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 one arc-minute larger than warranted by geometric considerations. Although the effect is clearly related to Earth's atmosphere, it's 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 minute. The basic idea is to record the instant when the most abrupt gradient at the umbra's edge crosses the apparent centre of the crater. In the case of large craters like Tycho and Copernicus, it's recommended that you 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, the predicted umbral immersion and emersion times for twenty well-defined craters has been generated for each lunar eclipse. The predictions assume a 2% enlargement of the umbra and include the effects of Earth's oblateness. Naturally, you should be thoroughly familiar with these features before 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 difficult to time accurately.
Observers are encouraged to make crater timings and to send their results to Sky and Telescope for analysis.
