What is the moons gravity relative to earth?

The acceleration due to gravity on the surface of the Moon is approximately i.625 m/south², about sixteen.6% that on Earth'southward surface or 0.166 ɡ .^[1] Over the entire surface, the variation in gravitational acceleration is about 0.0253 m/sⁱⁱ (1.6% of the dispatch due to gravity). Because weight is directly dependent upon gravitational acceleration, things on the Moon will weigh only 16.six% (= ane/half-dozen) 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 result, whereby the line-of-sight spacecraft dispatch can exist measured by modest 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 simply "stable" orbits are at inclinations about 27º, 50º, 76º, and 86 degrees.^[two] Because of the Moon's synchronous rotation information technology is not possible to track spacecraft from Earth much beyond the limbs of the Moon, and so until the contempo Gravity Recovery and Interior Laboratory (GRAIL) mission the far-side gravity field was not well mapped.

The missions with accurate Doppler tracking that accept been used for deriving gravity fields are in the accompanying table. The table gives the mission spacecraft proper noun, a brief designation, the number of mission spacecraft with authentic tracking, the country of origin, and the time span of the Doppler data. Apollos 15 and xvi released subsatellites. The Kaguya/SELENE mission had tracking between 3 satellites to go far-side tracking. GRAIL had very authentic tracking betwixt 2 spacecraft and tracking from Earth.

Missions Used for Lunar Gravity

Mission	ID	Number	Source	Years
Lunar Orbiter 1	LO1	1	Usa	1966
Lunar Orbiter two	LO2	1	US	1966–1967
Lunar Orbiter 3	LO3	one	Us	1967
Lunar Orbiter 4	LO4	ane	US	1967
Lunar Orbiter v	LO5	1	The states	1967–1968
Apollo 15 Subsatellite	A15	ane	Us	1971–1972
Apollo 16 Subsatellite	A16	1	US	1972
Clementine	Cl	1	United states	1994
Lunar Prospector	LP	1	United states	1998–1999
Kaguya/SELENE	K/S	iii	Japan	2007–2009
Chang'east i	Ch1	one	Prc	2007–2009
GRAIL	1000	2	The states	2012
Chang'e 5T1	Ch1T1	1	Red 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 authentic; other missions are non combined with GRAIL.

Lunar Gravity Fields

Designation	Degree	Mission IDs	Citation
LP165P	165	LO A15 A16 Cl LP	[iii]
GLGM3	150	LO A15 A16 Cl LP	[4]
CEGM01	50	Ch 1	[5]
SGM100h	100	LO A15 A16 Cl LP One thousand/South	[6]
SGM150J	150	LO A15 A16 Cl LP K/S	[7]
CEGM02	100	LO A15 A16 Cl LP K/S Ch1	[viii]
GL0420A	420	G	[ix]
GL0660B	660	G	[10]
GRGM660PRIM	660	G	[11]
GL0900D	900	Chiliad	[12]
GRGM900C	900	G	[13]
GRGM1200A	1200	Yard	[14]
CEGM03	100	LO A15 A16 Cl LP Ch1 K/S Ch5T1	[15]

A major feature of the Moon'south gravitational field is the presence of mascons, which are large positive gravity anomalies associated with some of the giant bear upon 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 assay of Lunar Orbiter tracking data:^[xvi] navigation tests prior to the Apollo plan showed positioning errors much larger than mission specifications.

Mascons are in role 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 too. Based on Lunar Prospector gravitational models, it has been suggested that some mascons be that exercise not show prove for mare basaltic volcanism.^[iii] The huge expanse of mare basaltic volcanism associated with Oceanus Procellarum does not cause a positive gravity anomaly. The eye of gravity of the Moon does not coincide exactly with its geometric center, merely is displaced toward the Earth by about 2 kilometers.^[18]

Mass of Moon [edit]

The Gravitational abiding G is less accurate than the production of G and masses for Earth and Moon. Consequently, it is conventional to limited the lunar mass M multiplied by the gravitational abiding Thousand. The lunar GM = 4902.8001 km^three/s^two from GRAIL analyses.^{[12] [eleven] [nineteen]} The mass of the Moon is M = 7.3458×x²² kg and the mean density is 3346 kg/m³. The lunar GM is 1/81.30057 of the Earth's GM.^[20]

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 Five at an external betoken is conventionally expressed as positive in astronomy and geophysics, only negative in physics. And so, with the former sign,

${\displaystyle 5=\left({\frac {GM}{r}}\correct)-\left({\frac {GM}{r}}\right)\sum \left({\frac {R}{r}}\right)^{n}J_{n}P_{n,0}(sin\phi )+\left({\frac {GM}{r}}\right)\sum \left({\frac {R}{r}}\right)^{n}[C_{n,m}P_{n,m}(sin\phi )cos(1000\lambda )+S_{north,m}P_{due north,m}(sin\phi )sin(thousand\lambda )]}$

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_{due north} , C_nm , and Southward_nm . Here nosotros volition 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 club, and m≤n. The sums first at n=two. The unnormalized degree-2 functions are

${\displaystyle P_{two,0}=\left({\frac {three}{2}}\right)sin^{2}\phi -\left({\frac {ane}{2}}\correct)}$

${\displaystyle P_{2,1}=3\sin \phi \cos \phi }$

${\displaystyle P_{2,two}=iii\cos ^{2}\phi }$

Note that of the three functions, only P ₂₀(±1)=1 is finite at the poles. More than more often than not, only P _n0(±1)=i are finite at the poles.

The gravitational dispatch of vector position r is

${\displaystyle \left({\frac {d^{2}r}{dt^{two}}}\right)=\nabla 5}$

${\displaystyle \left({\frac {d^{2}r}{dt^{ii}}}\correct)={\partial V \over \partial r}e_{r}+\left({\frac {1}{r}}\right){\partial V \over \partial \phi }e_{\phi }+\left({\frac {ane}{rcos\phi }}\right){\partial 5 \over \partial \lambda }{\mathsf {e_{\lambda }}}}$

where e_r , e _φ, and east _λ are unit vectors in the iii directions.

Gravity coefficients [edit]

The unnormalized gravity coefficients of degree 2 and iii that were adamant past the GRAIL mission are given in Tabular array i.^{[12] [eleven] [19]} The zero values of C ₂₁, S ₂₁, and S ₂₂ are because a main axis frame is being used. There are no degree-1 coefficients when the three axes are centered on the centre of mass.

Lunar Gravity Coefficients

nm	J north	Cnm	Snm
20	203.three×x−6	—	—
21	—	0	0
22	—	22.4×x−6	0
30	8.46×x−half-dozen	—	—
31	—	28.48×10−6	5.89×10−6
32	—	four.84×x−6	1.67×10−6
33	—	1.71×10−6	-0.25×10−vi

The J ₂ coefficient for an oblate shape to the gravity field is affected past 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]

In Jan 2022 People's republic of china was reported by the Southward Cathay Morning Postal service to accept congenital a small (threescore centimeters in diameter) research facility to simulate depression lunar gravity with the assistance of magnets.^{[21] [22]} The facility was reportedly partly inspired by the work of Andre Geim (who subsequently shared the 2010 Nobel Prize in Physics for his research on graphene) and Michael Drupe, who both shared the Ig Nobel Prize in Physics in 2000 for the magnetic levitation of a frog.^{[21] [22]}

See as well [edit]

• Magnetic field of the Moon
• Micro-g environs

References [edit]

1. ^ C. Hirt; West. Eastward. 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 .
2. ^ Bell, Trudy E. (November 6, 2006). Phillips, Tony (ed.). "Bizarre Lunar Orbits". Science@NASA. NASA. Retrieved 2017-09-08 .
3. ^ ^{a b} A. Konopliv; Southward. Asmar; E. Carranza; W. Sjogren; D. Yuan (2001). "Recent gravity models as a result of the Lunar Prospector mission". Icarus. fifty (ane): ane–18. Bibcode:2001Icar..150....1K. CiteSeerX10.1.1.18.1930. doi:10.1006/icar.2000.6573.
4. ^ Mazarico, Due east.; Lemoine, F. Thousand.; Han, Shin-Chan; Smith, D. Eastward. (2010). "GLGM-three: A degree-150 lunar gravity model from the historical tracking data of NASA Moon orbiters". Periodical of Geophysical Research. 115 (E5): E05001, 1–14. Bibcode:2010JGRE..115.5001M. doi:10.1029/2009JE003472. ISSN 0148-0227.
5. ^ Jianguo, Yan; Jinsong, Ping; Fei, Li; Jianfeng, Cao; Qian, Huang; Lihe, Fung (2010). "Chang'East-one precision orbit conclusion and lunar gravity field solution". Advances in Space Research. 46 (ane): 50–57. Bibcode:2010AdSpR..46...50J. doi:10.1016/j.asr.2010.03.002.
6. ^ Matsumoto, K.; Goossens, South.; Ishihara, Y.; Liu, Q.; Kikuchi, F.; Iwata, T.; Namiki, North.; Noda, H.; Hanada, H.; et al. (2010). "An improved lunar gravity field model from SELENE and historical tracking information: Revealing the farside gravity features". Periodical of Geophysical Research. 115 (E6): E06007, 1–20. Bibcode:2010JGRE..115.6007M. doi:ten.1029/2009JE003499. ISSN 0148-0227.
7. ^ Mazarico, E.; Lemoine, F. 1000.; 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 Inquiry. 115 (E5): E05001, 1–xiv. Bibcode:2010JGRE..115.5001M. doi:10.1029/2009JE003472. ISSN 0148-0227.
8. ^ 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 information". Planetary and Infinite Science. 62 (ane): 1–9. Bibcode:2012P&SS...62....1Y. doi:10.1016/j.pss.2011.11.010.
9. ^ Zuber, M. T.; Smith, D. East.; Neumann, G. A.; Goossens, S.; Andrews-Hanna, J. C.; Caput, J. W.; Kiefer, W. South.; Asmar, South. 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. PMC7462089. PMID 27789835.
10. ^ Konopliv, Alex S.; Park, Ryan S.; Yuan, Dah-Ning; Asmar, Sami W.; Watkins, Michael Thou.; Williams, James G.; Fahnestock, Eugene; Kruizinga, Gerhard; Paik, Meegyeong; et al. (2013). "The JPL lunar gravity field to spherical harmonic caste 660 from the GRAIL Primary Mission". Periodical of Geophysical Research: Planets. 118 (vii): 1415–1434. Bibcode:2013JGRE..118.1415K. doi:10.1002/jgre.20097. hdl:1721.1/85858.
11. ^ ^{a b c} 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 East. (2013). "High‒caste gravity models from GRAIL primary mission information". Journal of Geophysical Research: Planets. 118 (8): 1676–1698. Bibcode:2013JGRE..118.1676L. doi:ten.1002/jgre.20118. ISSN 2169-9097.
12. ^ ^{a b c} Konopliv, Alex S.; Park, Ryan Southward.; Yuan, Dah-Ning; Asmar, Sami W.; Watkins, Michael K.; Williams, James 1000.; Fahnestock, Eugene; Kruizinga, Gerhard; Paik, Meegyeong; Strekalov, Dmitry; Harvey, Nate (2014). "Loftier-resolution lunar gravity fields from the GRAIL Primary and Extended Missions". Geophysical Research Letters. 41 (v): 1452–1458. Bibcode:2014GeoRL..41.1452K. doi:ten.1002/2013GL059066.
13. ^ Lemoine, Frank K.; Goossens, Sander; Sabaka, Terence J.; Nicholas, Joseph B.; Mazarico, Erwan; Rowlands, David D.; Loomis, Bryant D.; Chinn, Douglas Southward.; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T. (2014). "GRGM900C: A degree 900 lunar gravity model from GRAIL main and extended mission data". Geophysical Research Messages. 41 (10): 3382–3389. Bibcode:2014GeoRL..41.3382L. doi:10.1002/2014GL060027. ISSN 0094-8276. PMC4459205. PMID 26074638.
14. ^ Goossens, Sander; et, al. (2016). "A global degree and guild 1200 model of the lunar gravity field using GRAIL mission data" (PDF). {{cite web}}: CS1 maint: url-status (link)
15. ^ Yan, Jianguo; Liu, Shanhong; Xiao, Chi; Ye, Mao; Cao, Jianfeng; Harada, Yuji; Li, Fei; Li, Xie; Barriot, Jean-Pierre (2020). "A caste-100 lunar gravity model from the Chang'east 5T1 mission". Astronomy & Astrophysics. 636: A45, i–eleven. Bibcode:2020A&A...636A..45Y. doi:x.1051/0004-6361/201936802. ISSN 0004-6361.
16. ^ P. Muller; W. Sjogren (1968). "Mascons: Lunar mass concentrations". Scientific discipline. 161 (3842): 680–84. Bibcode:1968Sci...161..680M. doi:10.1126/science.161.3842.680. PMID 17801458. S2CID 40110502.
17. ^ Richard A. Kerr (12 Apr 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.
18. ^ 9 Planets
19. ^ ^{a b} Williams, James G.; Konopliv, Alexander Due south.; Boggs, Dale H.; Park, Ryan Southward.; Yuan, Dah-Ning; Lemoine, Frank Thou.; Goossens, Sander; Mazarico, Erwan; Nimmo, Francis; Weber, Renee C.; Asmar, Sami Westward. (2014). "Lunar interior properties from the GRAIL mission". Periodical of Geophysical Research: Planets. 119 (7): 1546–1578. Bibcode:2014JGRE..119.1546W. doi:10.1002/2013JE004559.
20. ^ Park, Ryan S.; Folkner, William One thousand.; Williams, James G.; Boggs, Dale H. (2021). "The JPL Planetary and Lunar Ephemerides DE440 and DE441". The Astronomical Periodical. 161 (iii): 105. Bibcode:2021AJ....161..105P. doi:10.3847/1538-3881/abd414. ISSN 1538-3881. S2CID 233943954.
21. ^ ^{a b} "Communist china building "Artificial Moon" that simulates depression gravity with magnets". Futurism.com. Recurrent Ventures. Retrieved 17 January 2022. Interestingly, the facility was partly inspired by previous inquiry 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 inquiry. It's absurd that a quirky experiment involving floating a frog could lead to something approaching an honest-to-God antigravity sleeping accommodation.
22. ^ ^{a b} Stephen Chen (12 January 2022). "People's republic of china has built an artificial moon that simulates low-gravity conditions on Earth". South China Morn Post. Retrieved 17 January 2022. It is said to exist the first of its kind and could play a key role in the country's future lunar missions. Landscape is supported by a magnetic field and was inspired by experiments to levitate a frog.

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Source: https://en.wikipedia.org/wiki/Gravitation_of_the_Moon

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