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This story about receiving a roll of Space-Themed Florida State commemorative quarters from the Governor of Florida mentions that the New Horizons spacecraft had to be "spin-balanced" to grams-level precision.

What exactly does this mean mathematically? What exactly is being balanced?

I understand that New Horizons has both spin-stabilized (cruise) and three-axis stabilized (science) modes controlled entirely with hydrazine monopropellant, but does spin stabilization require careful balancing? I noticed that this answer about another spacecraft also explicitly mentions the need to balance carefully.

Stern accepted the roll from the governor, but explained he could only fly one. The others would be distributed to team members as a souvenir of the mission.

Less you think however, that the quarter flew simply as a gesture to the governor, it served a bonafide purpose on the spacecraft.

"For spin balance, we need to add a number of kilograms to various places [on New Horizons]," explained Stern. "We knew this was the case because the moments of inertia of the spacecraft and the dynamical properties of it, that we would have to trim it out down to literally the grams-level with balance weights. Of course, we had a whole variety of big ones and little ones; you start off with adding a kilogram here and a kilogram there and you end up getting smaller and smaller weights in various places until you're done. We used the coins to that purpose," he said. (emphasis added)

"Since we needed a counter balance to [the Florida state quarter], we decided to fly a second state quarter. We picked Maryland because that is where the spacecraft was built. And because we had so many people back in Maryland at the Applied Physics Lab and at Goddard, it was easy for someone to ship us a quarter really quick."

below: State of Florida Commemorative Quarter to be attached to New Horizons spacecraft. Maryland state quarter was also on board, but located at a different position for balance reasons. From here.

enter image description here


below: A separate example: LADEE going for a test spin. Looks frightening! Cropped from LADEE Spin Test:

To make sure that the spacecraft is perfectly balanced for flight, engineers mounted it onto a spin table and rotate it at high speeds, approximately one revolution per second. The team measured any offsets during the spinning, and then added small weights to the spacecraft to balance it. Once the spacecraft was balanced dry, the team loaded the propulsion tanks with fuel, oxidizer, and pressurant. The spin testing was performed again "wet," or with fuel, in order to see if the balance changed with the full fuel tanks.

enter image description here

below: A separate example: Curiosity(?) going for a test spin. Looks upside down! From Space Electronics:

Two-Plane Spin Balance Machines with Moment of Inertia Capability. Measure product of inertia, dynamic unbalance, center of gravity and moment of inertia.

enter image description here

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I am familiar with the spin dynamics of both New Horizons and Ladee, since I performed nutation fuel slosh tests on models of the spacecraft in my drop tower facility, Applied Dynamics Laboratories, in Oregon.

In the absence of on board liquids, primarily propellant, or other flexible elements, the spin motion will be stable about the intended principal axis. A small inbalance will produce a small wobble (motion of a desired spin axis around the principal axis) but this will not grow into an unstable motion causing increasing divergence between the two axes. Of course in the real world nothing is rigid and nearly all spacecraft carry on board liquids.

Their presence causes "nutation" which can either lead to either stable or unstable spin motion, depending on the spacecraft's inertia distribution. For an oblate shape (spin about the largest moment of inertia axis), the nutation is stable and will eventually die out. However most spacecraft (New Horizons and Ladee included) spin about their minimum axis of inertia and a small "seed" nutation will grow until the craft spins about the largest axis of inertia, resulting in a disastrous "flat spin" condition. To prevent this, an onboard active nutation control (ANC) system is used. This consists of a sensor (accelerometer or gyros) and small thrusters.

However, the ANC has to be robust enough to overpower the growing nutation, due primarily to propellant sloshing. This requires an understanding of the sloshing effect and that is done with the model drop tests.

You can read more about it here.

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    $\begingroup$ Welcome on the Space SE! $\endgroup$ – peterh - Reinstate Monica Aug 9 '18 at 16:44
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    $\begingroup$ Very nice answer, thank you! It seems to be in line with my speculation in comments below @Hobbes' answer, referring to this post though I'm still going to have to think a little more about this now. It's great that you found this question! $\endgroup$ – uhoh Aug 9 '18 at 19:33
  • $\begingroup$ Interesting that satellites are still sometimes designed to spin around their "wrong" axis; the problem of "flat spin" has been known for a long time. $\endgroup$ – Michael Seifert Jul 17 at 13:28
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During a spin stabilized cruise, the antenna dish should be pointed to earth precisely. The axis of rotation should be the axis of the antenna. If the space craft would be not precisely spin balanced, the axis of rotation and the antenna axis may be different and there may be a vibration. Both effects would disturb the antenna alignment to earth and impair data transmission in both directions from and to the spacecraft. For a clean rotation without vibrations, the space craft should be both static and dynamic balanced.
See https://en.wikipedia.org/wiki/Tire_balance and https://en.wikipedia.org/wiki/Rotating_unbalance

Careful balancing the spacecraft is also important to save the precious fuel for attitude control. For the rotation around the three axes there should be three pairs of thrusters. Each pair should be mounted symmetric to the center of mass. If there is a disbalance and the center of mass is not where it should be, firing one pair of thrusters may cause rotation of the spacecraft around more than one axis only. Stabilizing the attitude would require more fuel than necessary if unwanted rotations have to be controlled too.

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  • $\begingroup$ I can understand that it might be easier to add mass to align the principle axis with the antenna axis than to re-point the antenna along the existing principle axis, but it sounds like there is something more complicated going on. Isn't tire balance about centering the wheel center of mass on the fixed external shaft axis? There's no analogy of a drive shaft on a free spacecraft. $\endgroup$ – uhoh Apr 16 '17 at 14:49
  • $\begingroup$ The center of mass of the spacecraft should be on the axis of the antenna. All attitude control thrusters should be symmetric to the center of mass. If the axis of rotation is not parallel to the axis of the antenna, the direction of the antenna would change permanently during rotation. If the spacecraft is unbalanced, it would not rotate around the axis it should. $\endgroup$ – Uwe Apr 16 '17 at 18:02
  • $\begingroup$ Assuming the antenna is fixed to the spacecraft, I'm pretty sure that it's sufficient for the antenna's optical axis and spacecraft's principle axis to be parallel — at a distance of hundreds of millions of kilometers, an offset of even many meters can make no difference. $\endgroup$ – uhoh Apr 16 '17 at 18:30
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    $\begingroup$ Both axes may be parallel if they are not identical, but if there is an angle larger as the beam width between them, the direction of the antenna would be misaligned to earth during rotation. $\endgroup$ – Uwe Apr 16 '17 at 18:38
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As Uwe said, the axis of rotation should coincide with the pointing axis of the high-gain antenna. Exact balancing is required, according to Alan Stern (principal investigator, New Horizons):

The s/c has to be balanced for the spin to be stable and without any excessive nutation.

Having the rotation axes in a known location should also make using the thrusters for attitude control easier.

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  • $\begingroup$ About the quote snippet, I'm still thinking about the "...has to be balanced for the spin to be stable..." part. Of course if the mass distribution is weird like a three-axis tumbling asteroid, and the principle axes are a mess, it will not spin in a nice stable way. But is the deep-sub-kilogram fine-balancing really addressing stability, or just minimizing nutation? $\endgroup$ – uhoh Apr 17 '17 at 9:03
  • $\begingroup$ Reading a little further, I find this statement which I am not sure is really correct because nothing is perfect, there is always some amount of imbalance. "If it's to be spin-stabilized (which I'm thinking it is), then the mass balancing is even more important. It's exactly like the tire example you mentioned -- if there's a mass imbalance in a spinning object, the object will begin to wobble, and the wobble will reinforce itself until the object flies apart or until other motions couple into the wobble and the thing goes entirely out of control." (my emphasis) $\endgroup$ – uhoh Apr 17 '17 at 9:26
  • $\begingroup$ I think the object flying apart may be a large and fast rotating turbine or generator when one of its resonance frequencies are met, but not a slowly rotating spin stabilized space craft. $\endgroup$ – Uwe Apr 17 '17 at 20:25
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    $\begingroup$ Having the rotation axes in a known location would also help to save fuel for attitude control. $\endgroup$ – Uwe Apr 18 '17 at 11:27

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