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alà чӑвашла español فارسی հայերեն 日本語 한국어 norsk bokmål português română русский සිංහල українська tiếng việt 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia earth vs mars vs moon gravity at elevation rad gravity anomaly at the surface of the moon in mgal the acceleration due to gravity on the surface of the moon is approximately 1 625 m s 2 about 16 6 that on earth s surface or 0 166 ɡ 1 over the entire surface the variation in gravitational acceleration is about 0 0253 m s 2 1 6 of the acceleration due to gravity because weight is directly dependent upon gravitational acceleration things on the moon will weigh only 16 6 1 6 of what they weigh on the earth gravitational field edit 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 most low lunar orbits are unstable detailed data collected has shown that for low lunar orbit the only stable orbits are at inclinations near 27 50 76 and 86 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 gravity acceleration at the surface of the moon in m s 2 near side on the left far side on the right map from lunar gravity model 2011 3 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 apollos 15 and 16 released subsatellites the kaguya selene mission had tracking between 3 satellites to get far side tracking grail had very accurate tracking between 2 spacecraft and tracking from earth missions used for lunar gravity mission id number source years lunar orbiter 1 lo1 1 us 1966 lunar orbiter 2 lo2 1 us 1966 1967 lunar orbiter 3 lo3 1 us 1967 lunar orbiter 4 lo4 1 us 1967 lunar orbiter 5 lo5 1 us 1967 1968 apollo 15 subsatellite a15 1 us 1971 1972 apollo 16 subsatellite a16 1 us 1972 clementine cl 1 us 1994 lunar prospector lp 1 us 1998 1999 kaguya selene k s 3 japan 2007 2009 chang e 1 ch1 1 china 2007 2009 grail g 2 us 2012 chang e 5t1 ch1t1 1 china 2015 2018 the accompanying table below lists lunar gravity fields 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 mission id lo includes all 5 lunar orbiter missions the grail fields are very accurate other missions are not combined with grail lunar gravity fields designation degree mission ids citation lp165p 165 lo a15 a16 cl lp 4 glgm3 150 lo a15 a16 cl lp 5 cegm01 50 ch 1 6 sgm100h 100 lo a15 a16 cl lp k s 7 sgm150j 150 lo a15 a16 cl lp k s 8 cegm02 100 lo a15 a16 cl lp k s ch1 9 gl0420a 420 g 10 gl0660b 660 g 11 grgm660prim 660 g 12 gl0900d 900 g 13 grgm900c 900 g 14 grgm1200a 1200 g 15 cegm03 100 lo a15 a16 cl lp ch1 k s ch5t1 16 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 17 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 18 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 4 the huge expanse of mare basaltic volcanism associated with oceanus procellarum does not cause a positive gravity anomaly 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 19 moon oceanus procellarum ocean of storms ancient rift valleys rectangular structure visible topography grail gravity gradients october 1 2014 ancient rift valleys context ancient rift valleys closeup artist s concept mass of moon edit 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 13 12 20 the mass of the moon is m 7 3458 10 22 kg and the mean density is 3346 kg m 3 the lunar gm is 1 81 30057 of the earth s gm 21 theory edit 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 p nm the gravitational potential v at an external point is conventionally expressed as positive in astronomy and geophysics but negative in physics then with the former sign v g m r g m r r r n j n p n 0 sin ϕ g m r r r n c n m p n m sin ϕ cos m λ s n m p n m sin ϕ sin m λ displaystyle v left frac gm r right left frac gm r right sum left frac r r right n j_ n p_ n 0 sin phi left frac gm r right sum left frac r r right n c_ n m p_ n m sin phi cos m lambda s_ n m p_ n m sin phi sin m lambda where r is the radius to an external point with r r φ is the latitude of the external point and λ is the east longitude of the external point note that the spherical harmonic functions p nm can be normalized or unnormalized affecting the gravity coefficients j n c nm and s nm here we will use unnormalized functions and compatible coefficients the p n0 are called legendre polynomials and the p nm with m 0 are called the associated legendre polynomials where subscript n is the degree m is the order and m n the sums start at n 2 the unnormalized degree 2 functions are p 2 0 3 2 sin 2 ϕ 1 2 p 2 1 3 sin ϕ cos ϕ p 2 2 3 cos 2 ϕ displaystyle begin aligned p_ 2 0 frac 3 2 sin 2 phi frac 1 2 1ex p_ 2 1 3 sin phi cos phi 1ex p_ 2 2 3 cos 2 phi end aligned note that of the three functions only p 20 1 1 is finite at the poles more generally only p n0 1 1 are finite at the poles the gravitational acceleration of vector position r is d 2 r d t 2 v v r e r 1 r v ϕ e ϕ 1 r cos ϕ v λ e λ displaystyle begin aligned frac d 2 r dt 2 nabla v 1ex partial v over partial r e_ r frac 1 r partial v over partial phi e_ phi frac 1 r cos phi partial v over partial lambda e_ lambda end aligned where e r e φ and e λ are unit vectors in the three directions gravity coefficients edit the unnormalized gravity coefficients of degree 2 and 3 that were determined by the grail mission are given in table 1 13 12 20 the zero values of c 21 s 21 and s 22 are because a principal axis frame is being used there are no degree 1 coefficients when the three axes are centered on the center of mass lunar gravity coefficients nm j n c nm s nm 20 203 3 10 6 21 0 0 22 22 4 10 6 0 30 8 46 10 6 31 28 48 10 6 5 89 10 6 32 4 84 10 6 1 67 10 6 33 1 71 10 6 0 25 10 6 the j 2 coefficient for an oblate shape to the gravity field is affected by rotation and solid body tides whereas c 22 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 the c 31 coefficient is large simulating lunar gravity edit see also artificial gravity simulating lunar gravity 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 22 23 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 22 23 see also edit solar system portal magnetic field of the moon micro g environment references edit c hirt w e featherstone 2012 a 1 5 km resolution gravity field model of the moon earth and planetary science letters 329 330 22 30 bibcode 2012e psl 329 22h doi 10 1016 j epsl 2012 02 012 retrieved 2012 08 21 bell trudy e november 6 2006 phillips tony ed bizarre lunar orbits science nasa nasa archived from the original on 2021 12 04 retrieved 2017 09 08 lunar gravity model 2011 archived 2013 01 14 at the wayback machine 1 2 a konopliv s asmar e carranza w sjogren d yuan 2001 recent gravity models as a result of the lunar prospector mission icarus 50 1 1 18 bibcode 2001icar 150 1k doi 10 1006 icar 2000 6573 mazarico e lemoine f g han shin chan smith d e 2010 glgm 3 a degree 150 lunar gravity model from the historical tracking data of nasa moon orbiters journal of geophysical research 115 e5 e05001 1 14 bibcode 2010jgre 115 5001m doi 10 1029 2009je003472 issn 0148 0227 jianguo yan jinsong ping fei li jianfeng cao qian huang lihe fung 2010 chang e 1 precision orbit determination and lunar gravity field solution advances in space research 46 1 50 57 bibcode 2010adspr 46 50j doi 10 1016 j asr 2010 03 002 matsumoto k goossens s ishihara y liu q kikuchi f iwata t namiki n noda h hanada h et al 2010 an improved lunar gravity field model from selene and historical tracking data revealing the farside gravity features journal of geophysical research 115 e6 e06007 1 20 bibcode 2010jgre 115 6007m doi 10 1029 2009je003499 issn 0148 0227 mazarico e lemoine f g han shin chan smith d e 2010 glgm 3 a degree 150 lunar gravity model from the historical tracking data of nasa moon orbiters journal of geophysical research 115 e5 e05001 1 14 bibcode 2010jgre 115 5001m doi 10 1029 2009je003472 issn 0148 0227 yan jianguo goossens sander matsumoto koji ping jinsong harada yuji iwata takahiro namiki noriyuki li fei tang geshi et al 2012 cegm02 an improved lunar gravity model using chang e 1 orbital tracking data planetary and space science 62 1 1 9 bibcode 2012p ss 62 1y doi 10 1016 j pss 2011 11 010 zuber m t smith d e neumann g a goossens s andrews hanna j c head j w kiefer w s asmar s w konopliv a s et al 2016 gravity field of the orientale basin from the gravity recovery and interior laboratory mission science 354 6311 438 441 bibcode 2016sci 354 438z doi 10 1126 science aag0519 issn 0036 8075 pmc 7462089 pmid 27789835 konopliv alex s park ryan s yuan dah ning asmar sami w watkins michael m williams james g fahnestock eugene kruizinga gerhard paik meegyeong et al 2013 the jpl lunar gravity field to spherical harmonic degree 660 from the grail primary mission journal of geophysical research planets 118 7 1415 1434 bibcode 2013jgre 118 1415k doi 10 1002 jgre 20097 hdl 1721 1 85858 s2cid 16559256 1 2 3 lemoine frank g goossens sander sabaka terence j nicholas joseph b mazarico erwan rowlands david d loomis bryant d chinn douglas s caprette douglas s neumann gregory a smith david e 2013 high degree gravity models from grail primary mission data journal of geophysical research planets 118 8 1676 1698 bibcode 2013jgre 118 1676l doi 10 1002 jgre 20118 hdl 2060 20140010292 issn 2169 9097 1 2 3 konopliv alex s park ryan s yuan dah ning asmar sami w watkins michael m williams james g fahnestock eugene kruizinga gerhard paik meegyeong strekalov dmitry harvey nate 2014 high resolution lunar gravity fields from the grail primary and extended missions geophysical research letters 41 5 1452 1458 bibcode 2014georl 41 1452k doi 10 1002 2013gl059066 lemoine frank g goossens sander sabaka terence j nicholas joseph b mazarico erwan rowlands david d loomis bryant d chinn douglas s neumann gregory a smith david e zuber maria t 2014 grgm900c a degree 900 lunar gravity model from grail primary and extended mission data geophysical research letters 41 10 3382 3389 bibcode 2014georl 41 3382l doi 10 1002 2014gl060027 issn 0094 8276 pmc 4459205 pmid 26074638 goossens sander et al 2016 a global degree and order 1200 model of the lunar gravity field using grail mission data pdf yan jianguo liu shanhong xiao chi ye mao cao jianfeng harada yuji li fei li xie barriot jean pierre 2020 a degree 100 lunar gravity model from the chang e 5t1 mission astronomy astrophysics 636 a45 1 11 bibcode 2020a a 636a 45y doi 10 1051 0004 6361 201936802 issn 0004 6361 s2cid 216482920 p muller w sjogren 1968 mascons lunar mass concentrations science 161 3842 680 84 bibcode 1968sci 161 680m doi 10 1126 science 161 3842 680 pmid 17801458 s2cid 40110502 richard a kerr 12 april 2013 the mystery of our moon s gravitational bumps solved science 340 6129 138 39 doi 10 1126 science 340 6129 138 a pmid 23580504 nine planets 1 2 williams james g konopliv alexander s boggs dale h park ryan s yuan dah ning lemoine frank g goossens sander mazarico erwan nimmo francis weber renee c asmar sami w 2014 lunar interior properties from the grail mission journal of geophysical research planets 119 7 1546 1578 bibcode 2014jgre 119 1546w doi 10 1002 2013je004559 s2cid 7045590 park ryan s folkner william m williams james g boggs dale h 2021 the jpl planetary and lunar ephemerides de440 and de441 the astronomical journal 161 3 105 bibcode 2021aj 161 105p doi 10 3847 1538 3881 abd414 issn 1538 3881 s2cid 233943954 1 2 china building artificial moon that simulates low gravity with magnets futurism com recurrent ventures retrieved 17 january 2022 interestingly the facility was partly inspired by previous research conducted by russian physicist andrew geim in which he floated a frog with a magnet the experiment earned geim the ig nobel prize in physics a satirical award given to unusual scientific research it s cool that a quirky experiment involving floating a frog could lead to something approaching an honest to god antigravity chamber 1 2 stephen chen 12 january 2022 china has built an artificial moon that simulates low gravity conditions on earth south china morning post retrieved 17 january 2022 it is said to be the first of its kind and could play a key role in the co...