Gravity inside and outside the Earth

How does $g$ change as you go from the centre of a uniform Earth, up through the ground, and out into space? You will make the program draw it, read two values off the curve, and find the depth where $g$ is the same as $1000\ \text{km}$ up.

The idea. Outside, $g$ falls as $\dfrac{1}{r^2}$: $g\left(\dfrac{R}{r}\right)^2$. Inside a uniform Earth only the mass nearer the centre pulls, and $g$ grows in step with $r$: $g\dfrac{r}{R}$.

Your tasks.

1. Work out g_r, the value of $g$ at every distance in r.
2. Read off $g$ at $2.5R$ from the centre, and at $0.3R$.
3. Find the depth below the ground at which $g$ is the same as $1000\ \text{km}$ above it.