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The gravitational torque between the Moon and the tidal bulge of Earth causes the Moon to be constantly promoted to a slightly higher orbit (~3.8 cm per year) and Earth to be decelerated (by −25.858 ± 0.003″/cy²) in its rotation (the length of the day increases by ~1.7 ms per century, +2.3 ms from tidal effect and −0.6 ms from post ...
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. Part of the Earth's rotational energy can also be tapped using tidal power.
Here, the ratio of the rotation period of a body to its own orbital period is some simple fraction different from 1:1. A well known case is the rotation of Mercury, which is locked to its own orbit around the Sun in a 3:2 resonance. [2] This results in the rotation speed roughly matching the orbital speed around perihelion. [14]
Every 18.6 years, the angle between the Moon's orbit and Earth's equator reaches a maximum of 28°36′, the sum of Earth's equatorial tilt (23°27′) and the Moon's orbital inclination (5°09′) to the ecliptic. This is called major lunar standstill. Around this time, the Moon's declination will vary from −28°36′ to +28°36′.
Newton illustrates his formula with three examples. In the first two, the central force is a power law, F(r) = r n−3, so C(r) is proportional to r n. The formula above indicates that the angular motion is multiplied by a factor k = 1/ √ n, so that the apsidal angle α equals 180°/ √ n.
Many orbits, such as that of the Moon around the Earth, can be approximated by uniform circular motion. In such cases, the centripetal force is gravity, and by Newton's law of universal gravitation has magnitude G M m / r 2 {\displaystyle GMm/r^{2}} , where M {\displaystyle M} is the mass of the larger body being orbited.
t. e. In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler absent the third law in 1609 and fully in 1619, describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...