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My question is restricted to global positioning systems (Regional ones have geosynchronous constraints, which limits drastically the orbit choice)

The diagram in this question highlights different altitudes for different constellations. This difference is also present in this comparison table. All global positioning system satellites are orbiting between 19130km (GLONASS) and 23222 km (GALILEO) (almost 20% difference in altitude).

Given the mission (which is quite similar), I would have expected less difference. Why do their operators decide to operate them at different altitudes?

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    $\begingroup$ Engineering is always a series of trade-offs. Higher orbits mean less propellant spent for stationkeeping and longer time in sight, but weaker signals. Different operators are going to have different sets of tradeoffs. $\endgroup$ – zeta-band Jun 19 '18 at 16:02
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See a related question.

Navigation satellites systems need a very precisely predictable orbits. A low orbit is influenced by not precisely predictable drag. A higher orbit is necessary to keep the influence of drag very low. To limit the number of necessary satellites, a high orbit is necessary too. A larger distance to ground increases the area on Earth where the satellite is visible and receivable.

To get very precise orbital data, the positions of the satellites must be measured from ground stations frequently. For measurement an orbit period of about 12 hours is used, the satellites will pass a ground station twice a day. For exact calculation, the length of a siderial day, 23 hours, 56 minutes and 4 seconds is used.

GPS uses 1/2 of a sideral day, 11:58:02 and an orbit height of 20192 km.

Other satellite navigation use similar orbit periods, 17 orbits per 8 to 10 sideral days.

Glonass uses 8/17 of a sideral day, 11:15:48 and an orbit height of 19140 km.

BeiDou uses 9/17 of a sideral day, 12:40:16 and an orbit height of 21224 km.

Galileo uses 10/17 of a sideral day, 14:04:45 and an orbit height of 23232 km.

The ratio of 1/2 may be also written as 17/34, the other ones as 16/34 , 18/34 and 20/34. The differences are small. Thus all satellites could be measured about twice a day from the same ground stations.

I calculated the orbit heights using an online calculator, the resulting values differ a little from those found in Wikipedia.

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    $\begingroup$ What's the significance of the 17 common denominator? $\endgroup$ – Russell Borogove Jun 19 '18 at 21:48
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    $\begingroup$ Can you elaborate on why GPS, GLONASS, Beidou, Galileo, etc. have chosen those altitudes/orbital periods (beyond being in a region with negligible drag)? For example, GPS chose 1/2 a sidereal day so that they have repeating ground tracks. $\endgroup$ – costrom Jun 20 '18 at 15:13
  • $\begingroup$ @Uwe I'm not sure 17 means anything. The satellites would be regularly visible wether or not their periods were rational fractions of a sidereal day because they are just so high. Checking by propagating all of the GNSS TLEs in Celestrak shows that the orbits are not really repeat ground track, I think the answer you link to is misleading. So I've just asked Does the “17” really mean anything with respect to GNSS orbits being rational factions of a sidereal day? $\endgroup$ – uhoh Jun 22 '18 at 2:56

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