# earth_radius documentation

earth_radius gives the radius of the Earth.

## 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.