Question on the Problem of the three bodies

[Timoleon of Korinthos]

Guys, I have been looking for the boundary conditions for the problem of the three bodies applied to the system composed by the sun, the earth and the moon. I encountered a paper with the following figures, which refer to the so called Euler's solution:

For t=0
Xsun=0 Ysun=0
Xearth=1.0167122AMU Yearth=0 Uearth=0 Vearth=6.138542 AMU/year
Xmoon=1.019253AMU Ymoon=0 Umoon=0.002 AMU/year Vmoon=5.918001 AMU/year

Practically, the model assumes that the earth lies at the top of the major axis of its ecllipse, the sun lies at the distant focus of the ellipse and the moon lies 3.8x10^8 m away from earth on the exterior of its orbit.
Now, as I am totally unfamiliar with astronomy and the likes, can anyone tell me if these figures are accurate and by the way explain to me how can the velocity of the moon have a horizontal component at this point, even if it is that small? Isn't the moon supposed to be revolving in a circle around earth? Or is this motion apparent only on a micro-climax engulfing just the earth and the moon?

[Sphere]

I am fairly certain the moon does not orbit the Earth on the same plane as the Earth orbits the Sun. The moon orbits in a plane perpendicular to the Earths axis which is slightly tipped in terms of the Sun. Hence the whole seasons thing. That is why the some out of plain velocity would actually be expected.

Though I may be misunderstanding what you've posted, as the direction of your velocities are unclear.

[Timoleon of Korinthos]

I am fairly certain the moon does not orbit the Earth on the same plane as the Earth orbits the Sun. The moon orbits in a plane perpendicular to the Earths axis which is slightly tipped in terms of the Sun. Hence the whole seasons thing. That is why the some out of plain velocity would actually be expected.

Though I may be misunderstanding what you've posted, as the direction of your velocities are unclear.

Of course, you are right, how could have I missed that! By the way all the models I have looked up simplify the simulation by making the hypothesis that all the orbits lie on the same plane (common z, hence 3 unknown variables less) and I just took for granted that all bodies' axes are parallel to each other and perpenidulcar to the plane of their orbits, which is obviously wrong.