The Earth's palaeorotation, postglacial rebound and lower mantle viscosity from analysis of ancient Chinese eclipse records

Abstract

Of the forces changing the Earth's rotation, tidal braking and postglacial rebound predominate at a timescale≥10² yr (Hide andDickey, 1991;Dickey, 1992). Analysis of ancient eclipse records has given values for the clock error ΔT and the time derivative of the Earth's dynamic oblateness$\dot J_2$ for the past 3,300 yr. Since ΔT=AT-UT=ct ², whereAT is Atomic (cesium clock) Time,UT is Universal (Earth rotation) Time, andt is the number of centuries before 1800, the oldest data have the most weight. Sunrise and sunset eclipses are especially valuable, as they can be retrospectively timed.

TheBamboo Annals, entombed in 299 B.C. and unearthed in A.D. 281, states that “in the first year of King Yi of the Western Zhou dynasty the day dawned twice at Zheng (34.5°N, 109.8°E)”.Kaiyuan zhanjing (Siddhartha, A.D. 724) cites this passageand adds that “in the 2nd (actually 12th) year of Sheng Ping reign period of King Shang (actually King Xi) the day began twice at Zheng”. Matching these records with the April 21, 899 B.C. and April 4, A.D. 368 sunrise eclipses (Oppolzer eclipse Nos. 732 and 3747) gave ΔT values of 5.8±0.15 and 1.7±0.1 hr, respectively. The recurrence of a central solar eclipse at the same site under almost identical circumstances accurately links up an ancient ΔT value with a more precise medieval one, and makes the statistics of such early data more robust.

The brightness changes for the magnitudes 0.95–0.97 and 0.991–0.998 eclipses were greater than those for the January 4, 1992 “double sunset” over Southern California, U.S.A. (magnitude 0.91–0.92). David H. Levy noted that “... as annularity ended. Sunset had come and gone, but the sky began to brighten not darken. For almost 15 minutes it continued to brighten until the onrushing shadow of Earth took over and darkness fell again ...” (Sky Telesc.83, 694). We have analyzed even earlier records from the Shang dynasty.

Six solar eclipse records have been identified among 160,000 oracle bones unearthed from the Shang dynasty capital Anyang (36.1°N, 114.3°E). Four of the 12th-century-B.C. inscriptions have cyclic days of 18, 42, 17 and 25. The chinese 60-day cycle is like our week in design, and has been in continuous use from time immemorial. These records have been uniquely matched to the sunrise eclipses of June 7, 1172 B.C. and October 31, 1161 B.C., and sunset eclipses of October 21, 1198 B.C. and June 27, 1163 B.C., respectively. Using visibility constraints on the rising and setting eclipsed Sun from Anyang we have derived upper or lower limits on ΔT. Three of them cluster around 7 hr 10 min, consistent with a ΔT of 7 hr 20 min, from the analysis of a record of the June 5, 1302 B.C. total solar eclipse, which states that “three flames ate the Sun, big stars were seen”.

Analysis of our data gave an equation of best-fit of ΔT=(30±2.5)t ², for the secular lunar acceleration rate$\dot n_{moon} = - 26''/cen^2$ (Williams et al., 1992). From this we derived an$\dot \omega /\omega$ of −(19±1.6)×10⁻¹¹/yr, where ω is the angular velocity of the Earth's rotation. Subtracting a tidal$\dot \omega /\omega$ of −27.8×10⁻¹¹/yr (Lambeck, 1980) gave a nontidal$\dot \omega /\omega$ of (9±1.6)×10⁻¹¹/yr, which is equivalent to a$\dot J_2$ of −(4.5±0.8)×10⁻¹¹/yr. The average$\dot J_2$ for the past 3,300 yr is larger than the present$\dot J_2$ from satellite laser ranging, −3×10⁻¹¹/yr (Cheng et al., 1989), as expected. Both$\dot J_2$ values are consistent with postglacial rebound from an upper mantle of viscosity 10²¹ Pa s, and a lower mantle of viscosity (2–4)×10²¹ Pa s, deformed by Pleistocene ice sheet loading (Peltier, 1985).

Our mantle viscosity values are consistent with those from the analyses of free air gravity anomalies and relative sea-level variations (Mitrovica andPeltier, 1991, 1992). Accurate values of the mantle viscosity are critical to our understanding of thermal convection patterns, that are responsible for plate tectonics (Peltier, 1986). Finally, the bounceback to its less oblate interglacial shape makes the Earth spin faster, overcoming a third of the tidal braking by the Moon and Sun. The net effect has been lengthening the day by 1.64±0.14 msec/cen.