The Earth's orbit around the Sun is slightly elliptical (see Conceptual Example 12-7). At Earth's closest approach to the Sun (perihelion) the orbital radius is 1.471 × 1011 m, and at its farthest distance (aphelion) the orbital radius is 1.521 × 1011 m. Given that the mass of the Earth is 5.972 × 1024 kg, and that of the Sun is 1.989 × 1030 kg,

(a) Find the difference in gravitational potential energy between when the Earth is at its aphelion and perihelion radii.

(b) If the orbital speed of the Earth is 29,290 m/s at aphelion, what is its orbital speed at perihelion?