[seqfan] Sequence relating the mass of the planets to the mass of their most massive satellites
Felix FrÃ¶hlich
felix.froe at gmail.com
Tue Feb 6 13:20:24 CET 2018
Dear SeqFans,
here is a sequence idea related to the planets in the solar system and
their natural satellites:
Ratio of the mass of n-th planet from the Sun to the mass of its most
massive natural satellite, rounded to the nearest integer, or 0 if the
planet does not have any natural satellites.
The terms are 0, 0, 81, 60203584, 12809, 4225, 24620, 4786
Clearly, the larger the value of a(n), the smaller is the mass of the
satellite relative to its planet.
Two numerological curiosities can be discovered:
The ratios Saturn/Titan and Neptune/Triton are close to each other,
differing by only about 13 %.
The ratio Uranus/Titania is close to double the ratio Jupiter/Ganymede,
with a deviation of about 8 %.
Planets with a value of a(n) close to 1 are sometimes called "double
planets" (see for example page 309 of
https://books.google.com/books?id=XI_DCgAAQBAJ). Of the planets under the
current definition of the IAU, only Earth and the Moon come close to this
(if Pluto and Charon were included, their value would be even smaller).
Should I submit this (perhaps with keyword "dumb"), or is this considered
not okay? Of course, for one thing, it is not a mathematical sequence, but
we already have a number of sequences related to planets and in this
regard, I find this one also interesting. Another thing is that it is a
finite sequence where the initial two terms are 0, but that's just how the
solar system is. On the other hand, I would consider it one of the more
interesting "dumb" sequences.
I personally like the sequence (which may not mean anything), so what do
others think?
Regards
Felix
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