Gravitation of the Moon
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.
Since the gravitational field of the Moon affects the orbit of a spacecraft, one can use this tracking data to detect gravity anomalies.
[2] Because of the Moon's synchronous rotation it is not possible to track spacecraft from Earth much beyond the limbs of the Moon, so until the recent Gravity Recovery and Interior Laboratory (GRAIL) mission the far-side gravity field was not well mapped.
The missions with accurate Doppler tracking that have been used for deriving gravity fields are in the accompanying table.
The table gives the mission spacecraft name, a brief designation, the number of mission spacecraft with accurate tracking, the country of origin, and the time span of the Doppler data.
The accompanying table below lists lunar gravity fields.
A major feature of the Moon's gravitational field is the presence of mascons, which are large positive gravity anomalies associated with some of the giant impact basins.
These anomalies significantly influence the orbit of spacecraft around the Moon, and an accurate gravitational model is necessary in the planning of both crewed and uncrewed missions.
They were initially discovered by the analysis of Lunar Orbiter tracking data:[16] navigation tests prior to the Apollo program showed positioning errors much larger than mission specifications.
Mascons are in part due to the presence of dense mare basaltic lava flows that fill some of the impact basins.
[17] However, lava flows by themselves cannot fully explain the gravitational variations, and uplift of the crust-mantle interface is required as well.
Based on Lunar Prospector gravitational models, it has been suggested that some mascons exist that do not show evidence for mare basaltic volcanism.
[3] The huge expanse of mare basaltic volcanism associated with Oceanus Procellarum does not cause a positive gravity anomaly.
[18] The gravitational constant G is less accurate than the product of G and masses for Earth and Moon.
[20] For the lunar gravity field, it is conventional to use an equatorial radius of R = 1738.0 km.
The gravity potential is written with a series of spherical harmonic functions Pnm.
The gravitational potential V at an external point is conventionally expressed as positive in astronomy and geophysics, but negative in physics.
Note that the spherical harmonic functions Pnm can be normalized or unnormalized affecting the gravity coefficients Jn, Cnm, and Snm.
where er, eφ, and eλ are unit vectors in the three directions.
The unnormalized gravity coefficients of degree 2 and 3 that were determined by the GRAIL mission are given in Table 1.
The J2 coefficient for an oblate shape to the gravity field is affected by rotation and solid-body tides whereas C22 is affected by solid-body tides.
Both are larger than their equilibrium values showing that the upper layers of the Moon are strong enough to support elastic stress.
In January 2022 China was reported by the South China Morning Post to have built a small (60 centimeters in diameter) research facility to simulate low lunar gravity with the help of magnets.
[21][22] The facility was reportedly partly inspired by the work of Andre Geim (who later shared the 2010 Nobel Prize in Physics for his research on graphene) and Michael Berry, who both shared the Ig Nobel Prize in Physics in 2000 for the magnetic levitation of a frog.
