Caption: "Geometry of a total solar eclipse." (Slightly edited.)

Features:

1. Because the Moon's umbra is very small at the distance of the Earth, only a small part of the Earth experiences totality (when the solar photosphere is completely covered) or NONE at all.

2. The Moon is about a quarter of the Earth in diameter.

   However, its umbra is much smaller than a quarter of the Earth's diameter.

   The image shows why this is so diagrammatically.

   Analysis of umbra size is given in the IAL subsection Umbra Size.

   But we do not need that analysis here. We just take the small Moon's umbra as a given.

3. The two possibilities of total solar eclipse and annular solar eclipse exist because the Moon's distance from the Earth varies because of the Moon's orbital eccentricity.

   Solar eclipses can happen when the Moon is at any of its distances during an almost exact nodal algnment (during an eclipse season): but total solar eclipses only when the Moon is relatively near and its umbra touches down on the Earth.

4. The region of the umbra on the Earth's surface, is a region of totality: i.e., region where the solar photosphere is NOT visible.

   Note the Sun has no sharp edge. The solar atmosphere just morphs into the solar wind as one moves outward.

   However, there is a relatively sharp layer from which most light escapes the Sun. That is the solar photosphere.

   One should NEVER look at the solar photosphere even the smallest part thereof without proper protection: i.e., a valid astronomical solar filter. We're always catching little glimpses of the solar photosphere, and so one shouldn't be paranoid about this. But minimizing those glimpses is best.

5. The outer parts of the Sun beyond the solar photosphere can be seen a bit around the Moon during totality with the naked eye. They can never been seen by the

   Only during totality is it safe to look at the Sun with the naked eye.

6. When the umbra does NOT reach the Earth's surface, then one has an annular solar eclipse (AKA annular eclipse).

   In this case, if you are located below the tip of the umbra's cone, you see the night side of the Moon centered on the Sun with a bright ring (i.e., an annulus) of the solar photosphere surrounding it.

   Since part of the solar photosphere is visible, you should NOT look at the Sun without proper protection: i.e., a valid astronomical solar filter.

7. The decider between total solar eclipse and annular solar eclipse is the distance to the Moon relative to the distance to the Sun.

   Both of these distances vary due to the eccentricities of the Moon's orbit (mean value e = 0.0549006 ∼ 5.49 %) and the Earth's orbit (e = 0.0167086 ∼ 1.67 %: J2000).

   So as NOT to go into complexities, we'll just say the Earth-Moon distance has to be a little less than its average value (384,748 km = 60.3229 Earth equatorial radii (R_eq_⊕ = 6378.1370 km)) for total solar eclipses since total solar eclipses are a little less frequent than annular solar eclipses.

   The frequency of solar eclipse types during eclipse seasons for calendar years 2000 BCE--3000 CE is total solar eclipses 26.7 %, annular solar eclipses 33.2 %, hybrid solar eclipses 4.8 %, partial solar eclipses 35.3 %, and total solar eclipses plus hybrid solar eclipses 31.5 % (see Fred Espenak: MrEclipse.com: scroll down ∼ 60 %). Hybrid solar eclipses flick between being marginally total solar eclipses and annular solar eclipses.

8. On the Earth's surface, the lunar umbra or eclipse path has a maximum width is 267 km (which must occur at about the Moon's perigee 362,600 km = 56.3505 R_earth_eq: see Wikipedia: Solar eclipse: Path) and the approximate maximum east-west extend is probably a bit less. The longest totality for any one place is 7 m, 32 s (see Wikipedia: Solar eclipse: Occurrence and cycles; Wikipedia: Solar eclipse: Path).
   The umbra tip on a surface perpendicular to umbra axis is a circle.

   But if the surface is NOT perpendicular to the umbra axis, the umbra tip could be stretched out as shadows are at sunset.

   Presumably, this stretching out effect is accounted for in the 267 km at most value reported above. But I cannot find a discussion of this fine point.

9. The fiducial minimum eclipse path velocity is the mean orbital velocity of the Moon moving approximately eastward in space minus the tangential speed of a point on the Earth's equator (which is moving exactly eastward at the maximum Earth surface velocity):

     v = 1.022 - 0.46511 = 0.5569 km/s = 33.41 km/m = 2005 km/h  .  

   The actual minimum eclipse path velocity varies a bit depending on various factors and is more typically ∼ 1700 km/h (see Wikipedia: Solar eclipse: Occurrence and cycles).

   The maximum fiducial eclipse path velocity occurs at the Earth's poles where the Earth's tangential velocity is zero. This maximum value is, of course 1.022 km/s = 3679 km/h.

10. The region or partial solar eclipse (i.e., the region of the Moon's penumbra on the Earth) is much larger than that of totality.

    To first order, the diameter of the region is just that of the Moon: 3464.2 km ≅ 0.273 Earth mean diameters (see Wikipedia: Moon).

    This size is obtained by just assuming the Sun's rays are all parallel, the Earth is a flat disk, and all of the Moon's penumbra lands on the Earth.

11. See the animation of the Solar eclipse of August 11, 1999 at SE1999Aug11T.gif to get a dynamic understanding of the geometry of total solar eclipses