One would have thought that, having done the calculations, it would be easy to draw a diagram summarising the entire situation, showing axial rotation, precession and nutation all at the same time. But no! The diagrams below are all taken from the Internet, and they are all wrong in one way or another.
| This one has the direction of the the Earth's axial rotation correct but the precession direction incorrect. At least it mentions that the nutation is not to scale though! |
| Or maybe you would prefer both directions to be incorrect? Alternatively, perhaps it's supposed to be the view from above the south pole, rather than the conventional view from the north - I think that's being generous though! |
| This example might explain why many diagrams have the precession direction wrong - it shows the common error where the precession direction for the Earth is shown to be the same as for a spinning top, whereas in fact they precess in opposite directions because of the different geometries involved. Amusingly, the text of the webpage in which the diagram appears states that precession is in the opposite direction to the axial rotation! Pity they didn't check that the diagram actually showed this. |
| While admittedly being based on the planet Mars, this diagram again has the axial rotation direction wrong. Its other faux pas is more interesting, as it shows the nutation as having the form of an ellipse with secondary loops around its margin. This would indicate that the author has misunderstood what the "ellipse plus loops" diagram shows, assuming it represents the full nutational motion rather than just the periodic part. In fact, because the constant precession is greater than the nutational component, the axis never moves backwards and so there can be no loops in its actual motion. |
| Then we have this sort of diagram, which attempts to show the fine-structure of the nutation but again misunderstands the "ellipse plus loops" diagram. This leaves the reader wondering how the nutation nods can go in and out (or up-and-down tilting into in-and-out, as this diagram seems to show!) and in a loop at the same time. If the author had used the second nutation diagram in the section on the previous page rather than the last, all would have been clear(er). The precession direction is also wrong again, of course. |
Most of the diagrams also embody two more errors, one minor and one major. Firstly, the magnitude of the "nods" is far too great. However, because they would be imperceptible if shown in true scale one can easily see why the authors have chosen to exaggerate them and so no serious objection can be raised. More seriously though, the number of nods is incorrect by a large margin: there should in fact be 1385.6 of them (25,772 / 18.6). While it is true that it would be impractical to show this many nods, the number actually shown in the second example down is interesting - there are about 38 of them (allowing 1 for the gap). This is, of course, exactly the number of secondary loops on the ellipse shown on the previous page. Assuming that this is not purely a coincidence (and acknowledging that other diagrams have other numbers of nods), it would seem likely that the author of this diagram made a similar mistake to the one the authors of the final two examples made. The circuit on all the diagrams in fact represents one precession cycle of 25,772yrs, not one nutation cycle of 18.6yrs, and in any case the "ellipse plus loops" diagram represents the variation over the nutation cycle of the precession rate and the obliquity from the values they would have with no nutation, not the nutational motion itself: this is shown by the second nutation diagram on the previous page. The diagram thus actually shows the half-yearly variations in the nutation (caused by the Earth's orbit round the Sun), not the "basic" nutation at all!
 | Finally, however, a [very nearly] correct diagram! There are a few accurate representations on the Internet, but I decided to construct my own. I based it on the first example, corrected for direction, and used the idea embodied in the last one in order to show some detail of the nutation. The magnitude of the nods (and in fact of the fine structure in the nutation detail) is still too large, for the practical reason mentioned above, but there are now an indeterminate number of them, as in the last example: that way no conclusions can be drawn about the number of nods represented. Also, as it is not possible to directly show in a static diagram the variation in precession speed, which is in fact a much larger effect than the "nodding", I have coloured part of the precession cycle alternately red and green to suggest slow down and speed up: this would, of course, have to be explained in any text accompanying the diagram. |
So, what am I offered for the copyright to possibly the only correct representation of precession on the Internet?
