The acceleration of gravity on the surface of the planet is 4 times greater than on the surface of the Earth.

The acceleration of gravity on the surface of the planet is 4 times greater than on the surface of the Earth. What is the ratio of the radius of this planet to the radius of the Earth, if the mass of the planet is 16 times the mass of the Earth.

Let the mass of the Earth be m, then the mass of the planet is 16 * m.

Let the gravitational acceleration at the Earth’s surface be g, and at the planet’s surface 4 * g.

Because general formula for the acceleration of gravity:

a = (G * m) / R²,

then:

R = √ ((G * m) / a).

For the Earth we get:

R = √ ((G * m) / g).

For a planet, the radius will be as follows:

R = 2 * √ ((G * m) / g).

Answer: the radius of the planet is twice that of the Earth.