Radius of the sun used for eclipse calculations

[WimDeMeester]

Hi all,

There was a very interesting Solar Eclipse Conference 2 weeks ago in Leuven, Belgium. One of the topics there was the influence of the radius of the duration of total solar eclipses, especially close to the border of the eclipse path. More information can be found here: https://www.besselianelements.com/

Turns out that the radius of the sun needed for calculating the most precise timings is 959.95, and not 959.63'' which is used most of the time. Which value is used in the astronomy library? Is there a possibility to select the solar radius?

[WimDeMeester]

Some more information from Luca Quaglia, who is investigating the solar diameter. A possible solution would be to make sure that we can give the following parameters when we calculate the eclipse information (these can be optional):

• Solar radius
• Lunar radius
• Delta t

Here is the information from Luca:

I see that there is a constant in the library defining the solar radius in kilometers

_SUN_RADIUS_KM = 695700.0

This is equivalent to 959.23” at 1au. This is the IAU nominal solar radius. If you substitute this number with:

696221.3

you will set the solar radius to 959.95” at 1au, the value we recommend.

Something else that could be tweaked is DeltaT. According to the function defined in the module, DeltaT on 2025 June 01 amounts to:

74.7s

In reality, DeltaT on that date is

69.1s

This is a substantial difference. Polynomial forecasts are handy, but you could tweak the code by using the actual values. Formulae are described here:

https://en.m.wikipedia.org/wiki/%CE%94T_(timekeeping)

and measurements and forecasts are available from IERS Bulletin A:

https://datacenter.iers.org/bulletins.php

Of course for future eclipses we need a forecasts of dUT1. It is very unlikely that a leap second will be inserted before TSE2026 and dUT1 is forecast to hardly change.

Something else to check is if the module computes limb corrections. They can amount to 1-2s even around the centerline.

A way in which lunar limb corrections have been “fudged” in the past is to tweak the lunar radius by taking a smaller lunar radius representative of the bottom of lunar valleys.
People have used the following ratio between the lunar radius and the equatorial Earth’s radius:

K2 = 0.272281

This is equivalent to:

1736.6km

If the function that compute eclipses uses

_MEAN_MOON_RADIUS_KM

the value could easily be tweaked.