GPS Satellites Orbits: Resonance

Table 3

Amplitude and period of perturbations due to the 2 : 1 resonance: 𝐽₂+𝐽₂₂.

Orbital elements			Amplitude			Period
𝑎𝑜=26561.770km	𝑒	𝑖	▵𝑎max	▵𝑒max	▵𝑖max(°)	t(days)
𝑎𝑜 + 0.430	0.01	4°	12 km	0.014	8.7 × 10^-4	2500
𝑎𝑜 + 0.718	0.01	4°	12.5 km	0.0145	8.6 × 10^-4	7000
𝑎𝑜 + 0.290	0.01	4°	4.5 km	0.0065	3.6 × 10^-4	2000
𝑎𝑜 + 0.500	0.01	4°	3 km	0.0045	2.8 × 10^-4	1000
𝑎𝑜 −2.5	0.01	4°	6.5 km	0.0085	4 × 10^-4	1700
𝑎𝑜 −5	0.01	4°	1.4 km	0.0023	1.3 × 10^-6	500
𝑎𝑜	0.05	55°	1.8 km	0.005	2 × 10^-3	3200
𝑎𝑜 + 0.718	0.005	55°	2.75 km	0.006	2.8 × 10^-3	3900
𝑎𝑜 −1.770	0.005	55°	1.2 km	0.0045	1.4 × 10^-3	2000
𝑎𝑜 + 5.129	0.005	55°	900 m	0.0033	10^-3	1500
𝑎𝑜 + 3.729	0.005	55°	1.8 km	0.0055	1.9 × 10^-3	2500
𝑎𝑜	0.05	63.4°	7.5 km	0.003	10.8 × 10^-3	1000
𝑎𝑜 −2	0.05	63.4°	4 km	0.0015	5.7 × 10^-3	1000
𝑎𝑜	0.05	87°	7 km	0.0037	13.9 ×10^-3	2000
𝑎𝑜 −2	0.05	87°	3.5 km	0.002	10.3 × 10^-3	1900