#
`earth_radius` documentation

`earth_radius` gives the radius of the Earth.

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## Contents

## Syntax

r = earth_radius r = earth_radius(lat) r = earth_radius(...,'km')

## Description

`r = earth_radius` returns `6371000`, the nominal radius of the Earth in meters.

`r = earth_radius(lat)` gives the radius of the Earth as a function of latitude.

`r = earth_radius(...,'km')` returns values in kilometers.

## Example 1: Nominal radius

Get the nominal Earth radius in meters:

earth_radius

ans = 6371000

...or in kilometers:

```
earth_radius('km')
```

ans = 6371

## Example 2: Latitude dependence of Earth's radius

The Earth is more of an ellipsoid than a sphere, meaning its radius depends on latitude. Percentage-wise, how far off is the nomonal Earth radius at the Equator?

100*(earth_radius-earth_radius(0))/earth_radius(0)

ans = -0.1119

That says the nominal Earth radius of 6371 km is about a tenth of a percent smaller than the true radius at the Equator. Should we expect the same error at the North Pole?

100*(earth_radius-earth_radius(90))/earth_radius(90)

ans = 0.2241

In fact, the nominal radius is about *two* tenths of a percent larger than the true radius at the poles. Here's Earth's radius as a function of latitude:

lat = 0:90; r = earth_radius(lat,'km'); plot(lat,r) axis tight box off hline(earth_radius('km')) % the nominal earth radius xlabel latitude ylabel 'radius (km)' legend('latitude dependent','nominal') legend boxoff

## Example 3: A grid

Use `cdtgrid` to make a global grid, and `earth_radius` to get Earth's radius at each point on the grid:

```
[lat,lon] = cdtgrid;
r = earth_radius(lat,'km');
```

Plot them on a globe with `globepcolor`:

figure globepcolor(lat,lon,r) globeborders % plots political boundaries globegraticule % plots grid lines axis tight % removes empty space cb = colorbar; ylabel(cb,'radius (km)')

## Author Info

This function and supporting documentation were written by Natalie S. Wolfenbarger and Chad A. Greene for the Climate Data Toolbox for Matlab, 2019.