the distances from the two foci is the same for all points on the ellipse and equal to 2 a . Thus, the distance from a focus to the pencil (the length of one unknown side) is: Conclusion The entire length of the string is: c e c ea a =...
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- Fall '10
- Astronomy, Astronomical unit, Neptune, Pluto, eccentricity, exact string length