Compute g for the surface of a planet whose radius is double that of the earth and whose mass is also double that of the earth.

Sure, let's solve this step by step.

1. The formula for gravitational acceleration (g) on the surface of a planet is given by Newton's law of universal gravitation: g = GM/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

2. We know that the mass (M) of the planet is double that of Earth, so M = 2M_earth. Similarly, the radius (r) of the planet is double that of Earth, so r = 2r_earth.

3. Substituting these values into the formula, we get g = G(2M_earth)/(2r_earth)^2.

4. Simplifying this, we get g = GM_earth/r_earth^2, which is the gravitational acceleration on the surface of the Earth.

So, the gravitational acceleration on the surface of this planet is the same as that on the surface of the Earth.