- Anonymous, Rochester, NY Greetings! Many people believe that the Moon does not have any gravity. In fact, the Moon, like every other massive object in the Universe, attracts every other massive object gravitationally. Even subatomic particles such as protons and neutrons exert a gravitational pull on proximate objects, although it is so slight as to be negligible. We use the term "surface gravity" in reference to the downward "pull" that objects experience when resting or moving on a larger body. Earth's average surface gravity is about 9.8 meters per second per second. When an object is tossed off a building top or a cliff apex, for instance, it accelerates toward the ground at 9.8 meters per second per second. The Moon's surface gravity is about 1/6th as powerful or about 1.6 meters per second per second. The Moon's surface gravity is weaker because it is far less massive than Earth. A body's surface gravity is proportional to its mass, but inversely proportional to the square of its radius. (To see how one can calculate the Moon's surface gravity, consult the Math Zone 6: http://usm.maine.edu/planet/mz-6-calculating-planets-surface-gravity) The Apollo astronauts were able to walk on the lunar surface because the Moon exerted a gravitational pull on them. Of course, the astronauts were able to leap higher on the Moon than on Earth because the Moon's surface gravity is so comparatively weak. When on Earth, a fully suited Apollo astronaut weighed about 500 pounds, equipment included. His weight was only about 80 pounds on the Moon.* We also draw your attention to the now-famous hammer-feather drop demonstration that Apollo 15 astronaut David Scott performed on the lunar surface. He demonstrated that in a vacuum, the falcon feather and a hammer, when dropped simultaneously from the same height, reach the ground at the same time. www.youtube.com/watch?v=5C5_dOEyAfk You will notice that the objects fall slowly, because their acceleration toward the surface is only 1/6th what it would be on Earth. Commander Scott's demonstration proved that objects of unequal mass fall at the same rate and, of course, proved that the Moon does, indeed, have gravity. *Some people use the terms "mass" and "weight" interchangeably. In fact, these values are quite different. "Mass" measures body's resistance to inertia. Provided you don't add or lose body matter, your mass is the same here as it would be on the Moon, Pluto or any place in this or any other galaxy. "Weight" measures the gravitational attraction the planet exerts on your body. You do not have the same weight on Earth as you would on the Moon, Pluto, or even the Sun or a neutron star.  Radial 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/s2, 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/s2 (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. 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
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
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. 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.[18] 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 km3/s2 from GRAIL analyses.[12][11][19] The mass of the Moon is M = 7.3458 × 1022 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 Pnm. 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, 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 Pnm can be normalized or unnormalized affecting the gravity coefficients Jn, Cnm, and Snm. Here we will use unnormalized functions and compatible coefficients. The Pn0 are called Legendre polynomials and the Pnm 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
Note that of the three functions, only P20(±1)=1 is finite at the poles. More generally, only Pn0(±1)=1 are finite at the poles. The gravitational acceleration of vector position r is where er, eφ, and eλ 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.[12][11][19] The zero values of C21, S21, and S22 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
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. The C31 coefficient is large. Simulating lunar gravity[edit]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.[21][22] See also[edit]
References[edit]
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