lpetrich
Contributor
Our planet has not one highest mountain, but three highest mountains, depending on what definition one uses.
If one uses height above sea level, then the highest mountain is Mt. Everest in the Himalaya Mountains in Nepal and China.
If one uses distance from the center of the Earth, then the highest mountain is Mt. Chimborazo in the Andes in Ecuador.
If one uses height above neighboring terrain, then the highest mountain is Mauna Kea in the Hawaiian Islands in Hawaii, United States.
Of these, height above sea level is the most related to climbing difficulty, since it approximates the geopotential difference, where the geopotential is the sum of the gravitational and centrifugal potentials. Potential energy = geopotential * mass, meaning that one needs input to increase one's geopotential, and more geopotential increase means more energy.
To lowest order, (geopotential difference) = (acceleration of gravity) * (height), and that means that the same height of mountain will be a more difficult climb at the poles than at the equator, though the difference is only about 0.5%.
Sea level is at approximately constant geopotential, because any higher-geopotential bit of ocean would try to flow into some lower-geopotential bit of ocean. The same is true of the atmosphere, and its density and pressure are thus approximate functions of the geopotential. Higher geopotential is thus another measure of climbing difficulty, because air gets very thin at high altitudes.
If one uses height above sea level, then the highest mountain is Mt. Everest in the Himalaya Mountains in Nepal and China.
If one uses distance from the center of the Earth, then the highest mountain is Mt. Chimborazo in the Andes in Ecuador.
If one uses height above neighboring terrain, then the highest mountain is Mauna Kea in the Hawaiian Islands in Hawaii, United States.
Of these, height above sea level is the most related to climbing difficulty, since it approximates the geopotential difference, where the geopotential is the sum of the gravitational and centrifugal potentials. Potential energy = geopotential * mass, meaning that one needs input to increase one's geopotential, and more geopotential increase means more energy.
To lowest order, (geopotential difference) = (acceleration of gravity) * (height), and that means that the same height of mountain will be a more difficult climb at the poles than at the equator, though the difference is only about 0.5%.
Sea level is at approximately constant geopotential, because any higher-geopotential bit of ocean would try to flow into some lower-geopotential bit of ocean. The same is true of the atmosphere, and its density and pressure are thus approximate functions of the geopotential. Higher geopotential is thus another measure of climbing difficulty, because air gets very thin at high altitudes.