gravitation and orbits

Pluto is still moving gracefully along in its orbit, unaware that astronomers
on the planet Earth decided in 2006 to reclassify it as a `dwarf planet' rather
than a `planet'. Pluto's orbit is more elliptical than any of the eight plan-
ets. The aphelion distance of Pluto is raph = 49:3 AU = 7:38  1012 m,
and its perihelion distance is rper = 29:7 AU = 4:44  1012 m. Its mass is
1:31  1022 kg, approximately 1/500 that of Earth. At aphelion, its orbital
speed is vaph = 3:68103 m=s. Note: To distinguish aphelion and perihelion,
you may nd it useful to think of the phrase \the aphelion is afar"".
(a) What is the total mechanical energy of Pluto in its orbit around the Sun?
(b) What is the orbital speed of Pluto at perihelion?
(c) At perihelion, what is Pluto's escape speed with respect to the Sun?
(d) If at its perihelion distance Pluto had a speed equal to twice the escape
speed found in part (c), and as a result it left our solar system (never
to return), what would its speed be when it had reached a point far, far
away from our solar system?