Sky and Telescope - June 2015 - 30

The Size and Shape of Earth's Umbra

The Shape of the Umbra
Inﬂuence of a season
or meteor shower?

120
100

20
0

Jan

Feb Mar Apr May Jun

Jul

Geminids

Taurids

Leonids

Orionids

Perseids

Lyrids

Eta Aquarids

Delta Aquarids

80
Quadrantids

Atmospheric "Notional Eclipseforming Layer" (NEL) Height (km)

140

Aug Sep Oct Nov Dec

Month
Contrary to past reports, the atmosphere's eclipse-forming
layer seems unaﬀected by the time of year or by the major
annual meteor showers.
2.6

Umbral enlargement (%)

2.4
2.2
2.0

Best-ﬁt line

1.8
1.6
1.4

Umbral enlargement varies
slightly with Moon's distance

1.2
1.0
0

Lunar distance (Earth radii)

Atmospheric NEL height (km)

120

The Online Data

100
Best-ﬁt line

Deduced NEL height seems
unrelated to Moon's distance
40
20
55

Lunar distance (Earth radii)
Middle: The farther the Moon is from Earth, the more our
atmosphere enlarges Earth's umbra compared to the size the
umbra would have without the atmosphere. But this eﬀ ect (the
tilt of the best-ﬁt line) is slight compared to the scatter from
one eclipse to another. Bottom: Whatever causes that to happen, the height of the atmosphere's "notional eclipse-forming
layer" (NEL) remains unaﬀected.

The most enduring oddity claimed for the umbra relates
not to its size, but to its shape. For example, crater timings led French astronomer Guillaume Joseph Le Gentil
to announce in 1755 that the umbra was larger northsouth than it was east-west. But how could that be, given
that Earth itself is "squashed" at the poles?
Then in the 20th century, a contrary supposed
ﬂattening of the umbra caught on. At various times
Bouška, Link, Ashbrook, and Soulsby all reported the
umbra to be wider east-west than it ought to be, even
allowing for Earth's slight spread at the equator and the
geometrical distortion in a converging light cone at the
Moon's distance.
Following their lead, G. F. Schilling (Rand Corporation) wrote in the March 1965 Journal of the Atmospheric
Sciences that a variation in the height of Earth's mesosphere (a zone from roughly 50 to 100 kilometers up)
by latitude could explain the added oblateness of the
shadow. Using measurements of noctilucent clouds as a
guide, Schilling suggested that the mesosphere's height
might vary from roughly 100 km at the equator down to
82 km at latitude 60° north or south.
°
Once again, however, the new database fails to agree.
On average, the umbra appears as if an occulting layer
87 km thick uniformly surrounds the (oblate) Earth.
This thickness, deduced from timings, does not vary
in a predictable way with the position angle around the
umbra - which is closely related to the latitude on Earth
that accounts for a given piece of the shadow's edge.
Nor does it show any periodic or long-term trend
over 170 years, despite the slow global warming that has
happened during the last 100 years and especially the
last 40. The timings do show the umbra to be oblate, but

June 2015 sky & telescope

The new crater-timing catalog is publicly available at
vizier.u-strasbg.fr/viz-bin/VizieR , with the designation
VI/140. It includes timings for the umbra contacting the
Moon's limb as well as the ingress or egress of individual
spots and craters. Each of the 22,539 records is accompanied by two calculated quantities: the percent enlargement of the umbra, and the NEL height that the timing
implies for that point on the umbra's edge at that time.
Each record also shows the name of the individual or
group who submitted it (a few are unknown). There are
764 names in all, including some people who made timings in their youth and went on to become well-known
professional astronomers.
For a more detailed report on the database and the
conclusions we draw from it, see "Analysis of Lunar Crater Timings, 1842-2011" by David Herald and Roger W.
Sinnott in the October 2014 Journal of the British Astronomical Association, pages 247-253.

http://vizier.u-strasbg.fr/viz-bin/VizieR

Sky and Telescope - June 2015

Table of Contents for the Digital Edition of Sky and Telescope - June 2015