# Earthshine blog

## "Earthshine blog"

A blog about a system to determine terrestrial albedo by earthshine observations. Feasible thanks to sheer determination.

## Differential refraction

Data reduction issuesPosted by Daddy-o Aug 29, 2012 03:16PM
We have to determine the radius and centre of the lunar disc in order to reduce observations.

In doing that we must be aware that differential refraction causes the Moon to appear non-circular as it comes closer to the horizon. Using a formula from the Nautical Almanac Explanatory Supplement we generate the following table for 600 mmHg, 10 degrees C and 30% relative humidity:

Z d_refr am
------------------
27 1" 1.1
69 6" 2.8
75 12" 3.9

where z is the zenith distance in degrees, d_refr is the differential refraction in arc seconds and am is the airmass. The differential refraction is calculated over a 1-degree distance centred on the given zenith distance. Our FOV is about 1 degree wide and one pixel covers about 7".

We thus see that the Moon is differentially refracted by less than one pixel up to about 2.6 airmasses. Two pixels are reached about 26 degrees (4 airmasses) above the horizon.

Some of our observations are certainly close to the horizon, as we have tried to observe when the lunar phase is near or less than 30 degrees (at Newish Moon).

At 30 degrees the uncertainty in our determination of disc radius and disc centre (based on a circular assumption) is thus starting to be challenged by the differential refraction.