HW Question?

Question

If the core of Uranus has a radius twice that of planet Earth and an average density of 8000 kg/m^3
calculate the mass of Uranus outside the core. What fraction of the planet's total mass is core?

Answer 1

Start by determining the volume of a sphere with a radius twice that of earth. That will be the volume of Uranus' core.
Then multiply that times the density. This tells how much mass is in the core of Uranus.
Subtract the amount of mass in Uranus' core from the total mass of the planet. That will tell you how much mass is outside the core.
Divide the mass in the core by the mass of the entire planet and multiply that number times 100. That gives you the percent of the planet's mass that is inside the core.
After doing all this, keep in mind that what Marcus said is true in that although you have completed the homework problem, the answer did not take some things into consideration.

Answer 2

You question is very unclear. What assumptions are we to make? Is there a value given for the radius of Earth or core of Earth, or for the mass of Uranus? Are we supposed to research these ourselves?

Also, is the core of Uranus of a radius twice the radius of Earth? Or twice the radius of the core of Earth?

Do we assume the core is spherical? After all, the planet is oblate, if only by about 2%. The gravity of solid cores is generally enough to offset any centripetal force, but then again, in the real world, there is no core boundary. The core is joined to the outer atmosphere by very viscous liquid, and there are no boundaries.