First, to answer your question about whether the moon phase/tide plays a role in pellet trajectory, there is little to no evidence to suggest that it has a significant effect. The gravitational pull of the moon and tides are relatively weak compared to other factors that affect pellet trajectory, such as wind, temperature, and air pressure. So, for practical purposes, you can safely assume that the moon phase/tide has no effect on pellet trajectory.
However, there are two other factors that do affect ballistic trajectory over long distances, and that is the Coriolis effect and the Eötvös effect.
The Coriolis effect is a phenomenon caused by the rotation of the Earth, which causes moving objects to appear to veer to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This effect can cause bullets to drift off course over long distances.
The magnitude of the Coriolis effect is small. For us, it's probably almost inconsequential, in fact, for most small arms the magnitude of the Coriolis effect is generally insignificant (for high powered rifles in the order of about 10 cm (3.9 in) at 1,000 m (1,094 yd)), but for ballistic projectiles with long flight times, such as extreme long-range rifle projectiles, artillery, and rockets like ICBMs, it is a significant factor in calculating the trajectory. The magnitude of the drift depends on the firing and target location, azimuth of firing, projectile velocity and time of flight.
The Eötvös effect is largest at the equator and decreases to zero at the poles. It causes eastward-traveling projectiles to deflect upward, and westward-traveling projectiles to deflect downward. The effect is less pronounced for trajectories in other directions, and is zero for trajectories aimed due north or south. In the case of large changes of momentum, such as a spacecraft being launched into Earth orbit, the effect becomes significant. It contributes to the fastest and most fuel-efficient path to orbit: a launch from the equator that curves to a directly eastward heading. The Eötvös effect changes the perceived gravitational pull on a moving object based on the relationship between the direction and velocity of movement and the direction of the Earth's rotation.
In summary, air rifles don't typically shoot anywhere near far enough for these forces to be of concern - the moon phase/tide has little to no effect on trajectory, the Eötvös effect only matters when you shooting for the moon (literally), and while the Coriolis effect can cause bullets to drift off course over long distances, especially when shooting near the poles, that's really only of concern to a VERY small number of folks in this sport - you're gonna have to be REALLY REALLY good before that data will be of any use to you.
