Finding the ratio of moon to Earth density given surface gravity

[nns91]

Homework Statement

The mass of the Earth is 5.98*10^24 kg and its radius is 6370 km. The radius of the moon is 1738 km. The acceleration of gravity at the surface of the moon is 1.62 m/s^2. What is the ratio of the average density of the moon to that of the Earth ?

Homework Equations

New's law of gravity: F= G*m1*m2/r^2

The Attempt at a Solution

I understand that I need to find mass of the moon to get its density. How should I calculate the mass of the moon ??

 

[Dr.D]

Assume a 1 kg test mass and write a statement about what is true at the surface of the Earth and a similar statement for the same 1 kg mass at the surface of the moon.

 

[nns91]

On the Earth it will have the weight of 9.81 N and on the moon its weight going to be 1.62 N. Is that what you are talking about ?

 

[nns91]

Can I use Newton's Law of Gravity here ? But I don't know either F or r and one of the m though