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The gravitational field of the Moon has been measured by tracking the radio signals emitted by orbiting spacecraft. The principle used depends on the Doppler effect, whereby the line-of-sight spacecraft acceleration can be measured by small shifts in frequency of the radio signal, and the measurement of the distance from the spacecraft to a station on Earth.
It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r 12 and m instead of m 2 and define the gravitational field g(r) as:
The actual Hill radius for the Earth-Moon pair is on the order of 60,000 km (i.e., extending less than one-sixth the distance of the 378,000 km between the Moon and the Earth). [9] In the Earth-Sun example, the Earth (5.97 × 10 24 kg) orbits the Sun (1.99 × 10 30 kg) at a distance of 149.6 million km, or one astronomical unit (AU). The Hill ...
Tidal forces between Earth and the Moon have synchronized the Moon's orbital period (lunar month) with its rotation period at 29.5 Earth days, causing the same side of the Moon to always face Earth. The Moon's gravitational pull is the main driver of Earth's tides. In geophysical terms, the Moon is a planetary-mass object or satellite planet
Considering the Earth–Moon system as a binary planet, its centre of gravity is within Earth, about 4,671 km (2,902 miles) [24] or 73.3% of the Earth's radius from the centre of the Earth. This centre of gravity remains on the line between the centres of the Earth and Moon as the Earth completes its diurnal rotation.
The gravitational pull of the lunar surface is about 1/6 that of Earth's, meaning a person who weighs about 100 pounds would feel closer to just 17 pounds on the moon.
Variation of the distance between the centers of the Moon and the Earth over 700 days Distribution of perigee and apogee between 3000 BC and AD 3000. Because of the influence of the Sun and other perturbations, the Moon's orbit around the Earth is not a precise ellipse. Nevertheless, different methods have been used to define a semi-major axis.
Earth's sidereal day would eventually have the same length as the Moon's orbital period, about 47 times the length of the Earth day at present. However, Earth is not expected to become tidally locked to the Moon before the Sun becomes a red giant and engulfs Earth and the Moon. [10] [11] For bodies of similar size the effect may be of ...