If the sun were to suddenly vanish in our solar system, it would take about 8 minutes for the Earth to exit its orbit. This is because the gravitational field of the sun would vanish at a rate of $c$. I am basing this on a question where the sun suddenly disappeared.

However, suppose the sun was already present for, say, a million years. If I were to suddenly add a massive body, such as a planet, at a distance of 149.60 million kilometres (the current average radius of the Earth's orbit), then shouldn't the planet immediately be attracted to the sun? Would there be a delay? And, if so, why?

This question would also apply to charges and electromagnetic fields since they also travel at the speed of light.

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    $\begingroup$ If by 'suddenly' you mean instantaneously, then that in itself would of course break the speed limit of the Universe. $\endgroup$
    – Gert
    Jul 28 '16 at 19:09
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    $\begingroup$ Why should there be any difference between the two scenarios? $\endgroup$ Jul 28 '16 at 19:13
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    $\begingroup$ One can play this game with electromagnetic forces, but not with gravity, which is simply yet another indication that gravity is not a force. $\endgroup$
    – CuriousOne
    Jul 28 '16 at 19:15
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    $\begingroup$ Because @LewisMiller in this case the gravitational filed of the sun isn't disappearing. It already exists and the planet is placed within its boundaries (so the planet interacts with it immediately when it is placed). And I don't know if there will be a difference... that is what I'm trying to understand. $\endgroup$
    – Dieblitzen
    Jul 28 '16 at 19:16
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    $\begingroup$ @CuriousOne Why not? I am talking about the force of gravitation $\endgroup$
    – Dieblitzen
    Jul 28 '16 at 19:18

Note: your example isn't quite right, because Einstein's field equation implies $\partial_\mu T^{\mu\nu} = 0$, i.e. conservation of energy. Attempting to consider a situation where a mass suddenly appears 'out of nowhere' is mathematically self-contradictory in GR. But, putting this issue aside...

Yes, the planet would immediately be attracted to the sun. But the sun wouldn't be immediately attracted to the planet, since the effect of the planet needs to propagate at light speed!

You might think this is paradoxical, since it violates Newton's third law. Indeed, situations like this come up all the time when a mediating field is involved. For example, there are cases where the forces between two moving charges are not equal and opposite (see here).

The resolution is to view the field as a physical intermediate object: the charges are not acting on each other, but separately acting on the field, and these two force pairs each satisfy Newton's third law. Since the field can act and be acted on by forces, it must carry momentum. Total momentum is conserved, as long as we account for this field momentum.

However, this resolution doesn't work in GR, because we cannot define the energy/momentum of the gravitational field (see here). This goes back to my initial point, which is that this situation is not physical. But it does illustrate an important physical principle.

  • $\begingroup$ Ok... So assuming the planet was placed with 0 initial velocity, it would immediately start accelerating? And I know the mass can't appear out of no where, I was just trying to see if the reverse of this is possible physics.stackexchange.com/q/98936 $\endgroup$
    – Dieblitzen
    Jul 28 '16 at 19:22

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