Does the Center of Mass Affect Gravity?

[cragar]

I was thinking that objects like a sphere have a center of mass in the middle of the sphere and also if you were in the middle of the sphere you would feel no gravitational pull in any direction. So then I was wondering if all objects had a zero gravitational pull at their center of mass. But then I thought of a large lead ball connected to a smaller wood ball with a thin rod between them, and the center of mass would be closer to the larger lead ball, because that's where it would balance. But it seems that the pull would be zero closer to smaller wood ball.
Am I thinking about this correctly.

 

[Doc Al]

Yes. A body need not have zero gravitational field due to its own mass at its center of mass, as your example illustrates nicely. For some symmetrical arrangements, it will work out that way of course.

 

[cragar]

ok thanks for your answer .

 

[jewbinson]

The same effect happens with the Sun and the Earth.