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I'm sure the answer to this question is, "it depends" but I'm hoping for a ballpark number here.

Let's assume you design a smallish satellite to point at the earth while orbiting. You have the ability to dump momentum to a magnetorquer, no problems there. What I'm curious is, how often does that process usually occur? Is that something that you can get the rotation of the satellite pretty close and only dump the wheels once a month? Or does that process usually need to happen more often due to an accumulation of other forces acting on the satellite?

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    $\begingroup$ Just one data point, not an answer: ESA INTEGRAL used hydrazine thrusters to offload control wheels about 14 times over 8 months. But that was done on a target-of-opportunity basis, whenever the satellite needed to be repositioned or there was some other break in observation, so it might have "needed" to be done less often. $\endgroup$ – Bob Jacobsen May 30 '19 at 21:32
  • $\begingroup$ With torquers it is done continuously over a dead band. At the same time ensuring, it does not corrupt magnetic field readings. $\endgroup$ – Prakhar May 31 '19 at 18:04
  • $\begingroup$ @BobJacobsen your comment is getting more at the "why am I asking" part of the question. If this is a process that doesn't need to be done very often, is it something that the propulsion system can take care of? Your answer says that this has been done in the past with hydrazine thrusters, so that's interesting to me. $\endgroup$ – Russell Jun 1 '19 at 13:12
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For some small sats, the unloading is done automatically by the attitude control system when the wheel gets to a particular speed. So that would depend on how much wheel momentum you accumulate over time, and that would depend on the ratio of the moment of inertia of the spacecraft compared to the moment of inertia of the wheel. Say you've got your spacecraft always -Z to Nadir, you're going to get 1 revolution of the spacecraft per orbit. You're also going to accumulate momentum because you're countering various other torques on the spacecraft (magnetic fields, aero drag, solar pressure).

Wheel bearing drag also factors into this. Especially if you're moving your satellite around (say, to point an antenna at the ground for a comm pass) - you'll accelerate and decelerate the wheels to do this and there's always some friction losses.

One practical example I know of is for a 6U in GEO that is always sun pointed, there's a thruster desaturation once a week. (not enough magnetic field to use magnetorquers)

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    $\begingroup$ " for a 6U in GEO that is always sun pointed, there's a thruster desaturation once a week." Where does this information come from? btw I've just asked Are there cubesats in GEO? $\endgroup$ – uhoh Jun 1 '19 at 12:14
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    $\begingroup$ It's for a future mission called SunRISE. So it's not in GEO, yet. $\endgroup$ – jimlux Jun 2 '19 at 13:05
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From my experience it is pretty common to do on the order of twice an orbit, it is very commonly done.

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    $\begingroup$ Momentum wheels become saturated every 45 minutes? $\endgroup$ – uhoh Jun 1 '19 at 12:19
  • $\begingroup$ This seems high to me... can you elaborate or provide any reasoning why that needs to be done so often? What forces are acting on the spacecraft that the wheels become saturated so quickly? $\endgroup$ – Russell Jun 1 '19 at 13:09
  • $\begingroup$ The magnetorquers usually are doing lots of work. This is based on my own observation, although it has been a while since I've seen actual data on this, and I wasn't looking for it... $\endgroup$ – PearsonArtPhoto♦ Jun 2 '19 at 2:11
  • $\begingroup$ There are a lot of forces that act on LEO satellites. Often by design they are slightly unstable by sunlight, which means they will always eventually point at the sun. $\endgroup$ – PearsonArtPhoto♦ Jun 2 '19 at 2:13
  • $\begingroup$ Since the torque can be fairly small compared to a thruster, maybe it needs to run quite frequently. Also, the two smaller components ($B_r, B_{\phi}$) vary in sign and magnitude around an orbit, I wonder if it is common or even necessary for a magnetotorquer to have to power on and off during each orbit during one long desaturation session. $\endgroup$ – uhoh Jun 2 '19 at 15:22

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