Sedna. In November $2003,$ the now-most-distant-known object in the solar system was discovered by observation with a telescope on Mt. Palomar. This object, known as Sedna, is approximately 1700 $\mathrm{km}$ in diameter, takes about $10,500$ years to orbit our sun, and reaches a maximum speed of 4.64 $\mathrm{km} / \mathrm{s}$ . Calculations of its complete path, based on several measurements of its position, indicate that its orbit is highly elliptical, varying from 76 $\mathrm{AU}$ to 942 $\mathrm{AU}$ in its distance from the sun, where $\mathrm{AU}$ is the astronomical unit, which is the average distance of the earth from the sun $\left(1.50 \times 10^{8} \mathrm{km}\right)$ . (a) What is Sedna's minimum speed? (b) At what points in its orbit do its maximum and minimum speeds occur? (c) What is the ratio of Sedna's maximum kinetic energy to its minimum kinetic energy?