A spherically-symmetric planet is made of an empty inner core of radius a surrounded by a thick shell of radius 2a, which is surrounded by another thick shell of radius 3a. The inner shell has a volume density that only depends on radius and is given by s1(r) = br^3, where b is a known positive constant. The outer shell also has a volume density that only depends on radius and is given by s2(r) = y/(r^2), where y is a known positive constant.
[Planet 2]

b=alpha

s= rho

y=gamma

Find the gravitational field in the following regions in terms of G, b, y, a, and r.
r < a:
a < r < 2a:
2a < r < 3a:
r > 3a: