Earth Orbits

Orbits are complicated, because they involve both position and velocity in three spatial dimensions and time. Simple two-body "Kepler" orbits relate the position and velocity at one time to the position and velocity at other times. In reality, orbits are also complicated by drag, light pressure, and gravitational perturbations by other bodies, and in the extreme by relativistic effects. For this discussion, we will not consider the complications, so that we get closed-form algebraic solutions. Of course, in real life, we will need to include all the complications in our calculations of orbital properties. Thinsats are deployed in closely packed orbital families. One central orbit, perfectly circular and in the orbital plane, with a sidereal period of 14393 seconds and a radius of 12789 kilometers, surrounded by slightly inclined and slightly elliptical orbits that fill a toroidal region around that central orbit. By carefully assigning orbital parameters, this region can be filled with densely packed orbits and objects in them.

Describing Earth Orbits

Orbits are ellipses in a plane which also contains the center of the mass that defines the orbit.

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Earth Orbit Parameters

system	status	number	planes	#/plane	perigee	apogee	inclination	period	uplink GHz	downlink GHz
Space Station	in use	1	1	1	6727	6736	51.6	5480	x	x
Iridium	in use	66	6	11	7158	7158	86.4	6027	Ka band	Ka band
Teledesic	bankrupt	288	12	24	7778	7778	98.2	6827	28.6-29.2	18.9-19.3
Globalstar	in use	48	x	x	7792	7792	52	6845	x	x
m288 core	empty	0	1	0	12789	12789	0	14393	x	x
m288 outer	empty	0	many	0	12739	12839	2.24	14393	x	x
O3b	planned	12?	1	12	14441	14441	0	17271	x	x
Molniya	in use	3?	3?	1	7885	45683	63.4	43082	x	x
GPS	in use	31	6?	-	26600	26600	55	43082	x	x
GEO	in use	361	1	-	42164	42164	0 to 14.3	86164	-	-
Moon	natural	1	1	1	364397	406731	5.14	2360592	x	x

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M orbits

orbit	passes	radius	radius	altitude	sidereal	max	45N max	45N azim	45N	visible	rads
	/ day	km	RE	km	per secs	latitd	elevation	degrees	ping ms	fraction	/sec
m120	12	7639	1.2	1261	6645	33.5	-10.2	---	---	---	2e-4
m160	9	9099	1.4	2721	8638	45.6	0.6	22.5	43	0.04	6e-3
m240	6	11540	1.8	5162	12338	56.5	12.4	97.1	56	0.21	8e-3
m288	5	12789	2.0	6411	14393	60.1	16.5	109.9	63	0.25	2e-3
m360	4	14441	2.3	8063	17271	63.8	20.6	121.1	73	0.29	2e-3
m480	3	16756	2.6	10378	21585	67.7	24.8	131.5	87	0.32	2e-3
m720	2	20295	3.2	13917	28774	71.7	29.1	141.4	110	0.35	2e-2
m1440	1	26586	4.2	20208	43141	76.1	33.5	151.4	150	0.39	1e-2
GEO	0	42164	6.6	42164	86164	81.3	38.2	162.4	253	0.43	5e-4