How quickly does the Earth feel the effects of a halved Sun's mass?

[berkeman]

Quadrupole.

So I have a quick question which is hopefully still on-topic for the OP's thread...

In my simplified scenario below, would the splitting hemispheres be considered a dipole, or somehow a quadrupole? If only a dipole, how would the change in gravitation propagate away from the explosive splitting event? Thanks.

To try to give you a better physical scenario and also make it easier to visualize, suppose that the Sun exploded all of a sudden and broke into two hemispheres that flew apart at high velocity, with the 2 halves moving perpendicular to the Solar System's orbital (ecliptic) plane.

The change in the Sun's gravitational field would propagate outward at the same velocity as the light from the Sun, so the changes in the gravitational field from the Sun would be "noticed" on Earth at the same time that we "saw" the two hemispheres separating and flying apart.

 

[PeterDonis]

would the splitting hemispheres be considered a dipole

As you've defined it, I believe so, yes. So no gravitational waves would be emitted. There would be a "change in the gravitational field" (more precisely, a change in spacetime curvature), but it would not be describable as gravitational waves.

 

[Vanadium 50]

Since the hemispheres are the same "charge" its a quadrupole. It's magnitude should be ~mz²/2. (Assumes separation is large compared to the sphere radius).

It will radiate.

However, there is also the near-field effect. Consider you are on a line in the same direction that the two haves separate in. Now half is closer and half is farther. But since this is an inverse square force, the part that moves towards you has a greater increase in attraction than is compensated for by the smaller attraction from the half that moves away.

A complication - it takes energy to move things around like this, and that energy gravitates too. That needs to be considered as well.

 

[PeterDonis]

Since the hemispheres are the same "charge" its a quadrupole.

Oops, yes, you're right.

A complication - it takes energy to move things around like this, and that energy gravitates too. That needs to be considered as well.

Yes, this is a good point.