I gather that our planet (…erm, that might be a bit presumptuous in present company ;)) is not quite a perfect sphere. Does the system of latitude and longitude compensate for this imperfection? If it doesn’t, is it because the imperfection is so small that it doesn’t matter? And if it does, where is the compensation?
What do you mean by “compensate”? A degree of latitude does not measure the same linear distance at the equator as it does at the poles. I am not sure I would call that “compensating”.
It’s a little trickier to define latitude on an ellipsoid than it is on a sphere. And when they’re determining the coordinates of a point on the earth, I’m almost positive that they take into account the fact that the earth is ellipsoidal. However, I don’t know whether they take into account the fact that the oblateness is changing over time.
For navigation purposes we assume the earth is a perfect sphere. Latitude is a measure of angular distance from the equator along a meridian north or south. One degree of latitude is assumed to be sixty nautical miles. At the equator one degreeof latitude is actually 59.705 nautical miles and near the poles it is 60.310 nautical miles.
Navigators always ignore the difference.
Yes, latitude is given by the angle between the vertical and the plane of the equator. The vertical is the perpendicular to the horizontal (tangent plane).
Caling the intersection of the equatorial plane and the axis of rotation “the center of the Earth” the verticals of other places do not pass through this point. The vertical of where you live does not go to the center of the Earth. The line that unites your position ith the center of the Earth is not the vertical of your place and neither is it the vertical of your antipodes.
BTW, we are talking about geographical or astronomical latitude which is commonly used in maps. I believe there is such thing as geometrical latitude wich would be measured from angles to the center of the earth, but it is not commonly used.
The reason that there is a difference is because the system of lat/lon does not assume the Earth is a perfect sphere. It’s based upon an oblate ellipsoid.
The datum (the surface used as a reference for lat/lon/alt) is usually an oblate ellipsoid, but it has changed from place to place in the past. “NAD27” (North American Datum 1927) often appeared on topography maps, but newer maps and map systems are going to a worldwide datum, because of global precise location is now possible. No datum that I’m familiar with takes into account the “pear-shape”, and well it shouldn’t–for two reasons: 1) It’s not that big of a difference. The change in radius due to the Earth being an ellipsoid is twenty kilometers, the pear-shape effect is a few tens of meters. 2) The Earth is not really a pear-shape.
Ok, tetrahedron, I’ll by that. And thanks, everyone, for the answers, SDMB shines.