Documentation

# effearthradius

Effective earth radius

## Syntax

Re = effearthradius
Re = 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.

## More About

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### Effective Earth Radius

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.

## See Also

#### Hybrid Beamforming for Massive MIMO Phased Array Systems

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