[seqfan] Re: Sequence relating the mass of the planets to the mass of their most massive satellites
Charles Greathouse
charles.greathouse at case.edu
Tue Feb 6 17:57:19 CET 2018
If such a sequence were to be accepted it would be absolutely necessary
that each term submitted be known within standard error. I think
measurement errors are usually assumed to be normal, so using an
approximation (Marsaglia 2006, Ratios of normal variables; see section 5)
the lower and upper bounds would be
moonmass*planetmass ± sqrt(planetmass^2*stdevmoon^2 + (moonmass^2 -
stdevmoon^2)*stdevplanet^2)
----------------------------------------------------------------------------------------------------------------------------------------------
moonmass^2 - stdevmoon^2
and these would need to be between n and n+1 for some integer n.
Andert 2010, "Precise mass determination and the nature of Phobos" seems to
be the best source for the mass of the largest natural satellite of Mars,
and its value (1.0668 ± 0.003)*10^16 kg is far too imprecise to determine
a(4). So I don't think there's any reasonable way this sequence could be
accepted, interesting though it is.
Charles Greathouse
Case Western Reserve University
On Tue, Feb 6, 2018 at 8:46 AM, Hans Havermann <gladhobo at bell.net> wrote:
> > The terms are 0, 0, 81, 60203584, 12809, 4225, 24620, 4786
>
> One difficulty with such a sequence, based on measurement, is how accurate
> the measurements are. Your fourth term implies that we know them to have
> more than eight-digit precision. I don't believe that our mass
> determinations of Mars and Phobos are quite that accurate and I'm not sure
> that ratio-ing them makes them any more precise.
>
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