pyephem calculation of Mars opposition via earth_distance

StackOverflow https://stackoverflow.com/questions/22945754

  •  30-06-2023
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Question

I looped through all days in 2014 looking for the date with the smallest Earth-Mars distance. I expected this to occur on Mars opposition on Apr 8, 2014 but April 14 was the date with the lowest distance. Why?

    date     time     mars.earth_distance (AU)
    2014/4/1 00:00:00 0.636615
    2014/4/2 00:00:00 0.633898
    2014/4/3 00:00:00 0.631388
    2014/4/4 00:00:00 0.629085
    2014/4/5 00:00:00 0.626992
    2014/4/6 00:00:00 0.625109
    2014/4/7 00:00:00 0.623436
    2014/4/8 00:00:00 0.621973
    2014/4/9 00:00:00 0.620720
   2014/4/10 00:00:00 0.619676
   2014/4/11 00:00:00 0.618842
   2014/4/12 00:00:00 0.618216
   2014/4/13 00:00:00 0.617798
   2014/4/14 00:00:00 0.617585
   2014/4/15 00:00:00 0.617578
   2014/4/16 00:00:00 0.617774
   2014/4/17 00:00:00 0.618171
   2014/4/18 00:00:00 0.618768
   2014/4/19 00:00:00 0.619563
   2014/4/20 00:00:00 0.620554

Similarly, the largest apparent size occurs on 12/15 and brightest magnitude occurs on Apr 12 rather than at opposition on Apr 8.

Was it helpful?

Solution

The moment of “opposition” is not the moment that a planet is closest or brightest, but is (if I recall) the moment when the elliptical longitude of the planet is 180° — exactly halfway across the sky, which is as far as possible — away from that of the Sun from the point of view of Earth.

If the planets traveled in perfect circles centered on the sun and at a uniform velocity, then the moment of opposition would also be the moment when the planet is closest and brightest. But since the planets are in elliptical orbits and move at a non-uniform rate, they can pass opposition but still be moving toward each other — or already be moving away from each other.

Magnitude is affected by both the phase of the planet and its distance, so we would expect the maximum magnitude to fall between the moment when the phase is greatest (at the moment of opposition) and the moment when the distance is smallest — and that is in fact what your numbers seem to indicate.

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