Flattening in the context of "45th parallel north"

Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured passing through the poles, the circumference is 40,007.863 km (24,859.734 mi).

Treating the Earth as a sphere, its circumference would be its single most important measurement. The first known scientific measurement and calculation was done by Eratosthenes, by comparing altitudes of the mid-day sun at two places a known north–south distance apart. He achieved a great degree of precision in his computation. The Earth's shape deviates from spherical by flattening, but by only about 0.3%.

A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line.

Circles of latitude are often called parallels because they are parallel to each other; that is, planes that contain any of these circles never intersect each other. A location's position along a circle of latitude is given by its longitude. Circles of latitude are unlike circles of longitude, which are all great circles with the centre of Earth in the middle, as the circles of latitude get smaller as the distance from the Equator increases. Their length can be calculated by a common sine or cosine function. For example, the 60th parallel north or south is half as long as the Equator (disregarding Earth's minor flattening by 0.335%), stemming from ${\displaystyle \cos(60^{\circ })=0.5}$. On the Mercator projection or on the Gall-Peters projection, a circle of latitude is perpendicular to all meridians. On the ellipsoid or on spherical projection, all circles of latitude are rhumb lines, except the Equator.

A solar radius is a unit of distance, commonly understood as 695,700 km and expressed as ${\displaystyle R_{\odot }}$, used mostly to express the size of an astronomical objects relative to that of the Sun, or their distance from it. This length is also called the nominal solar radius. The sun's actual radius, from which the unit of measurement is derived, is usually calculated as the radius from the sun's center out to the layer in the Sun's photosphere where the optical depth equals 2/3. One solar radius can be described as follows:$${\displaystyle 1\,R_{\odot }=6.957\times 10^{8}{\hbox{ m}}}$$This is an approximation: both because such distance is difficult to measure and can be measured in various ways, and because the sun is not a perfectly spherical object itself, and thus the actual radius varies depending on the point(s) measured and modality of measurement employed.

695,700 kilometres (432,300 miles) is approximately 10 times the average radius of Jupiter; 109 times the 6378 km radius of the Earth at its equator; and ${\textstyle {1 \over 215}}$ or 0.0047 of an astronomical unit, the approximate average distance between Earth and the Sun. The solar radius to the sun's poles and that to the equator differ slightly due to the Sun's rotation, which induces an oblateness in the order of 10 parts per million.