How far away is the horizon?

This can be calculated very easily. We ignore the ocean haze and calculate how far it is to get to the point where our line of sight touches the surface of the earth. --[reporting2] Doing 'do snippet' - should be imbed--

Here the radius of the Earth is R, and the height above the ground of our vantage point is h. The distance to the horizon, which we want to calculate, is x. In the diagram we have exaggerated h compared to R for clarity.

The answer will of course depend on h.

We have a right angle triangle, even though quite a thin one, and we can use Pythagoras.

So from Pythagoras,
x² = (R+h)²-R² = 2hR + h²

h is so much smaller than R that we can safely ignore the h² term. This gives the final answer:
x = √(2hR)

This formula of course works on the moon and any other spherical body. On Earth R=6,378,000 metres approx (see Wikipedia) and therefore, if h is in metres and x is in km,
x = 3.57 x √(h)