The local zenith is perpendicular to the rotation axis of the Earth at a specific location. It represents the point directly above an observer, pointing towards the celestial sphere. The rotation axis of the Earth is an imaginary line around which the Earth spins.
You are allowed to run a spell checker on your questions. To answer your question, local zenith is a direction. It is upwards and it goes from the centre (Canadian spelling) of the earth, up thru (Engineering spelling) your head and onward into the sky. It is called local because it depends on your location. If you were standing on the equator then the local zenith is perpendicular to the earth's axis. If you were to stand at either pole, then the local zenith would be parallel to the earth's axis.
About eight thousand miles.
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Moonlight reaches Earth approximately 1.3 seconds after it reflects off the Moon's surface. This is because the Moon is about 238,855 miles away from Earth, and light travels at a speed of about 186,282 miles per second. Therefore, you can effectively consider moonlight as being nearly instantaneous for practical purposes, but it does take a tiny fraction of a second to arrive.