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The gravitational constant G is less accurate than the product of G and masses for Earth and Moon. Consequently, it is conventional to express the lunar mass M multiplied by the gravitational constant G. The lunar GM = 4902.8001 km 3 /s 2 from GRAIL analyses. [12] [11] [19] The mass of the Moon is M = 7.3458 × 10 22 kg and the mean density is ...
For two bodies, the parameter may be expressed as G(m 1 + m 2), or as GM when one body is much larger than the other: = (+). For several objects in the Solar System, the value of μ is known to greater accuracy than either G or M. The SI unit of the standard gravitational parameter is m 3 ⋅s −2.
The accuracy of the measured value of G has increased only modestly since the original Cavendish experiment. [19] G is quite difficult to measure because gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies.
The Moon is Earth's only natural satellite.It orbits at an average distance of 384,400 km (238,900 mi), about 30 times the diameter of Earth. 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.
One g is the force per unit mass due to gravity at the Earth's surface and is the standard gravity (symbol: g n), defined as 9.806 65 metres per second squared, [5] or equivalently 9.806 65 newtons of force per kilogram of mass. The unit definition does not vary with location—the g-force when standing on the Moon is almost exactly 1 ⁄ 6 that
The agreed-upon value for standard gravity is 9.80665 m/s 2 (32.1740 ft/s 2) by definition. [4] This quantity is denoted variously as g n, g e (though this sometimes means the normal gravity at the equator, 9.7803267715 m/s 2 (32.087686258 ft/s 2)), [5] g 0, or simply g (which is also used for the variable local value).
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where is the mean anomaly (more or less how moon has moved from perigee) and is the mean elongation (more or less how far it has moved from conjunction with the Sun at new moon). They can be calculated from G M = 134.963 411 38° + 13.064 992 953 630°/d · t D = 297.850 204 20° + 12.190 749 117 502°/d · t