# Specifying ellipsoid models¶

In this exercise we will introduce some of the many ways one can specify the ellipsoid model used in projections and transformations.

We will be using the Mercator projection to illustrate the different ellipsoid settings, but note that the same parameter settings can be used for setting the ellipsoid used for most PROJ projections and transformations.

Download the gie file for the exercise: `ellipsoids.gie`.

Use a sphere of radius 1 as the ellipsoid model

Hint

Check the Mercator documentation to find out how to specify an ellipsoid

```operation   +proj=merc  <your answer here>
tolerance   1 cm

accept      24.745          59.437          # Talinn
expect      0.4319          1.2975
```

## Exercise 2. Specifying a ellipsoid¶

Set up a Mercator projection that uses the Hayford (International) ellipsoid

Hint

Check the Mercator documentation to find out how to specify an ellipsoid

Hint

Running `proj -le` will return a list of ellipsoids and their parameters.

```operation   +proj=merc  <your answer here>
tolerance   1 cm

accept      24.745          59.437          # Talinn
expect      2754709.2020    8238786.4803
```

## Exercise 3. Semimajor axis and inverse flattening¶

Specify the Hayford ellipsoid by its semimajor axis radius and inverse flattening

Hint

Find the parameters in the list returned by `proj -le`

```operation   +proj=merc  <your answer here>
tolerance   1 cm

accept      24.745          59.437          # Talinn
expect      2754709.2020    8238786.4803
```

## Exercise 4. Semimajor and semiminor ellipsoid axes¶

Set the Clarke 1866 ellipsoid by its semimajor and semiminor axis radii

```operation   +proj=merc  <your answer here>
tolerance   1 cm

accept      24.745          59.437          # Talinn
expect      2754630.7723    8238298.4968
```