The sun's gravitational pull on the earth

[MeJennifer]

Not spherical. It has axial or cylindrical symmetry. That's appropriate, since it's rotating.

Ok, so then how can people use Birkhoff's theorem as an argument against gravitational waves for rotating balls?
Isn't his theorem pertaining to spherical symmetry?

 

[Labguy]

Ok, so then how can people use Birkhoff's theorem as an argument against gravitational waves for rotating balls?
Isn't his theorem pertaining to spherical symmetry?

Yes, spherical symmetry, BUT, of the gravitational field at a distance. It is not about the shape (spherical or oblate) of the object itself.

 

[MeJennifer]

Yes, spherical symmetry, BUT, of the gravitational field at a distance. It is not about the shape (spherical or oblate) of the object itself.

What do you mean by "at a distance"?
Anything asymmetrical within the ball would cause gravitational waves would it not?

 

[Labguy]

What do you mean by "at a distance"?
Anything asymmetrical within the ball would cause gravitational waves would it not?

Pick a distance, any distance from a ball, rotating or not.

If within the ball (sphere) the net gravity is zero, beyond the ball it would be the Schwartzchild coordinates. That gives the "spherical symmetry" of the gravitational field. Only some cataclysmic event, as explained by many other posts above, would create the gravity waves. Don't know how else to explain it without having you go read a book.

 

[MeJennifer]

If within the ball (sphere) the net gravity is zero...

I am not sure what you mean by "net gravity is zero" within the ball since there is obviously resistance from EM forces to the gravitational collapase.

But anyway is that the case for a rotating ball with an equatorial bulge, that, as you call it, the net gravity is zero?

 

[SpaceTiger]

Gravitational radiation requires a time-varying quadrupole moment. A spinning object, even if bulged in the middle, would have a constant quadrupole moment. However, if it were also precessing, this would not be the case and it would emit gravitational radiation.