#### Answer

They are orbiting at an altitude of $0.414 ~R$ above the surface (where R is the planet's radius).

#### Work Step by Step

We can write an expression for the free-fall acceleration on the planet's surface. Let $M$ be the planet's mass and let $R$ be the planet's radius.
$g = \frac{G~M}{R^2}$
Let $h$ be the altitude above the planet's surface. We can write an expression for the free-fall acceleration at the altitude $h$.
$\frac{g}{2} = \frac{G~M}{(R+h)^2}$
$g = \frac{2~G~M}{(R+h)^2}$
We can equate the two expressions for $g$ to find $h$.
$\frac{G~M}{R^2} = \frac{2~G~M}{(R+h)^2}$
$(R+h)^2 = 2~R^2$
$R+h = \sqrt{2}~R$
$h = (\sqrt{2}-1)~R$
$h = 0.414~R$
They are orbiting at an altitude of $0.414 ~R$ above the surface (where R is the planet's radius).