# Coriolis, Centrifugal and Gravitational Forces on the WGS84 Globe Model

The Calculator can be used to calculate the following accelerations on the WGS84 Reference Ellipsoid:

• Coriolis acceleration
• Centrifugal acceleration
• Sum of Coriolis and Centrifugal acceleration
• Gravitational acceleration due to earth's mass (not including Centrifugal acceleration)
• Effective Gravitational acceleration (including Centrifugal acceleration)
• Sum of Coriolis and Effective Gravitational acceleration (including Centrifugal acceleration)

All accelerations are presented as vector components in the following Coordinate Systems:

• (Forwd, Right, Up): local Coordinate System with respect to the moving object
• (X, Y, Z): global Earth Centered Earth Fixed (ECEF) Coordinate System
• (North, East): local North/East Coordinate System

The value Total is the magnitude of the acceleration, i.e. the length of the acceleration vector.

## Accuracy

The accuracy of the gravity calculations decreases with increasing altitude. If you want the result to an accuracy of ε (e.g. ε = 0.01 for 1% accuracy), Altitude h must not be greater than h = ε · a / 232 km, where a = 6378.137 km is the semi-major axis of the Reference Ellipsoid.

## Observations

The different accelerations have the following properties:

Coriolis: acts only in the X/Y plane, so it's Z component is always 0. Additionally it has only a left/right and up/down component with respect to the moving object, no forward component. The up/down component is called the Eötvös effect.

Centrifugal: acts only in the X/Y plane, so it's Z component is always 0, like the Coriolis acceleration. In the local coordinate system it has no east/west component, only a north/south and up component at any location on earth. Exceptions are the poles, where the centrifugal acceleration is 0, and the equator, where the north/south component is 0.

Coriolis + Centrifugal: act only in the X/Y, so it's Z component is always 0, because neither the Coriolis nor the Centrifugal acceleration have a Z component unequal 0.

Mass Gravity: The gravity vector that is caused by eart's mass alone is not perpendicular to the surface of the Reference Ellipsoid. It does not point to the center of the earth neither. Exceptions are the poles and the equator. The east/west component is always 0, but if the vector is not pointing exactly to the center of the earth, there is a small north/south component. The magnitude of the Mass Gravity is not constant, but depends on latitude. It can not be calculated by using the simple equation for Newton's law of gravitation, because this equation does only hold for exactly spherical bodies. The Calculator takes this into account.

Effective Gravity: This is the sum of the Mass Gravity and the Centrifugal accelerations. It acts alway exactly perpendicular to the surface of the Reference Ellipsoid, because the ellipsoidal shape of the earth is formed by the effective gravitational potential. Effective Gravity only has a down component everywhere on earth. It's magnitude depends on latitude. Note, the Effective Gravity vector does not point to the center of the earth. Exceptions are the poles and the equator.

Coriolis + Effective Gravity: In Effective Gravity the Centrifugal acceleration is included, so this is the sum of all accelerations acting on the rotating earth. Because neither the Coriolis nor the Effective Gravity accelerations have a forward component, the rotation of the earth and earth's gravity never create a forward acceleration. But there is a left/right and an additional up/down Coriolis acceleration, but only if the object is moving.

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