Path of Earth and Moon Around Sun
When viewed from the north celestial pole, i.e. from the star Polaris, the Moon orbits the Earth counterclockwise, the Earth orbits the Sun counterclockwise, and the Moon and Earth rotate on their own axes counterclockwise.
The right-hand rule can be used to indicate the direction of the angular velocity. If the thumb of the right hand points to the north celestial pole, its fingers curl in the direction that the Moon orbits the Earth, the Earth orbits the Sun, and the direction the Moon and Earth rotate on their own axes.
In representations of the Solar System, it is common to draw the trajectory of the Earth from the point of view of the Sun, and the trajectory of the Moon from the point of view of the Earth. This could give the impression that the Moon circles around the Earth in such a way that sometimes it goes backwards when viewed from the Sun's perspective. Since the orbital velocity of the Moon about the Earth (1 km/s) is small compared to the orbital velocity of the Earth about the Sun (30 km/s), this never occurs. There are no rearward loops in the Moon's solar orbit.
Considering the Earth–Moon system as a binary planet, their mutual centre of gravity is within the Earth, about 4624 km from its centre or 72.6% of its radius. This centre of gravity remains in-line towards the Moon as the Earth completes its diurnal rotation. It is this mutual centre of gravity that defines the path of the Earth–Moon system in solar orbit. Consequently the Earth's centre veers inside and outside the orbital path during each synodic month as the Moon moves in the opposite direction.
Unlike most other moons in the Solar System, the trajectory of the Moon is very similar to that of its planet. The Sun's gravitational pull on the Moon is over twice as great as the Earth's pull on the Moon; consequently, the Moon's trajectory is always convex (as seen when looking inward at the entire Moon/Earth/Sun system from a great distance off), and is nowhere concave (from the perspective just mentioned) or looped. If the gravitational attraction of the Sun could be "turned off" while maintaining the Earth–Moon gravitational attraction, the Moon would continue to orbit the Earth once every sidereal month.
Read more about this topic: Orbit Of The Moon
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—Ben Jonson (1572–1637)