The two inner planets, Venus and Mercury, are always close to the sun in the sky, because they are inside the orbit of the earth. The angle of separation between the Sun and the inner planets is called the angle of elongation. This angle varies throughout the year. When the angle is at a maximum, it is called greatest elongation. Because greatest elongations happen at different times, we can use this knowledge to plot the orbit of the inner planet.

As can be seen above, when a planet is at greatest elongation, then the site line from the earth to the planet is tangent to the orbit of the planet. If you have a list of dates when the planet is at greatest elongation, and what the elongations are, then it is pretty easy to plot the orbit of the planet. For each date, we know where the earth is in its orbit. Then we can draw a line at the angle of greatest elongation. Lastly, draw in the radius of the orbit that hits the site line at a 90 angle.

This works because the next time the inner planet is at greatest elongation, the earth will be in a different place in its orbit, so that we will be able to plot another point. With enough data, we can plot points all around the orbit.

We can also use greatest elongation to easily calculate the distance between the Sun and the inner planet. There is a right triangle, and the hypoteneuse is 1 astronomical unit (AU) by definition. Calling the distance between the Sun and the planet R, we can therefor say