For atorturedsoul: How Far Is the Horizon?

>> Thursday, April 23, 2009

For atorturedsoul: When you are looking out at the ocean and you can see the horizon, exactly how far away is the horizon?

Well, I'll be honest, I had no idea, but Wikipedia had the answer, of course. There are formulas, in general, for someone standing on the shore looking into the distance: in SI, it's Distance(km)=square root[13*height of the eye above sea level(m)]

Check the link for a similar formula for "standard" units (Yes, I'm pro-SI).

But there's an exact formula for finding the distance to a horizon that applies, even to satellites:

D=SQRT(2Rh+h^2) where R is the radius of the planet and h is the distance above the surface of the earth (same units)

Cool question, atorturedsoul. I love learning something I didn't know.

UPDATE: for those for whom math causes seizures or brain damage, for someone 1.7 m tall (~5'7"), the horizon would be ~4.7 km away.


  • Shakespeare

    Yes, only now we have to figure out how to actually RUN the equation...and since I became an English major primarily because I only had to take one math class that way in college (and you thought it was b/c I loved literature!), the prospect of actually figuring that out daunts me to no end. I'm sure it's supposed to be simple.

    I still won't do it. I'd rather play the petulant child.

  • Stephanie B

    For you, Shakespeare, I did the math for you. See the update.

    Mutter, mutter, mutter, grumble, I ALWAYS do the writing exercises, mumble.

  • Stephanie B

    It should be noted that, by providing a formula, I honestly thought I WAS giving an answer.

  • atorturedsoul

    Excellent answer, Stephanie! Thanks so much! Since the distance varies according to a person's height, I think the formula did answer the question perfectly.

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