Unformatted text preview: From this equation we can calculate that c must be equal to: c=(0.25)(40cm)=10 cm The distance between the two thumbtacks is: 2(c)=2(10 cm)=20cm 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 length 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 2a. Thus, the distance from a focus to the pencil (the length of one unknown side) is: 40 cm Conclusion The entire length of the string is: 2a + 2c = 2(40 cm)+2(10 cm)=100cm c e c ea a = a c b...
View Full Document
- Fall '10
- Astronomy, Astronomical unit, Neptune, Pluto, eccentricity