Background

How accurate is Moonfield?

Every number a model produces has an error bar, whether or not anyone prints it. This page states Moonfield's, where they come from, and when they stop being good enough.

Summary

The tide row is not a defect. See below.

Where the numbers come from

The Sun uses the low-precision method from Meeus, Astronomical Algorithms, chapter 25, a mean longitude plus a three-term equation of the centre. Meeus states 0.01° and our check against his worked example (JD 2448908.5) reproduces his apparent longitude to 199.90894° against his 199.90895°.

The Moon uses a truncated ELP-2000/82, Meeus chapter 47: 35 longitude and distance terms, 30 latitude terms, from a series with hundreds. Against Meeus's worked example (JD 2448724.5), we get 133.166783° against his 133.167265°, about 1.7 arcseconds, entirely from the truncation.

Full ELP-2000/82 would reach milliarcseconds. It would also be thousands of terms and unreadable, which defeats the purpose.

Rise and set are found by sampling every 10 minutes and then bisecting, rather than by a closed-form formula. Closed forms assume the body does not move during the day: acceptable for the Sun, poor for the Moon, which shifts about 13° between one sunset and the next.

Sunrise is defined at a geometric altitude of −0.833°: −0.567° for atmospheric refraction (Bennett's formula, Meeus ch. 16) and −0.267° for the Sun's radius, because "sunrise" means the upper limb.

What limits it

Refraction is genuinely uncertain. The standard formula assumes 10 °C and 1010 mb. Real refraction at the horizon varies with temperature, pressure and lapse rate, and on a cold clear morning over water it can differ by several arcminutes. This is a real physical limit, not a coding one, no algorithm fixes it, because the atmosphere is not in the algorithm.

For sunrise timing, refraction uncertainty dominates everything else we do.

Your horizon is not flat. All rise/set times assume a level, sea-level horizon. A hill to your east delays sunrise by far more than any error here. So does altitude, in the other direction.

Truncation. More terms would help the Moon slightly. The current error is smaller than the effects above, so it is not the bottleneck.

ΔT. For historical dates, the difference between Terrestrial Time and UT matters. Moonfield ignores it, which is fine for the present day and increasingly wrong before about 1900.

Why the tides are different

The tide model is not an approximation of a good model. It is a deliberately introductory model that is physically correct and operationally inadequate, for reasons explained at length in why local tides are hard.

Briefly: it computes the equilibrium tide, which assumes a deep uniform ocean responding instantly. The real ocean cannot move fast enough, is full of continents, and resonates. Real prediction requires harmonic analysis of a year or more of measurements at each specific station.

Errors of several hours in timing and a factor of several in range are normal and expected. moonfield tide compare exists to help you measure your local error rather than pretend it is not there.

Do not use Moonfield's tide output for anything where being wrong has consequences. The LICENSE says this too.

How this is checked

The test suite validates against three independent kinds of reference:

1. Textbook worked examples. Meeus's own examples, to his stated precision.
2. Published ephemeris values. New and full Moon times, solstices, sunrise

and sunset for known locations and dates.

1. Physical identities. Noon altitude must equal 90° − |latitude −

declination|. Equinox sunrise must be due east everywhere. Hemispheres must be opposite. These tests survive an algorithm rewrite, which stored numbers do not.

python -m pytest -v

If you find a case where Moonfield is worse than the table above claims, open an issue. A reproducible accuracy failure is a valuable contribution.

The general point

Every model here has a domain where it is useful and a boundary past which it is not. Knowing where that boundary is (and saying so out loud) is the difference between a tool and a black box.

That is why this page exists, and why the tide module is in the curriculum at all.