Measuring the Atmosphere from Inside the Moon's Shadow

On 12 August 2026, I spent a very hot afternoon waiting for the Moon to turn day into night. We were staying with friends in Portugal, so the observing site had been chosen by balancing driving distance, the weather forecast, an unobstructed western horizon, and a suitably memorable setting. The result was the Castillo de Coyanza at Valencia de Don Juan in Spain. The iPhone Weather app showed 36°C while I waited in the shade below the castle, hoping that the eclipse would at least provide some natural air conditioning.

Nir Shaviv waiting in the shade beside the Castillo de Coyanza before the eclipse — Figure 1.Waiting below the Castillo de Coyanza at 18:07 CEST, about 85 minutes before first contact.

Waiting for the shadow

This was the first total solar eclipse visible from the Iberian Peninsula in more than a century. It was also an awkward eclipse: totality arrived shortly before sunset, with the Sun only about $9.4^\circ$ above the horizon. A clear view toward the west-northwest mattered as much as being inside the path of totality. The Instituto Geográfico Nacional gave first contact at 19:33:19 CEST, maximum eclipse at 20:29:44, and a little under 100 seconds of totality at Valencia de Don Juan.

The fully eclipsed Sun was extraordinary, of course. Yet the photograph that became most interesting scientifically was not the close view of the corona. It was the panorama of the entire western sky.

The dark disk of the Moon surrounded by the solar corona above silhouetted leaves — Figure 2.The fully eclipsed Sun only about nine degrees above the western horizon. The foreground leaves help convey how low it was.

A panorama with geometry

The original panorama retains unusually useful metadata. It was recorded at 20:29:19 CEST—only 25 seconds before maximum eclipse—from latitude $42.291108^\circ$ N, longitude $5.522514^\circ$ W, and an indicated elevation of about $762\,\mathrm{m}$ . The recorded camera direction was $269.0^\circ$ , almost due west, while the Sun was at azimuth $281.5^\circ$ .

The image therefore spans approximately the southern, western, and northern horizons, with the eclipsed Sun near the middle. Across the horizon one can see the dark atmosphere inside the Moon’s shadow bordered by warmer yellow and orange light where sunlight still reaches the air outside it.

The strongest warm boundary begins at an azimuth of about $261^\circ$ , roughly $20^\circ$ south of the Sun, and rises to approximately the Sun’s apparent elevation of $9.4^\circ$ . Those two angles, together with the exposure time, provide the geometry needed for a better estimate.

Wide panorama during totality showing the eclipsed Sun above a dark horizon with orange illuminated atmosphere on both sides — Figure 3.The Moon's shadow projected through the atmosphere above Valencia de Don Juan at 20:29:19 CEST. The eclipsed Sun is near the center; the especially useful boundary for the estimate below is the southwestern, left-hand side of the illuminated atmosphere.Select the photograph to open the full-resolution panorama.

The shadow at 20:29:19

The NASA eclipse path was about $300\,\mathrm{km}$ wide in this part of Spain. The castle lay roughly $67\,\mathrm{km}$ south of the centerline and $81\,\mathrm{km}$ from the nearest southern limit of the complete ground track. That is useful for locating the observing site within the path, but it is not the relevant distance for a particular direction at a particular instant.

The Moon’s shadow on the ground was highly elongated because the Sun was so low. The purple curve below is the instantaneous umbral footprint calculated for the exposure time from NASA’s Besselian elements. The same calculation gives second and third contact at 20:28:47 and 20:30:29 CEST, within about two seconds of the independently predicted local circumstances. The plotted boundary uses the standard smooth-limb, no-refraction model; kilometre-scale corrections do not affect the precision claimed below.

Official IGN map of the 2026 eclipse path over northwestern Spain, overlaid with the instantaneous umbral footprint and the observed azimuth from Valencia de Don Juan — Figure 4.The official Spanish IGN eclipse-path map with the instantaneous ground umbra at 20:29:19 CEST superposed in purple. The red sightline is at azimuth 261°. It crosses the ground edge after about 76 km; the diamond is the plan projection of the point where the rising sightline exits the three-dimensional shadow. Map adapted from Observatorio Astronómico Nacional–IGN, CC BY 4.0 ign.es; shadow calculation and annotation by ScienceBits from NASA's Besselian elements.Select the map to open the complete official path map.

How high was the illuminated air?

Hand-drawn oblique diagram of the Sun, Moon, Earth's atmosphere, the umbral cone, and a red sightline from an observer crossing the cone into illuminated air — Figure 5.Qualitative geometry, not to scale. The observer is inside the umbra; the red sightline points generally sunward but obliquely across the three-dimensional cone, leaving the shadow before reaching sunlit upper atmosphere. The calculation below replaces this notebook sketch with the Besselian geometry.

Consider a ray leaving the camera at azimuth $A=261^\circ$ and elevation $\alpha=9.4^\circ$ ,

\boldsymbol r(s)=\boldsymbol r_0+s\,\hat{\boldsymbol n}(A,\alpha).

For every point on this ray, the Besselian elements give its coordinates $(\xi,\eta,\zeta)$ in the fundamental plane. The point leaves the umbra when its distance from the shadow axis equals the local radius of the umbral cone,

(x-\xi)^2+(y-\eta)^2 =\left[-\left(l_2-\zeta\tan f_2\right)\right]^2.

Solving this equation at 20:29:19 CEST gives $s\simeq89\,\mathrm{km}$ . The intersection lies at a height of $15.9\,\mathrm{km}$ above sea level, which I would simply quote as about $16\,\mathrm{km}$ . The projection of that point onto the Earth is about $88\,\mathrm{km}$ from the castle along azimuth $261^\circ$ .

That is close to the tropopause in summer at this latitude. The agreement is enticing, but the number should not be over-interpreted. The colored band is not light reflected from a solid atmospheric ceiling. It is light scattered along an extended path through air whose density, illumination, aerosols, and extinction all change continuously. The calculation estimates an effective scattering height, not the “height of the atmosphere.”

How much did the eclipse cool the air?

The temperature question has two different answers. The direct solar heating felt by a person disappears almost immediately, so the subjective cooling can be dramatic. The air temperature responds more slowly because the ground, vegetation, and a substantial layer of air all store heat.

A simple clear-sky calculation gives the approximate solar power that would have reached a horizontal surface in the absence of the eclipse:

Time	Solar elevation	Uneclipsed irradiance
First contact, 19:33	$19.8^\circ$	$312\,\mathrm{W\,m^{-2}}$
20:00	$14.9^\circ$	$224\,\mathrm{W\,m^{-2}}$
20:15	$12.1^\circ$	$174\,\mathrm{W\,m^{-2}}$
Panorama, 20:29:19	$9.4^\circ$	$125\,\mathrm{W\,m^{-2}}$

If $f_{\rm occ}(t)$ is the fraction of the solar disk hidden by the Moon and $G_{\rm clear}(t)$ is the clear-sky irradiance, the solar energy missing up to the time of the panorama is approximately

Q_{\rm miss}(t_{\rm photo}) =\int_{t_1}^{t_{\rm photo}} f_{\rm occ}(t)G_{\rm clear}(t)\,dt \simeq3.7\times10^5\,\mathrm{J\,m^{-2}}.

This is not the deficit over the complete eclipse. It stops at 20:29:19, about 30 seconds after totality began. Only about $4\times10^3\,\mathrm{J\,m^{-2}}$ accumulated during those first 30 seconds of totality; nearly all the missing energy by then came from the preceding partial phase. The temperature estimate below is therefore the decrease accumulated by the time of the photograph, relative to the uneclipsed evening—not additional cooling after totality.

For an illustrative near-surface layer of depth $H$ , the temperature response can be written

\Delta T\sim \frac{\eta Q_{\rm miss}}{\rho c_p H},

where $\eta$ is the fraction of the missing solar energy that would otherwise have become sensible heat. Taking $\eta=0.3$ – $0.5$ , $H=100$ – $200\,\mathrm{m}$ , $\rho\simeq1.1\,\mathrm{kg\,m^{-3}}$ , and $c_p\simeq1005\,\mathrm{J\,kg^{-1}\,K^{-1}}$ gives an eclipse-induced cooling of roughly $0.5$ – $1.7^\circ\mathrm{C}$ . I would quote the result more conservatively as about $0.5$ – $1.5^\circ\mathrm{C}$ relative to an evening without an eclipse, perhaps approaching $2^\circ\mathrm{C}$ under especially calm conditions.

This is smaller than the ordinary cooling between a scorching late afternoon and sunset. It is also smaller than many midday eclipse measurements: observations during the 2024 total eclipse in New York found an average peak cooling of $2.8^\circ\mathrm{C}$ , occurring about 17 minutes after totality (Wang et al., 2024). Our Sun was already low and weakening quickly. Without a shielded thermometer and a nearby uneclipsed control, the eclipse contribution cannot be separated cleanly from the normal evening decline.

A moving sunset

The first returning piece of the photosphere ended totality, but it did not restore the afternoon. Sunset was already approaching. The atmosphere had experienced a rapid radiative switch-off superposed on its normal evening transition—an abbreviated night that moved across Spain at supersonic speed.

The first bright portion of the Sun returning at the end of totality above silhouetted leaves — Figure 6.The first brilliant photosphere returns at the end of totality. Air temperature responds with a lag, even though the return of direct radiant heating is immediate.

That night we drove back to Portugal in time for a second astronomical event: the Perseid meteor shower. It was, rather obviously, a moonless night—the Moon had just passed in front of the Sun. We counted about 40–50 meteors before finally going to sleep, very happy.

The eclipse had been planned as an astronomical observation. The panorama turned it into a small atmospheric experiment as well. That is a fitting way to reopen ScienceBits on its upgraded site after a six-year lull—years in which I was busy with other things, including a pandemic and a war. Start with a spectacular sight, ask what else the photograph contains, and then see how far a few geometrical and thermodynamical estimates can take us.