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About 2.5 km
- The horizon for an average human1.75 m tall would be about 2.5 km. As the Moon is smaller than Earth, the horizon on our satellite would be closer than Earth's. To compute the distance of the horizon on the Moon, follow these easy steps: Sum the radius of the Moon and your height, and compute the square of the result: (1,737,500 + 1.75)².
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Jul 28, 2024 · The horizon for an average human 1.75 m tall would be about 2.5 km. As the Moon is smaller than Earth, the horizon on our satellite would be closer than Earth's. To compute the distance of the horizon on the Moon, follow these easy steps: Sum the radius of the Moon and your height, and compute the square of the result: (1,737,500 + 1.75)².
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Thus, the horizon on Mercury is 62% as far away from the observer as it is on Earth, on Mars the figure is 73%, on the Moon the figure is 52%, on Mimas the figure is 18%, and so on.
Jan 26, 2024 · If you’ve made it this far, let’s crunch the numbers. If your eyes are 1.5 meters off the ground, then the horizon is 3.58 x √1.5, which equals about 4.4 km away. Neat!
- Overview
- Calculating Distance Using Geometry
- Calculating Distance Using Trigonometry
- Alternate Geometrical Calculation
The distance to the horizon depends almost completely on the height above sea-level that the observer is looking from.
Knowing this number is extremely useful and often necessary when navigating over the ocean or going on a hike, though just being curious is reason enough! There are also a few other factors that you might have to consider depending on where you are in the world and the time at which you are viewing, such as temperature and weather conditions. Once you have all the measures you need, you can quickly get the calculation and know the exact distance you are from the horizon.
Measure your "height of eye."
Measure the length between the ground and your eyes in meters or feet. One way to calculate this is to measure the distance between your eyes and the top of your head.
this value from your total height and what will be left is the distance between your eyes and the surface you're standing on. If you are standing exactly at sea level, with the bottom of your feet level with the water, this is the only measurement you'll need.
Add your "local elevation" if you're standing on a raised surface, such as a hill, building or boat.
How many meters or feet above the true horizon are you standing? 1 meter? 4,000 feet? Add that number to your height of eye (in the same units, of course).
by 13m if you took the measurement in meters, or multiply by 1.
Calculate the actual distance you'd have to traverse to get to the horizon by using the following formula.
d = R * arccos (R/ (R + h)), where
• d = distance to horizon
• R = radius of the Earth
• h = height of eye
Increase R by 20% to compensate for the distorting refraction of light rays and to arrive at a more accurate measurement.
Assume a flat plane or the ocean.
This method is a simpler version of the first set of instructions presented in this article, and applies only in feet and miles.
Solve for the distance in miles by plugging in your height of eye in feet (h) into the formula.
The formula you will be using is d = 1.2246* SQRT (h).
Derive the formula from the Pythagorean theorem.
Solving for h (making the assumption that R>>h and expressing the radius of the earth in miles, approx. 3959) yields the expression:
The following table compares horizon distances for 'flat' parts of the Earth (R E = 6371 km), the Moon (R L = 1737 km) and Mars (R M = 3390 km). Note that these radii are mean radii. The observer heights are in metres, but the horizon distances in the main part of the table are in kilometres.
How far away is the horizon? - BBC Science Focus Magazine
From the top of Mauna Kea on Hawaii, an extinct volcano about 4 km high (also the site of important astronomical observatories), the horizon should be about twice as distant, 226 km.
