Final answer:
Earth and the Moon share a common center of gravity, known as the barycenter, located around 1700 km beneath Earth's surface. The Moon orbits this point and is approximately 30 Earth-diameters away from Earth. Earth's gravitational pull governs this orbit and causes lunar eclipses when specific alignments occur.
Step-by-step explanation:
The exact position of the Earth in the orbit of the Moon is not at the center, instead Earth and Moon both orbit a common center of mass, known as the barycenter. This barycenter is positioned about 1700 km below Earth's surface due to Earth's larger mass in comparison to the Moon.
The Moon is approximately 30 Earth-diameters away from us, and because its orbit is tilted relative to Earth's orbital plane, and not perfectly circular, Earth's shadow only intersects the Moon during specific alignments, resulting in lunar eclipses. Earth's gravitational force is responsible for the Moon's orbit around this barycenter, which is evident from the centripetal accelerations observed.