Of all the objects in Table 13.1, Pluto has the orbit with the greatest eccentricity.

(a) What is the ratio of the orbit's semiminor axis \(b\) to its semimajor axis \(a\) ?

(b) What is the ratio of Pluto's speed at perihelion to its speed at aphelion?

Data from Table 13.1

Mass Equatorial radius (kg) (ME) (m) (RE) Orbit+ semimajor axis eccentricity period (m) (ap) (s) (years) Sun 2.0 1030 3.3 105 7x108 110 Mercury 3.30 X 1023 0.06 2.440 x 106 0.38 5.79 x 1010 0.39 0.206 7.60 x 106 0.24 Venus 4.87 x 1024 0.81 6.052 106 0.95 1.082 x 1011 0.72 0.007 1.94 x 107 0.62 Earth 5.97 x 1024 1 6.378 106 1 1.496 X 1011 1 0.017 3.16 x 107 1 Mars 6.42 1023 0.11 3.396 106 0.53 2.279 10 1.52 0.09 5.94 x 107 1.88 Jupiter 1.90 x 1027 318 7.149 x 107 11.2 7.783 x 10 5.20 0.05 3.74 10% 11.86 Saturn 5.68 x 1026 95.2 6.027 x 107 9.45 1.427 x 1012 9.54 0.05 9.29 108 29.45 Uranus 8.68 x 1025 14.5 2.556 107 4.01 2.871 x 1012 19.2 0.05 2.65 x 10 84.02 Neptune 1.02 x 1026 17.1 2.476 x 107 3.88 4.498 x 1012 30.1 0.01 5.20 x 10 164.8 Pluto 1.31 x 1022 0.002 1.151 x 106 0.18 5.906 X 1012 39.5 0.25 7.82 x 109 247.9 Moon 7.3 x 1022 0.012 1.737 x 106 0.27 3.84 X 108 0.0026 0.055 2.36 x 106 0.075