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In astrophysics, the Darwin–Radau equation (named after Rodolphe Radau and Charles Galton Darwin) gives an approximate relation between the moment of inertia factor of a planetary body and its rotational speed and shape. The moment of inertia factor is directly related to the largest principal moment of inertia, C.
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
Polar motion in arc-seconds as function of time in days (0.1 arcsec ≈ 3 meters). [1] Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. [2]: 1 This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called Earth-centered, Earth-fixed or ECEF reference frame). This ...
An example is the calculation of the rotational kinetic energy of the Earth. As the Earth has a sidereal rotation period of 23.93 hours, it has an angular velocity of 7.29 × 10 −5 rad·s −1. [2] The Earth has a moment of inertia, I = 8.04 × 10 37 kg·m 2. [3] Therefore, it has a rotational kinetic energy of 2.14 × 10 29 J.
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
Assuming that the Earth was a completely rigid body, they calculated the period of Earth’s polhode wobble to be about 9–10 months. [ citation needed ] During the mid 19th century, Louis Poinsot developed a geometric interpretation of the physics of rotating bodies that provided a visual counterpart to Euler’s algebraic equations.
In general a torus is almost determined by three parameters: the ratios of the second and third moments of inertia to the highest of the three moments of inertia, and the ratio / relating the angular momentum to the energy times the highest moment of inertia. But for any such a set of parameters there are two tori, because there are two "tacos ...
The portable gravimeter developed in 1890 by Thomas C. Mendenhall provided the most accurate relative measurements of the local gravitational field of the Earth. A compound pendulum is a body formed from an assembly of particles of continuous shape that rotates rigidly around a pivot. Its moment of inertia is the sum of the moments of inertia ...