Abstract
The orbital data for the Moon was inadvertently omitted from table 1. A supplementary Excel file has also been added which shows the original data in table 1 and how the equivalent 26 inch bike wheel tolerances were calculated.
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In table 1, the orbital data of the Moon was inadvertently left out. Here is a reproduction of the table with the lunar data included. In the case of the Moon, the closest point in the orbit to the Earth is perigee and farthest point apogee.
Table 1. Orbital characteristics of the Moon and eight planets. All values in the first five numerical columns are in millions of kilometres, f = focus, a = semi-major axis, b = semi-minor axis, e = eccentricity. The tolerance is based on the semi-major axis of the orbit being the rim of a 26 inch bicycle wheel. In the last column the tolerance is expressed as a percentage of 26 inches or 660.4 mm.
| Body | Aphelion | Perihelion | f | a | b | e | tol. (mm) | tol. (%) |
|---|---|---|---|---|---|---|---|---|
| Mercury | 69.8 | 46 | 11.90 | 57.9 | 56.7 | 0.206 | 14.099 | 2.135 |
| Venus | 108.9 | 107.5 | 0.70 | 108.2 | 108.2 | 0.006 | 0.014 | 0.002 |
| Earth | 152.1 | 147.1 | 2.50 | 149.6 | 149.6 | 0.017 | 0.092 | 0.014 |
| Mars | 249.3 | 206.7 | 21.30 | 228 | 227.0 | 0.093 | 2.888 | 0.437 |
| Jupiter | 816.4 | 740.6 | 37.90 | 778.5 | 777.6 | 0.049 | 0.783 | 0.119 |
| Saturn | 1506.5 | 1357.6 | 74.45 | 1432.05 | 1430.1 | 0.052 | 0.893 | 0.135 |
| Uranus | 3001.4 | 2732.7 | 134.35 | 2867.05 | 2863.9 | 0.047 | 0.725 | 0.110 |
| Neptune | 4558.9 | 4471.1 | 43.90 | 4515 | 4514.8 | 0.010 | 0.031 | 0.005 |
| Moon | 0.4054 | 0.3626 | 0.02 | 0.384 | 0.383 | 0.056 | 1.026 | 0.155 |
Note that even although the distance between the Earth and Moon changes quite markedly (apogee 405 000 km, perigee 362 000 km) the orbit of the Moon is close to circular due to the Earth being at a foci of the orbit. If the lunar orbit around the Earth were a 26 inch bike wheel, the deviation from a perfect circle would be only 1 mm.
A supplementary Excel file has been included with the above data and shows how the mm and % tolerances were calculated.
Supplementary data (<0.1 MB XLSX)