Measuring the elongation of Venus

Updated 30 Apr 26

Given Mercury's proximity to the Sun, let's take it that measuring elongation will always be a challenge, so let's limit our investigation to Venus for now.

Measuring the elongation of Venus when it's distant from the Sun may seem easy enough in principle, if you have a clear view of the horizon -  just measure the direction on the horizon (azimuth) of the centre of the setting Sun and at the same time, record the azimuth of Venus and its altitude above the horizon and then determine the angular difference. However, given that the Sun will be bright and Venus much less so, perhaps it's going to be difficult in practice to observe both at the same time?

Wait then until the Sun has almost fully set, with just a remnant showing on the horizon, and Venus may be more obvious. Take measurements as before, but note the Sun's altitude is now one solar diameter (~ 0.5°) below the horizon, which we should probably take into account.

However,  refraction by the Earth's atmosphere will also make a difference to the measurements of azimuth of both Venus and of the Sun. At the moment we don't know how to quantify this effect, but hope that it will be similar in both. Let's not worry too much about this and consider our measurement an estimate only. One or two degrees in measuring greatest elongation is unlikely to make a massive difference to our estimate of the radius of the orbit of Venus, although it will of course have more significance for estimating that of Mercury.