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Mercury | 33 |
,
and equate it to that of the circle supposed described about that focus with the length of radius . This geometrically is the point of intersection of the two curves, since the value of r is common to both.
Consequently for the point sought whence, since
,
whence, since ,
,
and .
In the case of Mercury, e = .205605; v, the true anomaly of the point of maximum libration, is therefore 98° 55'.13.
But ,
where E is the eccentric anomaly; and , where M is the mean anomaly; whence , which is the amount of the maximum libration, is 23° 40' 38".
The gain or loss of the rotation over the revolution is the same thing as the equation of the centre.
We have, then, in the libration, a most conclusive and interesting proof of the isochronism of rotation and revolution.
The next point to consider is what caused this