Believe it or not, it is true that when the Moon is in its 'New' phase, the force of gravity it feels from the Sun is about twice as strong as what it receives from the Earth. The result of this, however, is not that the Moon gets wrenched from its orbit about the Earth but that its orbital period is about 53 minutes LONGER than it would be without the Sun present. Also, the path of the Moon about the Earth does NOT form a closed orbit like those of the planets about the Sun. The net result of the Sun constantly trying to pull the Moon away from the Earth is that the so-called Line of Apsides rotate to the east, completing a full 360 degree change every 8.85 years. This means that the position in the sky of the Moon's closest approach to the Earth moves eastward in the sky in this period of time. In some respects, you can think of the Earth and Moon as being separate 'planets' orbiting the Sun with the Moon and the Earth periodically switching positions much as Neptune and Pluto do.