# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

## Syntax

`Re = effearthradiusRe = effearthradius(RGradient)`

## Description

`Re = effearthradius` returns the effective radius of spherical earth in meters. The calculation uses a refractivity gradient of `-39e-9`. As a result, `Re` is approximately 4/3 of the actual earth radius.

`Re = effearthradius(RGradient)` specifies the refractivity gradient.

## Input Arguments

 `RGradient` Refractivity gradient in units of 1/meter. This value must be a nonpositive scalar. Default: `-39e-9`

## Output Arguments

 `Re` Effective earth radius in meters.

collapse all

The effective earth radius is a scaling of the actual earth radius. The scale factor is:

`$\frac{1}{1+r\cdot \text{RGradient}}$`

where r is the actual earth radius in meters and `RGradient` is the refractivity gradient. The refractivity gradient, which depends on the altitude, is the rate of change of refraction index with altitude. The refraction index for a given altitude is the ratio between the free-space propagation speed and the propagation speed in the air band at that altitude.

The most commonly used scale factor is 4/3. This value corresponds to a refractivity gradient of .

## References

[1] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.