Re: Moon's synchronism

[Jim Green <JMGreen@sisna.com>]

John, the following I understand and in fact agree with -- but I think this
will prove helpful to the list (at least to those who care) -- it is a fine
review.  I thought you were delving into ocean tides for this "Tidal
Torque".  As you now say it, you just mean the "Earth's total gravitational
field gradient", which might possibly include some effect of the ocean tides
(or earth tides for that matter), but you are not focusing on them.  If this
is so, I completely agree with this fine review.  But I still worry about
your last sentence. (:-)

Jim Green


John says -

> The Moon is a prolate ellipsoid with its long (low moment of 
> inertia) axis pointing generally toward Earth and stabilized in 
> this orientation via the torque produced by its interaction with 
> Earth's gravitational field gradient--what I have called the 
> "tidal torque."  This much is well-known.  The same effect has 
> been put to practical use in stabilizing satellites such as the 
> "Long Duration Exposure Facility" so that one end always points 
> toward Earth and the other toward outer space.
>
> Now, the Moon's rotational inertia tends to maintain its 
> *rotational* angular velocity.  But, because the Moon is in an 
> elliptical orbit, its *orbital* angular velocity is *not* 
> constant.  As a result, its "long axis" oscillates about the 
> instantaneous direction of the gravitational field gradient and 
> we, correspondingly, see a slightly different face of the moon at 
> different times during the month.  (I'm afraid I'm just going to 
> have to ask you to draw some pictures for yourself if my words 
> still don't do the job for which they were intended.)
>
> *If* the Moon's rotational inertia were relatively small or the 
> tidal torque were relatively large, then the Moon would be kept 
> tightly in the grip of the tidal torque.  The result of this 
> domination by the torque would be very little deviation of the 
> long axis from the direction of the gravitational field gradient 
> and correspondingly little deviation in the face that the moon 
> present to us during its orbit.  (This behavior is analogous to 
> that of an object with small inertial mass on the end of a stiff 
> spring with the free end forced back and forth at a moderate 
> frequency.  It is the kind of behavior that one gets from driving 
> *any* mechanical oscillator well below its natural frequency.)  
> This is *not* what we see.
>
> What we *do* see is a moon with relatively *constant* rotational 
> angular velocity--the result of its relatively large rotational 
> inertia and the relatively small tidal torque.  That is, the 
> moon's behavior is dominated by its rotational inertia.  (This 
> behavior is analogous to that of an object with large inertial 
> mass on the end of a weak spring with the free end forced back and 
> forth at a moderate frequency.  It is the kind of behavior that 
> one gets from driving *any* mechanical oscillator well above its 
> natural frequency.)
>
> The calculations I shared merely corroborate what the evidence
> demands--that the natural frequency of the moon oscillating in the 
> field gradient of Earth is significantly lower than the drive 
> frequency due to the "monthly" variations in the tidal torque.