# Re: Changing AO-40's attitude

```At 06:08 PM 2/1/01 , John P. Toscano wrote:
>Doug Braun NA1DB wrote:
>
> > If you despun it with a momentum wheel, the spacecraft would no
> > longer be spinning, but the momentum wheel would be, and it would
> > have the same gyroscopic effect that the spinning spacecraft
>
>True (I suppose) about the gyroscopic effect, but at least the lack
>of spacecraft rotation would have the benefit of stopping the
>repetitive interruption of telemetry.
>
>
>I guess it should be possible to compute if the wheels could or
>couldn't absorb the 17.7 RPM rotation rate in theory (if it
>wouldn't be destructive, and if it wouldn't be prevented by the
>controller hardware, and if it wouldn't be prevented by prudence).
>
>My Physics is a bit rusty, but I think that the wheel would need
>to spin at a rate of:
>
>        (Mass of AO-40) - (Mass of that reaction wheel)
>17.7 x -----------------------------------------------
>                (Mass of that reaction wheel)
>
>The various masses are known, and the maximum allowable spin rate
>of the wheels has also been set.  I don't have those figures at
>this location, however.
>
>(Conservation of angular momentum, unless I've omitted something
>else needed by the calculation such as the diameter of the spinning
>masses in question, or some such thing.)

You are on the right track, but you really have to compare not the masses,
but the "moments of inertia" of the wheels vs. the rest of the spacecraft.
And the moment of inertia is basically: mass x radius.

Let's say that the ratio is something like 500:1.  This would mean
the wheel would have to spin at 8800 RPM, which it definitely cannot do!

I think that you could spin the wheel whose axis is parallel to
the spacecraft's Z axis.  But if you tried spinning any others,
they would experience a severe gyroscopic force, and their magnetic
bearings would get wrecked.

Remember one thing about the momentum wheels:  They CANNOT change
the total angular momentum of the spacecraft!  Also remember that
angular momentum is a vector quantity, which means that you cannot
changes its magnitude OR its direction.

BTW, it is interesting examine the intended purpose of the wheels: to keep
the non-spinning spacecraft pointed in the right direction.  (John's
original ASCII art illustrated this well).  During the course of
one orbit, the spacecraft has to be turned about 150 degrees and back
again, over a period of a few hours.  You can do some math to figure
out about how much the wheels have to be accelerated to accomplish this.
It's only a few RPM, I believe.

Doug
NA1DB

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