How Does the Sun's Position Affect the Earth-Moon Barycenter?

[bunburryist]

My understanding is that the Earth-Moon barycenter is about 6 kilometers from the Earth's center of mass in the direction of the moon. My question -

If the Sun is on the opposite side of the moon from the Earth, would that pull the Moon slightly away from the Earth, thus moving the Earth-Moon barycenter farther from the Earth's center of mass? Would the same thing happen if the Sun was on the opposite side of the Earth from the Moon. Would the barycenter move closer and farther from the Earth's center of mass as the Sun went (relatively) "around" our Earth-Moon system? Would it be farther when the Sun is in line with the Earth and Moon, and closer when the Sun's direction is perpendicular to the Moon-Earth line?

 

[LURCH]

Yes to all, with the addition that the barycenter is also further from the moon when the three bodies are all lined up. This effect is similar to the way the Moon influences tides on the surface of the Earth. When the Earth and Moon are aligned with the Sun, the Earth-Moon system is “stretched out” along the path of that alignment. This can happen because the entire Moon and a little bit of the Earth are located on one side of the barycenter, while the majority of the Earth’s mass is on the other side.

But these changes in distance would be tiny, and only relative to what the distances would be if the Sun did not exert a pull. The eccentricity of the Moon’s orbit is far greater. It’s never crossed my mind to calculate the actual tidal force that the Sun has on the Earth-Moon system. Sounds like fun, actually. Think I’ll give it a go, and come back with my results.

 

[Bandersnatch]

My understanding is that the Earth-Moon barycenter is about 6 kilometers from the Earth's center of mass in the direction of the moon.

It's not though. Earth is approx 83 times more massive than the Moon, so the barycentre is at 1/83 of the Earth-Moon distance. Using the mean distance, that's approx. 4600 km from the centre of Earth, not 6.

 

[bunburryist]

I can't remember where I heard that 6 kilometer bit. Thanks for straightening me out!
Some of the higher geosynchronous satellites must do a little "bobbing up and down" (relative to the earth) as the moon goes around the earth.

 

[Erut Gudahl]

In addition to the barycenter being 4600 KM from the Earth's core in the current direction of the moon, it is also the case that the barycenter is the point in space that orbits the sun. This point is always moving inside the earth, both due to the rotation of the Earth and the moon's position in space relative to the earth. This means all points on the surface of the Earth (except the two places where the "line" of the Earth's orbit enters and exits the Earth's surface, passing through the barycenter), all other points on the Earth are moving at an orbital speed around the sun different from the speed they would naturally have under Kepler's 2nd law. We're held to a different speed by the rigidity of the Earth. We also feel the speed difference as a force acting on us. If you're inside the orbit of the barycenter, your body wants to orbit faster, so there is force on you toward the east (and south if your're north of the barycenter line). If you're outside the orbit line of the barycenter, your body wants to orbit slower, so there's a force on you to the west (and north or south). It's a small force for a human, but it acts on all particles around the earth, not all of them rigid --ie. water in the oceans actually starts moving in the direction that the force wants it to move. This is the solar component of tides. There's a separate Lunar component which is derived from differential of moon's gravity acting on the near vs the far side of the earth. The main point here though, is you're almost continually not going the orbital speed that physics wants you to be moving, The Earth itself is wobbling around its moving barycenter as the barycenter moves in a eliptical orbit around the sun.