Moon gravity gta 5 number series#

V = ( G M r ) в€’ ( G M r ) в€‘ ( R r ) n J n P n, 0 ( s i n П• ) + ( G M r ) в€‘ ( R r ) n The Gravitational potential V at an external point is conventionally expressed as positive in astronomy and geophysics, but negative in physics.

Moon gravity gta 5 number series#

The gravity potential is written with a series of spherical harmonic functions P nm. Theory ДЇor the lunar gravity field, it is conventional to use an equatorial radius of R=1738.0В km. The lunar GM is 1/81.30057 of the EarthвЂ™s GM. The mass of the Moon is M = 7.3458Г—10 22 kg and the mean density is 3346В kg/m 3. The lunar GM = 4902.8001В km 3/s 2 from GRAIL analyses.

Consequently, it is conventional to express the lunar mass M multiplied by the gravitational constant G. The Gravitational constant G is less accurate than the product of G and masses for Earth and Moon. ДЄncient rift valleys вЂ“ closeup (artist's concept). The center of gravity of the Moon does not coincide exactly with its geometric center, but is displaced toward the Earth by about 2 kilometers. The huge expanse of mare basaltic volcanism associated with Oceanus Procellarum does not cause a positive gravity anomaly. Based on Lunar Prospector gravitational models, it has been suggested that some mascons exist that do not show evidence for mare basaltic volcanism. However, lava flows by themselves cannot fully explain the gravitational variations, and uplift of the crust- mantle interface is required as well. Mascons are in part due to the presence of dense mare basaltic lava flows that fill some of the impact basins. They were initially discovered by the analysis of Lunar Orbiter tracking data: navigation tests prior to the Apollo program showed positioning errors much larger than mission specifications. These anomalies significantly influence the orbit of spacecraft around the Moon, and an accurate gravitational model is necessary in the planning of both manned and unmanned missions. The GRAIL fields are very accurate other missions are not combined with GRAIL.ДЄ 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. Mission ID LO includes all 5 Lunar Orbiter missions. The table lists the designation of the gravity field, the highest degree and order, a list of mission IDs that were analyzed together, and a citation. The accompanying table below lists lunar gravity fields. GRAIL had very accurate tracking between 2 spacecraft and tracking from Earth. The Kaguya/SELENE mission had tracking between 3 satellites to get far-side tracking. Apollos 15 and 16 released subsatellites. 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 missions with accurate Doppler tracking that have been used for deriving gravity fields are in the accompanying table. Near side on the left, far side on the right. Gravity acceleration at the surface of the Moon in m/s 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. Detailed data collected has shown that for low lunar orbit the only ' stable' orbits are at inclinations near 27Вє, 50Вє, 76Вє, and 86 degrees. Since the gravitational field of the Moon affects the orbit of a spacecraft, one can use this tracking data to detect gravity anomalies. 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.

The gravitational field of the Moon has been measured by tracking the radio signals emitted by orbiting spacecraft.