Flattening
The title of this article is ambiguous. For shaping in woodwork, furniture and interior design, see flaking.
Flattening 
is the deformation of a planet or other celestial body due to its rotation.
The geometric oblateness of an ellipsoidal body is the relative difference in radii a at the equator and b at the poles:
The flattening is usually given in the form "1:x" with a value x > 1, which is also called the numerus of flattening; a strong flattening corresponds to a comparatively small value of x.
The dynamic flattening is less than the geometric flattening.
One also speaks of flattening at an irregular body, e.g. if its meridian section is no ellipse but a spheroid. This has the effect of clear anomalies of the gravity field, which also cause orbital disturbances of satellites or moons.
Haumea with moons, artistic representation. Due to the strong rotational motion the dwarf planet is strongly flattened.
Causes
Gravity alone forms spherical bodies, the oblateness results from the centrifugal force 
, which results from rotation:
with
- the mass
of a mass element - its angular velocity ω
- its distance
from the axis of rotation.
The deformation of two orbiting celestial bodies into elongated ellipsoids, which is caused by tidal friction and is directed in the direction of the mutual gravitational forces, runs counter to the flattening. Mostly, however, the flattening of the bodies caused by the centrifugal force predominates, so that the shape of the elongated ellipsoid can hardly be observed.
Interrelationships
If one considers rigid bodies of - simplifying - constant dense material, then both the gravitational force and the centrifugal force (each on a sample mass) increase linearly with the radius of the body. Therefore, the flattening of such bodies is determined only by the frequency of rotation, regardless of their radius: If a body rotates faster (= smaller period of revolution or higher angular velocity), it will flatten more than another of the same structure.
Differences of density cause, if flows are possible, concentric layering - lightest (at earth: air and water) at top, most dense at core at centre of sphere. Such bodies with different density-layers within behave likely at surface, thus flatten same amount, as long as average densities of each complete body correspond.
However, a lower average density causes a lower gravity at the surface and thus a larger oblateness at the same rotation frequency (example gas planets).
A core of higher density will therefore flatten less than the overall body with lighter higher layers.
More complex are observations of gaseous stars with zones of different rotation frequency, as they occur on the Sun (differential rotation).
When a body contracts, expands, or changes its density locally, its angular velocity generally changes with the moment of inertia, and so does the oblateness, while the angular momentum remains constant. This is particularly relevant when stars or galaxies change greatly in diameter. See also Coriolis force.
Similar to regional density irregularities causing gravity anomalies, the flattening of an entire body or even its core causes gravity flattening, i.e. the gravitational force on the surface of the body is not the same everywhere, but depends on the location.
