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Updated: May 13, 2025
Because of the difference in the velocities of Mercury and the earth in their revolutions around the sun, one synodic revolution of Mercury, i.e., from one inferior conjunction to the next, requires nearly one hundred and sixteen days.
They invented the gnomon and the polos, two kinds of sundial, by means of which they were able to measure time during the day, and to fix the true length of the solar day, with sufficient accuracy. They determined correctly within a small fraction the length of the synodic revolution of the moon. They knew that the true length of the solar year was 365 days and a quarter, nearly.
The intervals between her successive reappearances in the evening sky, measured by her synodic period of 584 days, are sufficiently long to give an element of surprise and novelty to every return of so dazzling a phenomenon. Even the light of the full moon silvering the tree tops does not exercise greater enchantment over the mind of the contemplative observer.
Now since the angular distance between P and R is 120°, and since in a period of three synodic revolutions or 21,758 days, the line of conjunction travels through an arc of 8°, it follows that in 892 years the conjunction of the two planets will have advanced from P, P' to R, R'. In reality, the time of travelling from P, P' to R, R' is somewhat longer from the indirect effects of planetary perturbation, amounting to 920 years.
Now if the orbits of both planets were perfectly circular, the retarding and accelerating effects of the disturbing force of either planet would neutralize each other in the course of a synodic revolution, and therefore both planets would return to the same condition at each successive conjunction.
Venus thus overtakes and passes the earth once in five hundred and eighty-four days, or nearly two and a half of her own years, constituting what is called her synodic period of apparent revolution as seen from this globe.
But in consequence of the ellipticity of the orbits, the retarding effect of the disturbing force is manifestly no longer exactly compensated by the accelerative effect, and hence at the close of each synodic revolution, there remains a minute outstanding alteration in the movement of each planet.
It is also obvious, that during the interval which elapses between the occurrence of two conjunctions in the same points of the orbits, and which includes three synodic revolutions of the planets, Jupiter will have accomplished five revolutions around the sun, and Saturn will have accomplished two revolutions.
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