In 1702, Pierre de La Hire made a curious observation about Earth's umbra. In order to accurately predict the duration of a lunar eclipse, he found it necessary to increase the radius of the shadow about 1% more than is warranted by geometric considerations. Although the effect is clearly related to Earth's atmosphere, it is not completely understood, since the shadow enlargement seems to vary from one eclipse to the next. The enlargement can be measured through careful timings of lunar craters as they enter and exit the umbra.
Such observations are best made using a low-power telescope and a clock or watch synchronized with radio time signals. Timings should be made to a precision of 0.1 min. Record the instant when the most abrupt gradient at the umbra's edge crosses the apparent center of the crater. In the case of large craters like Tycho and Copernicus, record the times when the shadow touches the two opposite edges of the crater. The average of these times is equal to the instant of crater bisection.
As a planning guide, tables of predicted umbral immersion and emersion times for up to 20 well-defined craters are given for every total and partial lunar eclipse each year. You should be thoroughly familiar with these features before viewing an eclipse in order to prevent confusion and misidentification. The four umbral contacts with the Moon's limb can also be used in determining the shadow's enlargement. However, these events are less distinct and therefore difficult to time accurately. Observers are encouraged to make crater timings and to send their results to Sky & Telescope (Sky & Telescope, 90 Sherman Street, Cambridge MA 02140-3264, USA) for analysis.
Note that all predictions presented here use Danjon's rule of shadow enlargement (see: Shadow Diameters and Lunar Eclipses). In particular, the diameter of the umbral shadow has been calculated assuming an enlargement of Earth's radius of 1/85 to account for the opacity of the terrestrial atmosphere. The effects of Earth's oblateness have also been included.