Does the Moon's gravity affect the Earth's gravity in a satellite's trajectory?

[Deadstar]

Perhaps this is a really dumb/simple/obvious question but it just came to mind...

Let's say there are two scenarios.

1) A satellite is in space far from Earth. There is nothing between it and the Earth.

1) A satellite in the same position as before except the moon is now directly between it and the Earth.

Is the gravitational effect/potential experienced by the satellite from Earth the same in both cases? I.e, does the moons gravity affect the Earths gravity (make it weaker for example..?)

 

[bcrowell]

Your scenario is one in which Newtonian gravity is an excellent approximation. In Newtonian gravity, gravitational forces add like vectors, and gravitational potentials add like scalars. The force and potential experienced by the satellite are different in #2 than in #1. I wouldn't describe it as the moon's gravity affecting the Earth's gravity. The moon's gravity and the Earth's gravity just add.

 

[Deadstar]

Your scenario is one in which Newtonian gravity is an excellent approximation. In Newtonian gravity, gravitational forces add like vectors, and gravitational potentials add like scalars. The force and potential experienced by the satellite are different in #2 than in #1. I wouldn't describe it as the moon's gravity affecting the Earth's gravity. The moon's gravity and the Earth's gravity just add.

I realized that the force is different in both cases of course since the moon is there in one of them. I am asking specifically about the Earth contribution in both cases. I figured that in Newtonian gravity it would be the same but perhaps things would be different when you took a relativistic look at it...

 

[Pengwuino]

So you're basically asking if there is a "screening" effect if the moon gets in the way. In the Newtonian sense, no, gravity adds like normal vectors. Relativistically, they don't add up like that but I'm not sure if it would have a screening effect or if it would be greater than what you would expect from Newtonian gravity.

 

[PAllen]

Your scenario is one in which Newtonian gravity is an excellent approximation. In Newtonian gravity, gravitational forces add like vectors, and gravitational potentials add like scalars. The force and potential experienced by the satellite are different in #2 than in #1. I wouldn't describe it as the moon's gravity affecting the Earth's gravity. The moon's gravity and the Earth's gravity just add.

I think what is being asked is, suppose you measure moon's mass in isolation, and the Earth's (you can freely move planets fare away from everything else). Then you put them in position as described by the OP, and apply Newton's gravitation law. Is there a theoretical correction that should be applied due to the binding energy of the Earth moon system? I think the answer is yes - the total attractions feld by the satellite will be ininitesimally smaller than predicted by applying Newton to the independently measured masses.

 

[Deadstar]

I think what is being asked is, suppose you measure moon's mass in isolation, and the Earth's (you can freely move planets fare away from everything else). Then you put them in position as described by the OP, and apply Newton's gravitation law. Is there a theoretical correction that should be applied due to the binding energy of the Earth moon system? I think the answer is yes - the total attractions feld by the satellite will be ininitesimally smaller than predicted by applying Newton to the independently measured masses.

Yeah that's pretty much it. I used the Earth and Moon but it can be any two masses really. I figured if there was any difference it would be negligible.

 

[bcrowell]

I think what is being asked is, suppose you measure moon's mass in isolation, and the Earth's (you can freely move planets fare away from everything else). Then you put them in position as described by the OP, and apply Newton's gravitation law. Is there a theoretical correction that should be applied due to the binding energy of the Earth moon system? I think the answer is yes - the total attractions feld by the satellite will be ininitesimally smaller than predicted by applying Newton to the independently measured masses.

I think the answer in this case would depend on how the system was prepared. For example, suppose you release the Earth and moon at rest, then let them free-fall toward one another and crash together. I think a distant observer sees no change in the static part of the field (there will be gravitational waves) until later, when the heat of the collision is radiated away. Only then would the distant field decrease. The reason I think there is no change at first in the static part of the distant field is that the Bondi mass is conserved, and the Bondi mass is basically a measure of how much of a field you get from an object at a distant point.

A simpler and more straightforward answer to the OP's question is that yes, GR is nonlinear.