Technical Note: Solar Eclipse Functionality

• For years up to 2006: values are taken from Jean Meeus Astronomical Algorithms, 2nd Ed., p.79 Table 10.A
• For years 2006 - 2024, values are from http://maia.usno.navy.mil/ser7/deltat.data
• For years 2024 - 2034, values are from http://maia.usno.navy.mil/ser7/deltat.preds
• For years beyond 2034, we implement these expressions: https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html

On a case-by-case basis, we update the Delta-T values contained in the NASA Besselian elements to match updated values from the USNO sites linked above. For example, TSE2017 has been updated from 70.3s (NASA) to 68.8373s (USNO) which better reflects the actual value vs predicted.

Calculation Methods

• Calculation of general eclipse characteristics is based on Jean Meeus, Astronomical Algorithms, 2nd Ed.
• Calculation of eclipse local circumstances and eclipse paths is based on Jean Meeus, Elements of Solar Eclipses 1951 - 2200; The Astronomical Almanac 2023; The Explanatory Supplement to the Astronomical Almanac, 3rd Ed.
• Eclipse paths are shown with a resolution of 0.1 degrees in longitude calculated for an observer at sea level (see Limitations)
• Azimuth, altitude and semidiameters of the Sun and Moon are derived from the Besselian elements for the purposes of the eclipse paths, simulator, and contact times.
• Elsewhere in the app, these values are calculated independently. The ephemerides used to derive the Besselian elements are not necessarily the same algorithms as used by the app and so minor discrepancies may be observed (in the order of 0.01 degrees or less).

Limitations

• Contact times are calculated assuming a smooth spherical moon. No correction is made for the lunar limb profile, which typically affects the timing of C2 and C3 by a few seconds, but up to ~15s in extreme cases.
• The assumption of a smooth moon restricts accuracy of the northern and southern eclipse path limits to within ±1-2km
• Eclipse path points are calculated at intervals of 0.1° longitude (11.1km intervals at the equator, 7.8km at ±45° latitude), including path end points. Always check the local circumstances by placing the primary (red) map pin - the timeline and simulator are unaffected by any approximations or inaccuracies in the calculated path
• Eclipse paths are calculated assuming an observer at sea level. For northern hemisphere observers located above sea level, the path will move southwards by some amount based on the circumstances of the eclipse, the height above sea level and the azimuth of the sea-level derived eclipse path. The adjustment is typically of the order of ~500m per 1000m of elevation, but becomes more extreme at locations towards the extreme of the eclipse path (i.e. when the sun/moon are low above the horizon)

Known Issues

• Eclipse paths crossing polar regions (latitude > ~|66°|) or which cross the anti-meridian (|180°|) may be incomplete or display discontinuities
• Occasionally an individual limit line may show single 'stray' points with a latitude discontinuity
• Some limit lines for eclipses with larger |ɣ| may on close inspection show zig-zagging near path ends
• We hope to correct these issues in future releases
• UPDATE: July 30 2023 - paths for the eclipses of Aug 1 2008 and June 21 2039 have been corrected (these previously showed phantom anti-meridian crossings)

Eclipse Simulator

The simulation accounts for:

• Passage of the moon in front of the sun, with positions and semidiameters derived from the Besselian elements
• Display of the diamond ring effect at the predicted contact position angles
• A simulation of the corona, chromosphere and solar prominences
• Darkening and lightening of the sky (illustrative, non-rigorous)
• The position of the horizon for eclipses near sunrise or sunset
• Changes in the parallactic angle and the physical ephemeris of the Sun and Moon over time
• Libration and the true lunar limb profile (details)
• Baily's beads

The simulation does NOT account for:

• Differential refraction near the horizon: the altitude of the Sun/Moon is corrected for refraction using the US Standard Atmosphere model, but the apparent limb shape of each body remains circular (or referenced to a circle in the case of the Moon)

Notes:

• The images used for the simulation come from the 2017 total solar eclipse (credit: Alison Craig and Stephen Trainor).
• The actual appearance of the corona and solar prominences varies over time and will not exactly match the simulation.
• The appearance, shape, and brightness of both the diamond ring and corona vary significantly based on your shot exposure and exact timing.
• The chromosphere is depicted with a thickness of 3.45 arc seconds, based on NASA's value of 2,500 km, and scaling up from 959.22″ (IAU) to 959.95″ (Quaglia et al.). See Advanced Solar Eclipse Planning for further details of simulator behavior with respect to the chromosphere.

Lunar Limb and Baily's Beads

Variations in the elevation profile around the lunar limb affect the appearance of Baily's Beads, especially at locations on the edge of the path of totality, and also the observed position angle of C2 and C3. 

• Lunar limb data courtesy of Kaguya/David Herald
• The simulator shows either a smooth limb or a libration adjust profile (Kaguya/Herald) as follows:
  • Kaguya/Herald limb is shown for PRO subscribers for all eclipses
  • Kaguya/Herald limb is shown for non-PRO subscribers for past eclipses only
  • Otherwise, or in case of network or web service outage, a smooth limb is used.
• You can check which limb is displayed by putting the simulator into outline mode. If a smooth limb is employed, anything that may look like a 'bead' is an artifact of pixel aliasing only.
• The full resolution (1800 points at 0.2° spacing) of the Kaguya/Herald data is always used for 'standard' bead appearance (i.e. raw pixels). For 'enhanced' beads (i.e. with 'bead flare') the resolution is determined by the resolution slider.
• The default solar radius used in the simulator only (not for purposes of contact time calculation) is 959.95″ (Quaglia, et al., 2021). The value is user adjustable.
• In photorealistic mode, for total eclipses the simulated diamond ring is shown at the standard smooth limb contact position angle. Use outline mode to visually identify limb corrected contact points.

Planning Recommendations

• For general planning and for locations well within the displayed path limits (i.e. > ~10km from path ends and northern/southern limits) the data provided is expected to be more than adequate  for planning purposes
• If you are planning to observe an eclipse from a location near the edge of the path of totality or annularity, or from a location high above sea level, you should consult multiple reliable sources in your planning, and in particular those which consider the lunar limb profile. We recommend:
  • Xavier Jubier's site
  • Fred Espenak's NASA pages
  • Occultation planning software via the International Occultation Timing Association
• Weather is a key consideration in observing an eclipse: for recommendations, historical research and more, see eclipsophile.com
• For detailed eclipse maps that show information not included on this site, see Great American Eclipse