Evaluation of 14th-order harmonics in the geopotential

The Earth's gravitational potential is now usually expressed in terms of a double series of tesseral harmonics with several hundred terms, up to order and degree at least 20. The harmonics of order 14 can be evaluated by analysing changes in satellite orbits which experience 14th-order resonance, when the track over the Earth repeats after 14 revolutions.In this paper we describe our first evaluation of individual 14th-order coefficients in the geopotential from analysis of the variations in inclination and eccentricity of satellite orbits passing through 14th-order resonance under the action of air drag. Using results from eleven satellites, we find the following values for normalized coefficients of harmonics of order 14 and degree l, C?_{l, 14} and S?_{l, 14}, for l=14, 154. 22:

$\text{l}$	109C?$\text{l,14}$	109S?l,14
-	-	-
14	?38.5 ±2.9	?7.8 ±2.2
15	4.5 ±1.1	?23.8 ±0.3
16	?22.3 ±3.6	?36.0 ±3.8
17	?15.0 ±2.6	16.8 ±1.2
18	?24.0±4.9	?3.2 ±3.7
19	?1.6 ±2.8	?7.6 ±1.0
20	8.8 ±5.8	?15.4 ±4.6
21	18.2 ±3.6	?10.6 ±1.9
22	?14.5 ±8.1	9.9 ±6.4
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