One model for a certain planet has a core of radius r and mass m surrounded by an outer shell of inner radius r, outer radius 2r, and mass 4m. if m = 2.48 × 1024 kg and r = 1.17 × 106 m, what is the gravitational acceleration of a particle at points (a) r and (b) 3r from the center of the planet?

(a) 120.8 m/s^2

The gravitational acceleration at a generic distance r from the centre of the planet is

where

G is the gravitational constant

M' is the mass enclosed by the spherical surface of radius r

r is the distance from the centre

For this part of the problem,

so the mass enclosed is just the mass of the core:

So the gravitational acceleration is

(b) 67.1 m/s^2

In this part of the problem,

and the mass enclosed here is the sum of the mass of the core and the mass of the shell, so

so the gravitational acceleration is

truck y has a greater velocity than truck x.