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seen Oct 14 at 21:49

the mean square The Mean Square
(with one standard deviation and several unusual ones)

aka Rob Johnson

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Sep
24
awarded  Autobiographer
Nov
19
comment rotational oblateness
Thanks for your answer. I will have to take some time to digest it. I am also glad that you provided a link to Mark Eichenlaub's question. I will read the answers there as well.
Oct
7
comment rotational oblateness
I am looking at the first order contributions. Since $\omega^2r/g\doteq0.003433$, approximating the denominator with $g$ rather than $g-\omega^2r\cos^2(\phi)$ will alter the result by at most $0.34\%$. That is much smaller than the difference seen.
Oct
7
awarded  Commentator
Oct
7
comment rotational oblateness
I am assuming that $\omega^2r$ is small compared to $g$, not that it is insignificant. If it were insignificant, there would be no oblateness at all. This means that second order terms in $\omega^2r$ will be even smaller compared to $g^2$.
Oct
7
comment rotational oblateness
I am including the contribution from centrifugal force; that's the $\omega^2r\cos(\phi)$. It is the contribution from the redistribution of mass that I was assuming was negligible. Evidently, it is not.
Jul
21
comment rotational oblateness
I'm going to assume that there are unstated assumptions in the Wikipedia formula and that the result is affected by the mass redistribution caused by the flattening. If anyone has a more complete answer, or a formula that actually works to compute the oblateness of a rotating planet, I am still interested.
Jun
30
comment rotational oblateness
@Will: if that were the case, then I would expect the error to be dependent on the density map of the oblate spheroid. The formula in Wikipedia is not specifically for the Earth, yet it is twice what I got, seemingly independent of the density.
Jun
29
comment rotational oblateness
@WojciechMorawiec: By symmetry, integrating through the southern hemisphere should bring $r_{\text{eq}}$ back to $r_{\text{np}}$.
Jun
29
comment rotational oblateness
I see that this is related to Why is the Earth so fat?. One possibility for the error in my computation might be the direction of gravity generated by an oblate spheroid. However, this would seem to be dependent on the mass distribution inside the spheroid. The factor of $2$ between my estimate and Wikipedia's seems to discount that the mass distribution would be the cause.
Jun
29
awarded  Student
Jun
29
asked rotational oblateness
May
18
awarded  Yearling
Jan
21
answered What does this quote about the four dimensional divergence of an antisymmetric tensor mean?
Dec
11
comment Blue-shifting as opposed to violet-shifting
@Kitchi: actually, that plot is "Relative spectral distribution of the uneclipsed or partially eclipsed sky for solar elevation angle less than 51°" The blue responses look to be pretty similar for all plots.
Dec
11
comment Blue-shifting as opposed to violet-shifting
@Kitchi: Wouldn't the spectral response curve above include the effects of Rayleigh scattering? It is data from a ground-based spectrograph. Some details of the instrument are given in this paper.
Dec
11
answered Blue-shifting as opposed to violet-shifting
May
19
awarded  Teacher
May
18
awarded  Supporter
May
18
comment High school double lens optics question
@DohnJoe: The original question was simply stated poorly. Since the answers match, the assumption I made was evidently correct. However, if the problem were stated better, no such assumption would be necessary.