# Absolute height of a mountain

## Highest Mountains (according to standard view)

 Asia Qomolangma Feng 8848m South America Aconcagua 6959m North America Mt. McKinley 6193m Africa Kibo 5895m Europe Elbruz 5642m Antartica Vinson Massif 5140m Australia & Oceania Punjak Jaya 5030m

The absolute height of a mountain *

By Karl G.B. Wendekreis
**

We define the absolute height of a mountain as its relative height, which is the height which appears in most reference works, plus the distance to the centre of the earth.

Eq.
1

To determine the absolute height, we need some standard geometrical formulae.

Eq.
2

Eq.
3

Eq. 4

Figure 1 gives a graphical explanation of the used equations.

Figure
1. Graphical representation of key parameters.

As the distance from the poles to the centre of the earth is smaller than the distance from the equator to the centre of the earth, one can expect mountains with a small latitude (situated close to the equator) to have a large absolute height.

It is straigthforward that the absolute height can be calculated by combining the well-known eleptoic earth constants together with the latitude and the relative height.

This will be shown by comparing the absolute height of Quomolangma Feng with some mountains situated close to the equator. The necessary data are presented in Table 1 and Table 2.

 Name Country Height (standard view) Latitude Quomolangma Feng China/Nepal 8848m 28°, N Nev. de Huascarán Equador 6768m 9°, S Chimborazo Equador 6310m 2°, S Cayambe Peru 5790m 0°, S

Table
1. Relative height and latitude of key mountains.

 Distance to the equator (a) 6378137m Distance to the poles (b) 6356752m

Table
2. Ellipsoid Constants (GRS-1980).

The derivation is not left as an exercise to the reader.

 Eq. 3 Eq. 5 Eq. 2 Eq. 6 Eq. 5, Eq. 6 Eq. 7 Eq. 6, Eq. 7 Eq. 8 Eq. 4, Eq. 8 Eq. 9 Eq. 1, Eq. 9 Eq. 10

By applying Eq. 10 to the given data, the results *** become apparent (Table 3). It is evident that the absolute heighest mountain on earth is the Chimborazo.

 Name h z |h| Chimborazo 6310m 6378110m 6384420m Nev. de Huascarán 6768m 6377611m 6384379m Cayambe 5790m 6378137m 6383927m Quomolangma Feng 8848m 6373405m 6382253m

Table
3. Absolute height of key mountains.

* An extented version of this paper is published in the Journal of Derived Mathematics, Is. Jan. 1999.

** Doctor Karl G.B. Wendekreis is lector at the Elbruz Science Institute in Chamonix (Fr.). He publishes on various mathematical subjects.

*** The calculations were made on a multi-processor Cytrix-306. The FORTRAN program lasted 17 hours.