[seth (OP)]

Does the moon exist outside of the Hill radius of the earth?

[DoctorBeaver]

No, it is a long way inside.

The Moon is approximately 0.4 million km from Earth and the Earth's Hill radius (also known as the Roche radius) is 1.5 million km.

[Soul Surfer]

To clarify this question to general readers.  The Hill radius of the earth is the distance at which the gravitation of the earth controls the motion of an object orbiting the earth.  It essentially means that it is the distance at which the as one moves in orbit with the earth towards the sun that the grvitational influence of the earth is stronger than that of the sun.

[lyner]

SS
You might swap the word 'controls' with the word 'dominates'. We all have some effect on each other.