In section 12.3 on page 287 it "proves" that the gravitational field necessarily exerts a force at the center of mass and not elsewhere.
As the saying goes, it's bad luck to prove things that aren't true. For example, if you go to the beach, you can observe rather strong evidence that the gravitational field of the moon does not act solely on the center-of-mass of the earth.
It may be that for a rigid object in a locally _uniform_ gravitational field, the force produces no net torque around the center of mass.
Suggestion: The footnote should be more carefully worded. Sticking in the word uniform would help a lot.
In section 12.3 on page 287 it "proves" that the gravitational field necessarily exerts a force at the center of mass and not elsewhere.
As the saying goes, it's bad luck to prove things that aren't true. For example, if you go to the beach, you can observe rather strong evidence that the gravitational field of the moon does not act solely on the center-of-mass of the earth.
It may be that for a rigid object in a locally _uniform_ gravitational field, the force produces no net torque around the center of mass.
Suggestion: The footnote should be more carefully worded. Sticking in the word uniform would help a lot.