The sphere of influence (SOI) is poorly named and should include the word dominant because the influence of other objects is not excluded. It is the outer edge of orbital stability, making a stable orbit difficult to achieve at that location. The SOI is tied to a less massive object that orbits a more massive object. So the sphere of influence for the moon is that space where the gravitational pull of the moon is stronger than the Earth's. The SOI for the Earth is a space where Earth's gravity is stronger than the Suns which extends out about 1 million miles from the Earth. So in effect, the SOI for the moon is a hole in the SOI for the Earth. The SOI for the Moon extends out about 40 thousand miles from the Moon's surface. Inside this sphere, the gravitational pull of the Sun and Earth is still there, just weaker than that of the Moon. Escape velocity is the velocity required to get to the SOI when launching from the surface.
