If an object at the surface of the Earth has a weight Wt, what would be the weight of the object if it was transported to the surface of a planet that is one-sixth the mass of Earth and has a radius one third that of Earth

We know that the gravitational acceleration in the surface of the Earth can be written as:

g = G*M/r^2

Where:

M = mass of the Earth

r = radius of the Earth.

G = gravitational constant.

The weight of an object of mass m, is written as:

W = m*g = m*(G*M/r^2)

Now, if we move our object to a place that has a mass equal to 1/6 times the mass of the Earth, and 1/3 the radius of the earth.

The gravitational acceleration on this planet is written as:

g' = G*(M/6)/(r/3)^2 = (1/6)*(G*M)/(r^2/9) = (9/6)*(G*M/r^2) = (3/2)*g

then the weight on this planet is:

W' = m*g' = m*(3/2)*g = (3/2)*(m*g)

and m*g was the weight on Earth, then:

W' = (3/2)*(m*g) = (3/2)*W

The new weight is 3/2 times the weight on Earth.