Under the presentation ppt for how mass, density and volume affect gravitational force, I am wondering why the denominator r squared does not change when the radius of the sphere in example 1 is doubling.  I am therefore having confusion about problem #11 and 12 in the powerpoint.

Dawn, Since the spheres' radii are doubled in problem #11, the mass's also increase! If you click on the small "globe" link in the bottom left corner of the problem, you will get a video that explains it. Same thing for problem #12. If you can't, I'll snip the screen with the solution and send it to you. Please let me know.

The slides following "How Mass, Density and Volume Affect Gravitational Force" explain the methodology also.  They start on slide 40 on the powerpoint.
John

Thanks John.  I understand the math in #11 and 12, but not in the example problem 1 with planet X and Y.  Planet X's radius doubles, but little "r" in the denominator stayed the same.

Dawn, the intent of the problem was that the distance between the centers of the two planets stays the same. In that case, r stays the same, and only R sub X doubles. I will add a clarification to the problem as it was not as clear as it should be. Thanks for the question! John

Thank you for your response. My students did not even ask about it LOL