Earth's polar radius, often denoted as "r," is the distance from the center of the Earth to a point on the Earth's surface near either the North Pole or the South Pole. It represents the Earth's radius when measured from its center to a point along its polar axis. The polar radius is shorter than the equatorial radius because the Earth is slightly flattened at the poles and bulges at the equator due to its rotation.
The approximate value for Earth's polar radius is about 6,357 kilometers (or approximately 3,949 miles). This value may vary slightly depending on the reference ellipsoid used for modeling the Earth's shape, but the given value is a commonly used and accurate approximation for most purposes.
In contrast to the polar radius, Earth's equatorial radius (measured from the center to a point on the equator) is slightly longer, approximately 6,378.1 kilometers (3,963.2 miles).
In the field of atomic and molecular physics, an "atomic unit of length" is a unit of measurement that is used to express distances at the atomic and molecular scale in a dimensionless way. It is part of a system of atomic units (a.u.) that simplifies calculations involving fundamental physical constants and properties of atoms and molecules.
The atomic unit of length (a.u. of length) is defined in terms of the Bohr radius (a₀), which is a fundamental constant in atomic physics. The Bohr radius is approximately 0.52917721067 angstroms (Å) or 5.2917721067 x 10^-11 meters (m).
In atomic units, the Bohr radius is set to exactly 1 a.u. of length. Therefore, when using atomic units, distances are expressed relative to the Bohr radius, and the value of 1 a.u. of length corresponds to the typical size scale of atomic and molecular structures.
The use of atomic units simplifies many quantum mechanical calculations and allows physicists and chemists to work with dimensionless quantities, making it easier to compare and analyze atomic and molecular properties.