A planet has mass M and radius 2R.
a) Derive an expression for the escape speed from the planet.
b) A projectile of mass m is shot directly away from the surface of the planet at ⅓ of the escape
speed from the planet. Derive an expression for the maximum distance from the center of the
planet the projectile reaches, in terms of R. Simplify as far as possible. (Ignore the existence of
all other celestial objects.)