Richard Fitzpatrick discusses the rotational flattening of a celestial body. A model that assumes homogenous density arrives at a difference between the Earth's equatorial and polar radii of 27.5 kilometer, significantly larger than the actual difference of about 21.4 kilometer.
My goal is to create a plot that gives flattening as a function of angular velocity of an Earth-size, Earth-mass celestial body. For what I will be using it for an error under 10% is sufficient.
For the rotation rate: the range of interest is from zero rotation rate to at most double the rotation rate of the actual Earth. (Most texts that discuss rotation of celestial bodies focus on extremely high rotation rates. It is surprisingly hard to find discussion of Earth-like rotation rate.)
A crude approach would be to assume that at at any rotation rate (close to actual Earth rotation rate) the error of the homogenous-density-model will be in the same ratio. So then, to get to within an error of 10%, it would be enough to always apply an adjustment factor of 21.4/27.5
Can anyone confirm or disconfirm that?
(Most material I found aims for far higher accuracy, and the formula's are complicated. For my particular purpose that level of accuracy is overkill.)