![Earth vs Mars gravity at elevation](https://upload.wikimedia.org/wikipedia/commons/4/48/Earth_vs_Mars_gravity_at_elevation.webp)
The gravity of Mars is a natural phenomenon, due to the
law of gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
, or gravitation, by which all things with mass around the planet
Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...
are brought towards it. It is weaker than
Earth's gravity
The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).
It is a vector quanti ...
due to the planet's smaller mass. The average
gravitational acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies ...
on Mars is 3.72076 ms
−2 (about 38% of
that of Earth) and it varies.
In general, topography-controlled
isostasy
Isostasy (Greek ''ísos'' "equal", ''stásis'' "standstill") or isostatic equilibrium is the state of gravitational equilibrium between Earth's crust (or lithosphere) and mantle such that the crust "floats" at an elevation that depends on its ...
drives the short wavelength free-air
gravity anomalies.
At the same time,
convective flow and finite strength of the mantle lead to long-wavelength planetary-scale
free-air gravity anomalies over the entire planet.
Variation in crustal thickness, magmatic and volcanic activities, impact-induced
Moho-uplift, seasonal variation of polar ice caps, atmospheric mass variation and variation of
porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
of the crust could also correlate to the lateral variations.
Over the years models consisting of an increasing but limited number of
spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields.
Since the spherical harmonics form a ...
have been produced. Maps produced have included
free-air gravity anomaly In geophysics, the free-air gravity anomaly, often simply called the free-air anomaly, is the measured gravity anomaly after a free-air correction is applied to account for the elevation at which a measurement is made. It does so by adjusting these ...
,
Bouguer gravity anomaly, and crustal thickness. In some areas of Mars there is a correlation between gravity anomalies and topography. Given the known topography, higher resolution gravity field can be inferred. Tidal deformation of Mars by the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
or
Phobos can be measured by its gravity. This reveals how stiff the interior is, and shows that the core is partially liquid.
The study of surface gravity of Mars can therefore yield information about different features and provide beneficial information for future landings.
Measurement
![Rotating spherical harmonics](https://upload.wikimedia.org/wikipedia/commons/1/12/Rotating_spherical_harmonics.gif)
To understand the gravity of Mars, its
gravitational field strength
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
''g'' and gravitational potential ''U'' are often measured. Simply, if Mars is assumed to be a static perfectly spherical body of radius ''R
M'', provided that there is only one satellite revolving around Mars in a circular orbit and such gravitation interaction is the only force acting in the system, the equation would be
:
where ''G'' is the
universal constant of gravitation (commonly taken as ''G'' = 6.674 × 10
−11 m
3 kg
−1 s
−2), ''M'' is the mass of Mars (most updated value: 6.41693 × 10
23 kg), ''m'' is the mass of the satellite, ''r'' is the distance between Mars and the satellite, and
is the
angular velocity of the satellite, which is also equivalent to
(''T'' is the orbiting period of the satellite).
Therefore,
, where ''R
M'' is the radius of Mars. With proper measurement, ''r'', ''T'', and ''R
M'' are obtainable parameters from Earth.
However, as Mars is a generic, non-spherical planetary body and influenced by complex geological processes, more accurately, the
gravitational potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric ...
is described with
spherical harmonic functions, following convention in geodesy; see
Geopotential model.
:
where
are spherical coordinates of the test point.
is longitude and
is latitude.
and
are dimensionless harmonic coefficients of degree
and order
.
is the Legendre polynomial of degree
with
and is the associated Legendre polynomial with
. These are used to describe solutions of
Laplace's equation.
is the mean radius of the planet.
The coefficient
is sometimes written as
.
# The lower the degree
and order
, the longer wavelength of anomaly it represents. In turn, long-wavelength gravity anomaly is influenced by global geophysical structures.
# The higher the degree
and order
, the shorter wavelength of anomaly it represents. For degree over 50, it has been shown that those variations have high correlation with the topography.
Geophysical interpretation of surface features could further help deriving a more complete picture of the Martian gravity field, though misleading results could be produced.
The oldest technique in determining the gravity of Mars is through Earth-based observation. Later with the arrival of unmanned spacecraft, subsequent gravity models were developed from radio tracking data.
Earth-based observation
Before the arrival of the
Mariner 9
Mariner 9 (Mariner Mars '71 / Mariner-I) was a robotic spacecraft that contributed greatly to the exploration of Mars and was part of the NASA Mariner program. Mariner 9 was launched toward Mars on May 30, 1971 from LC-36B at Cape Canaveral Air ...
and
Viking orbiter
The ''Viking'' program consisted of a pair of identical American space probes, ''Viking 1'' and ''Viking 2'', which landed on Mars in 1976. Each spacecraft was composed of two main parts: an orbiter designed to photograph the surface of Mars f ...
spacecraft at Mars, only an estimate of the Mars gravitational constant GM, i.e. the
universal constant of gravitation times the mass of Mars, was available for deducing the properties of the Martian gravity field.
GM could be obtained through observations of the motions of the natural satellites of Mars (
Phobos and
Deimos) and spacecraft flybys of Mars (
Mariner 4
Mariner 4 (together with Mariner 3 known as Mariner-Mars 1964) was the fourth in a series of spacecraft intended for planetary exploration in a flyby mode. It was designed to conduct closeup scientific observations of Mars and to transmit the ...
and
Mariner 6
A sailor, seaman, mariner, or seafarer is a person who works aboard a watercraft as part of its crew, and may work in any one of a number of different fields that are related to the operation and maintenance of a ship.
The profession of the s ...
).
Long term Earth-based observations of the motions of Phobos and Deimos provide physical parameters including
semi-major axis,
eccentricity
Eccentricity or eccentric may refer to:
* Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal"
Mathematics, science and technology Mathematics
* Off-Centre (geometry), center, in geometry
* Eccentricity (g ...
, inclination angle to the
Laplacian plane The Laplace plane or Laplacian plane of a planetary satellite, named after its discoverer Pierre-Simon Laplace (1749–1827), is a mean or reference plane about whose axis the instantaneous orbital plane of that satellite precesses.
Laplace's na ...
etc.,
which allow calculation of the ratio of solar mass to the mass of Mars,
moment of inertia and coefficient of the gravitational potential of Mars, and give initial estimates of the gravity field of Mars.
Inferred from radio tracking data
![Three way doppler](https://upload.wikimedia.org/wikipedia/commons/f/fe/Three_way_doppler.jpg)
Precise tracking of spacecraft is of prime importance for accurate gravity modeling, as gravity models are developed from observing tiny perturbation of spacecraft, i.e. small variation in velocity and altitude. The tracking is done basically by the antennae of the
Deep Space Network
The NASA Deep Space Network (DSN) is a worldwide network of American spacecraft communication ground segment facilities, located in the United States (California), Spain (Madrid), and Australia (Canberra), that supports NASA's interplanetary ...
(DSN), with one-way, two-way and three-way Doppler and range tracking applied.
One-way tracking means the data is transmitted in one way to the DSN from the spacecraft, while two-way and three-way involve transmitting signals from Earth to the spacecraft (uplink), and thereafter transponded coherently back to the Earth (downlink).
The difference between two-way and three-way tracking is, the former one has the same signal transmitter and receiver on Earth, while the latter one has the transmitter and receiver at different locations on Earth.
The use of these three types of tracking data enhances the coverage and quality of the data, as one could fill in the data gap of another.
Doppler tracking is a common technique in tracking the spacecraft, utilizing radial velocity method, which involves detection of Doppler shifts.
As the spacecraft moves away from us along line of sight, there would be redshift of signal, while for the reverse, there would be blueshift of signal. Such technique has also been applied for observation of the motion of exoplanets. While for the range tracking, it is done through measurement of round trip propagation time of the signal.
Combination of
Doppler shift and range observation promotes higher tracking accuracy of the spacecraft.
The tracking data would then be converted to develop global gravity models using the spherical harmonic equation displayed above. However, further elimination of the effects due to affect of
solid tide, various relativistic effects due to the Sun, Jupiter and Saturn,
non-conservative force
In physics, a conservative force is a force with the property that the total work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done (the sum o ...
s (e.g.
angular momentum desaturation
Angular may refer to:
Anatomy
* Angular artery, the terminal part of the facial artery
* Angular bone, a large bone in the lower jaw of amphibians and reptiles
* Angular incisure, a small anatomical notch on the stomach
* Angular gyrus, a region o ...
s (AMD),
atmospheric drag
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
and
solar radiation pressure
Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is a ...
) have to be done,
otherwise, considerable errors result.
History
The latest gravity model for Mars is the Goddard Mars Model 3 (GMM-3), produced in 2016, with spherical harmonics solution up to degree and order 120.
This model is developed from 16 years of radio tracking data from Mars Global Surveyor (MGS), Mars Odyssey and Mars Reconnaissance Orbiter (MRO), as well as the MOLA topography model and provides a global resolution of 115 km.
A separate free-air gravity anomaly map, Bouguer gravity anomaly map and a map of crustal thickness were produced along with this model.
Compared with MRO110C and other previous models, major improvement of the estimation of the gravity field comes from more careful modeling of the non-conservative forces applied to the spacecraft.
The techniques in tracking the spacecraft and geophysical interpretation of surface features can affect the resolution of the strength of gravity field. The better technique favors spherical harmonic solutions to higher degrees and orders. Independent analysis on
Mariner 9
Mariner 9 (Mariner Mars '71 / Mariner-I) was a robotic spacecraft that contributed greatly to the exploration of Mars and was part of the NASA Mariner program. Mariner 9 was launched toward Mars on May 30, 1971 from LC-36B at Cape Canaveral Air ...
and
Viking Orbiter
The ''Viking'' program consisted of a pair of identical American space probes, ''Viking 1'' and ''Viking 2'', which landed on Mars in 1976. Each spacecraft was composed of two main parts: an orbiter designed to photograph the surface of Mars f ...
tracking data yielded a degree and order of 6 spherical harmonic solution.,
Further combination of the two data sets, along with correlation of anomalies with volcanic features (positive anomaly) and deep-printed depression (negative anomaly) assisted by image data allows a degree and order of 18 spherical harmonic solution produced.
Further use of spatial a priori constraint method, which had taken the topography into account in solving the Kaula power law constraint, had favored model of up to degree 50 spherical harmonic solution in global resolution (
Goddard Mars Model-1 Goddard may refer to:
People
* Goddard (given name)
* Goddard (surname)
Places in the United States
* Goddard, Kansas
*Goddard, Kentucky
*Goddard, Maryland
*Goddard College, a low-residency college with campuses in Vermont and Washington
*God ...
, or GMM-1)
then the subsequent models with higher completeness and degree and order up to 120 for the latest GMM-3.
![GMM-3 Free air gravity anomaly](https://upload.wikimedia.org/wikipedia/commons/2/2d/GMM-3_Free_air_gravity_anomaly.jpg)
Therefore, gravity models nowadays are not directly produced through transfer of the measured gravity data to any spatial information system because there is difficulty in producing model with sufficiently high resolution.
Topography
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps.
Topography is a field of geoscience and planetary sci ...
data obtained from the
MOLA instrument aboard the Mars Global Surveyor thus becomes a useful tool in producing a more detailed short-scale gravity model, utilizing the gravity-topography correlation in short-wavelength.
However, not all regions on Mars show such correlation, notably the northern lowland and the poles.
Misleading results could be easily produced, which could lead to wrong geophysics interpretation.
The later modifications of gravity model include taking other non-conservative forces acting on spacecraft into account, including
atmospheric drag
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
,
solar radiation pressure
Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is a ...
, Mars reflected
solar radiation pressure
Radiation pressure is the mechanical pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is a ...
, Mars
thermal emission
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
, and spacecraft thrusting which despins or desaturates the
angular moment wheels
Angular may refer to:
Anatomy
* Angular artery, the terminal part of the facial artery
* Angular bone, a large bone in the lower jaw of amphibians and reptiles
* Angular incisure, a small anatomical notch on the stomach
* Angular gyrus, a region o ...
.
In addition, Martian
precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
and third body attraction due to the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
,
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
and planets, which could affect the spacecraft orbit, as well as
relavistic effects on the measurements should also be corrected.
These factors could lead to offset of the true gravity field. Accurate modeling is thus required to eliminate the offset. Such work is still ongoing.
Static gravity field
Many researchers have outlined the correlation between short-wavelength (locally varying) free-air gravity anomalies and topography. For regions with higher correlation, free-air gravity anomalies could be expanded to higher degree strength through geophysical interpretation of surface features,
so that the gravity map could offer higher resolution. It has been found that the southern highland has high gravity/topography correlation but not for the northern lowland.
Therefore, the resolution of free-air gravity anomaly model typically has higher resolution for the southern hemisphere, as high as over 100 km.
Free-air gravity anomalies are relatively easier to measure than the
Bouguer anomalies as long as topography data is available because it does not need to eliminate the gravitational effect due to the effect of mass surplus or deficit of the terrain after the gravity is reduced to sea level. However, to interpret the crustal structure, further elimination of such gravitational effect is necessary so that the reduced gravity would only be the result of the core, mantle and crust below datum.
The product after elimination is the Bouguer anomalies. However, density of the material in building up the terrain would be the most important constraint in the calculation, which may vary laterally on the planet and is affected by porosity and geochemistry of the rock.
Relevant information could be obtained from Martian meteorites and in-situ analysis.
Local gravity anomalies
Since Bouguer gravity anomalies have strong links with depth of crust-mantle boundary, one with positive Bouguer anomalies may mean that it has a thinner crust composed of lower density material and is influenced more strongly by the denser mantle, and vice versa. However, it could also be contributed by the difference in density of the erupted volcanic load and sedimentary load, as well as subsurface intrusion and removal of material.
Many of these anomalies are associated with either geological or topographic features.
Few exception includes the 63°E, 71°N anomaly,
which may represent an extensive buried structure as large as over 600 km, predated the early-Noachian buried surface.
Topography anomalies
Strong correlation between topography and short-wavelength free-air gravity anomalies has been shown for both study of the gravity field of the Earth and the Moon,
and it can be explained by the wide occurrence of isostasy.
High correlation is expected for degree over 50 (short-wavelength anomaly) on Mars.
And it could be as high as 0.9 for degrees between 70 and 85.
Such correlation could be explained by flexural compensation of topographic loads.
It is noted that older regions on Mars are isostatically compensated when the younger region are usually only partially compensated.
Anomalies from volcanic constructs
Different volcanic constructs could behave differently in terms of gravity anomalies. Volcanoes
Olympus Mons
Olympus Mons (; Latin for Mount Olympus) is a large shield volcano on Mars. The volcano has a height of over 21.9 km (13.6 mi or 72,000 ft) as measured by the Mars Orbiter Laser Altimeter (MOLA). Olympus Mons is about two and a h ...
and the
Tharsis Montes
The Tharsis Montes () are three large shield volcanoes in the Tharsis region of the planet Mars. From north to south, the volcanoes are Ascraeus Mons, Pavonis Mons and Arsia Mons. Mons (plural ''montes'') is the Latin word for mountain; it is a ...
produce the smallest positive free-air gravity anomalies in the solar system.
Alba Patera
Alba Mons (formerly and still occasionally known as Alba Patera, a term that has since been restricted to the volcano's summit caldera; also initially known as the Arcadia ring) is a volcano located in the northern Tharsis region of the planet Ma ...
, also a volcanic rise, north of the
Tharsis Montes
The Tharsis Montes () are three large shield volcanoes in the Tharsis region of the planet Mars. From north to south, the volcanoes are Ascraeus Mons, Pavonis Mons and Arsia Mons. Mons (plural ''montes'') is the Latin word for mountain; it is a ...
, however, produces negative Bouguer anomaly, though its extension is similar to that of Olympus Mons.
And for the
Elysium Mons
Elysium Mons is a volcano on Mars located in the volcanic province Elysium, at , in the Martian eastern hemisphere. It stands about above its base, and about above the Martian ''datum'', making it the third tallest Martian mountain in terms o ...
, its center is found to have slight increase in Bouguer anomalies in an overall broad negative anomaly context in the Elysium rise.
The knowledge of anomaly of volcanoes, along with density of the volcanic material, would be useful in determining the lithospheric composition and crustal evolution of different volcanic edifices.
It has been suggested that the extruded lava could range from
andesite
Andesite () is a volcanic rock of intermediate composition. In a general sense, it is the intermediate type between silica-poor basalt and silica-rich rhyolite. It is fine-grained (aphanitic) to porphyritic in texture, and is composed predomi ...
(low density) to
basalt
Basalt (; ) is an aphanite, aphanitic (fine-grained) extrusive igneous rock formed from the rapid cooling of low-viscosity lava rich in magnesium and iron (mafic lava) exposed at or very near the planetary surface, surface of a terrestrial ...
ic (high density) and the composition could change during the construction of the volcanic shield, which contributes to the anomaly.
Another scenario is it is possible for high density material intruded beneath the volcano.
Such setting has already been observed over the famous Syrtis major, which has been inferred to have an extinct
magma chamber
A magma chamber is a large pool of liquid rock beneath the surface of the Earth. The molten rock, or magma, in such a chamber is less dense than the surrounding country rock, which produces buoyant forces on the magma that tend to drive it up ...
with 3300 kg m
3 underlying the volcano, evident from positive Bouguer anomaly.
Anomalies from depressions
Different depressions also behave differently in Bouguer anomaly. Giant impact basins like
Argyre,
Isidis,
Hellas and
Utopia
A utopia ( ) typically describes an imaginary community or society that possesses highly desirable or nearly perfect qualities for its members. It was coined by Sir Thomas More for his 1516 book ''Utopia (book), Utopia'', describing a fictional ...
basins also exhibit very strong positive Bouguer anomalies in circular manner.
These basins have been debated for their impact crater origin. If they are, the positive anomalies may be due to uplift of Moho, crustal thinning and modification events by sedimentary and volcanic surface loads after impacting.
But at the same time there are also some large basins that are not associated with such positive Bouguer anomaly, for example,
Daedalia, northern Tharsis and
Elysium
Elysium (, ), otherwise known as the Elysian Fields ( grc, Ἠλύσιον πεδίον, ''Ēlýsion pedíon'') or Elysian Plains, is a conception of the afterlife that developed over time and was maintained by some Greek religious and philos ...
, which are believed to be underlain by the
northern lowland
The North German Plain or Northern Lowland (german: Norddeutsches Tiefland) is one of the major geographical regions of Germany. It is the German part of the North European Plain. The region is bounded by the coasts of the North Sea and the Balti ...
plain.
In addition, certain portions of
Coprates,
Eos Chasma
Eos Chasma is a chasma in the southern part of the Valles Marineris canyon system of the Coprates quadrangle and the Margaritifer Sinus quadrangles of the planet Mars.
Eos Chasma’s western floor is mainly composed of an etched massive mater ...
and
Kasei Valles
The Kasei Valles are a giant system of canyons in Mare Acidalium and Lunae Palus quadrangles on Mars, centered at 24.6° north latitude and 65.0° west longitude. They are long and were named for the word for "Mars" in Japanese. This is one ...
are also found to have positive Bouguer anomalies,
though they are topographic depressions. This may suggest that these depressions are underlain by shallow dense intrusion body.
Global gravity anomalies
Global gravity anomalies, also termed as long-wavelength gravity anomalies, are the low-degree harmonics of the gravity field,
which cannot be attributed to local isostasy, but rather finite strength of the mantle and density differences in the convection current.
For Mars, the largest component of Bouguer anomaly is the degree one harmonic, which represents the mass deficit in the southern hemisphere and excess in the northern hemisphere.
The second largest component corresponds to the
planet flattening
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young ...
and
Tharsis
Tharsis () is a vast volcanic plateau centered near the equator in the western hemisphere of Mars. The region is home to the largest volcanoes in the Solar System, including the three enormous shield volcanoes Arsia Mons, Pavonis Mons, and Asc ...
bulge.
Early study of the geoid in the 1950s and 1960s has focused on the low-degree harmonics of the Earth's gravity field in order to understand its interior structure.
It has been suggested that such long-wavelength anomalies on Earth could be contributed by the sources located in deep mantle and not in the crust, for example, caused by the density differences in driving the
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
current,
which has been evolving with time. The correlation between certain topography anomalies and long-wavelength gravity anomalies, for example, the
mid-Atlantic ridge
The Mid-Atlantic Ridge is a mid-ocean ridge (a divergent or constructive plate boundary) located along the floor of the Atlantic Ocean, and part of the longest mountain range in the world. In the North Atlantic, the ridge separates the North ...
and
Carlsberg ridge, which are topography high and gravity high on the ocean floor, thus became the argument for the convection current idea on Earth in the 1970s, though such correlations are weak in the global picture.
Another possible explanation for the global scale anomalies is the
finite strength of the mantle (in contrast to zero stress), which makes the gravity deviated from
hydrostatic equilibrium
In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...
.
[Jeffreys, H. (1959). The Earth 4th ed., 420.] For this theory, because of the finite strength, flow may not exist for most of the region that are understressed.
And the variations of density of the deep mantle could be the result of chemical inhomogeneities associated with continent separations,
and scars left on Earth after the torn away of the moon.
These are the cases suggested to work when slow flow is allowed to happen under certain circumstances.
However, it has been argued that the theory may not be physically feasible.
Time-variable gravity field
Seasonal change of gravity field at the poles
The
sublimation-
condensation cycle of
carbon dioxide
Carbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transpar ...
on Mars between the
atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
and
cryosphere
]
The cryosphere (from the Ancient Greek, Greek ''kryos'', "cold", "frost" or "ice" and ''sphaira'', "globe, ball") is an all-encompassing term for those portions of Earth's surface where water is in solid form, including sea ice, lake ice, ri ...
(polar ice cap) operates seasonally.
This cycle contributes as almost the only variable accounting for changes in gravity field on Mars.
The measured gravitational potential of Mars from orbiters could be generalized as the equation below,
:
In turn, when there is more mass in the seasonal caps due to the more condensation of carbon dioxide from the atmosphere, the mass of the atmosphere would drop. They have inverse relationship with each other. And the change in mass has direct effect towards the measured gravitational potential.
The seasonal mass exchange between the northern polar cap and southern polar cap exhibits long-wavelength gravity variation with time.
Long years of continuous observation has found that the determination of even zonal, normalized gravity coefficient C
l=2, m=0, and odd zonal, normalized gravity coefficient C
l=3, m=0 are crucial for outlining the time-variable gravity due to such mass exchange,
where
is the degree while
is the order. More commonly, they are represented in form of C
lm in research papers.
If we regard the two poles as two distinct point masses, then, their masses are defined as,
:
:
Data has indicated that the maximum mass variation of the southern polar cap is approximately 8.4 × 10
15 kg,
occurring near the
Equinox, autumnal equinox,
while for that of the northern polar is approximately 6.2 × 10
15 kg,
occurring in between the
winter solstice
The winter solstice, also called the hibernal solstice, occurs when either of Earth's poles reaches its maximum tilt away from the Sun. This happens twice yearly, once in each hemisphere (Northern and Southern). For that hemisphere, the winter ...
and
spring equinox.
In long term speaking, it has been found that the mass of ice stored in North Pole would increase by (1.4 ± 0.5) × 10
11 kg,
while in South Pole it would decrease by (0.8 ± 0.6) × 10
11 kg.
In addition, the atmosphere would have decrease in term of the mass of carbon dioxide by (0.6 ± 0.6) × 10
11 kg in long term as well.
Due to existence of uncertainties, it is unclear whether migration of material from the South Pole to the North Pole is ongoing, though such a possibility cannot be ruled out.
Tide
The two major
tidal force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
s acting on Mars are the solar
tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravity, gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.
Tide t ...
and Phobos tide.
Love number
The Love numbers (''h'', ''k'', and ''l'') are dimensionless parameters that measure the rigidity of a planetary body and the susceptibility of its shape to change in response to a tidal potential.
In 1909, Augustus Edward Hough Love introduced ...
k
2 is an important proportional dimensionless constant relating the tidal field acting to the body with the multipolar moment resulting from the mass distribution of the body. Usually k
2 can tell quadrupolar deformation.
Finding k
2 is helpful in understanding the interior structure on Mars.
The most updated k
2 obtained by Genova's team is 0.1697 ± 0.0009.
As if k
2 is smaller than 0.10 a solid core would be indicated, this tells that at least the outer core is liquid on Mars,
and the predicted core radius is 1520–1840 km.
However, current radio tracking data from MGS, ODY and MRO does not allow the effect of phase lag on the tides to be detected because it is too weak and needs more precise measurement on the perturbation of spacecraft in the future.
Geophysical implications
Crustal thickness
![MarsCrustThickness](https://upload.wikimedia.org/wikipedia/commons/e/e7/MarsCrustThickness.jpg)
No direct measurement of crustal thickness on Mars is currently available. Geochemical implications from
SNC meteorites
A Martian meteorite is a rock that formed on Mars, was ejected from the planet by an impact event, and traversed interplanetary space before landing on Earth as a meteorite. , 277 meteorites had been classified as Martian, less than half a perc ...
and
orthopyroxenite meteorite
ALH84001
Allan Hills 84001 (ALH84001) is a fragment of a Martian meteorite that was found in the Allan Hills in Antarctica on December 27, 1984, by a team of American meteorite hunters from the ANSMET project. Like other members of the shergottite– nak ...
suggested that mean crustal thickness of Mars is 100–250 km. Viscous relaxation analysis suggested that the maximum thickness is 50–100 km. Such thickness is critical in maintaining hemispheric crustal variations and preventing channel flow. Combination studies on geophysics and geochemistry suggested that average crustal thickness could be down to 50 ± 12 km.
Measurement of gravity field by different orbiters allows higher-resolution global
Bouguer potential model to be produced.
With local shallow density anomalies and effect of
core flattening
Core or cores may refer to:
Science and technology
* Core (anatomy), everything except the appendages
* Core (manufacturing), used in casting and molding
* Core (optical fiber), the signal-carrying portion of an optical fiber
* Core, the centra ...
eliminated,
the residual Bouguer potential is produced, as indicated by the following equation:
:
The residual Bouguer potential is contributed by the mantle.
The undulation of the crust-mantle boundary, or the
Moho surface, with mass of terrain corrected, should have resulted in varying residual anomaly.
In turn, if undulating boundary is observed, there should be changes in crustal thickness.
Global study of residual Bouguer anomaly data indicates that crustal thickness of Mars varies from 5.8 km to 102 km.
Two major peaks at 32 km and 58 km are identified from an equal-area histogram of crustal thickness.
These two peaks are linked to the
crustal dichotomy
Crust may refer to:
Common meanings Food
* Crust (baking), the outer layer composed of pastry or salt
* Crust, the bread foundation of pizza
* Bread crust, the dense surface layer of bread
Physical sciences
* Crust (geology), the outer l ...
of Mars.
Almost all the crust thicker than 60 km are contributed by the southern highland, with generally uniform thickness.
And the northern lowland in general has thinner crust. The crustal thickness of the
Arabia Terra
Arabia Terra is a large upland region in the north of Mars that lies mostly in the Arabia quadrangle, but a small part is in the Mare Acidalium quadrangle. It is densely cratered and heavily eroded. This battered topography indicates great age ...
region and northern hemisphere are found to be latitude-dependent.
The more southward towards the
Sinai Planum
This is a list of plains on Mars. Such features are named after the nearest classical albedo feature in compliance with the International Astronomical Union's rules of planetary nomenclature. Plains may be named denoted "planitia" or "planum", de ...
and
Lunae Planum
The Lunae Palus quadrangle is one of a series of 30 quadrangle maps of Mars used by the United States Geological Survey (USGS) Astrogeology Research Program. The quadrangle is also referred to as MC-10 (Mars Chart-10). Lunae Planum and parts of ...
, the more thickened the crust is.
Among all regions, the
Thaumasia and
Claritis contain the thickest portion of crust on Mars that account for the histogram > 70 km.
The
Hellas and
Argyre basins are observed to have crust thinner than 30 km,
which are the exceptionally thin area in the southern hemisphere.
Isidis and
Utopia
A utopia ( ) typically describes an imaginary community or society that possesses highly desirable or nearly perfect qualities for its members. It was coined by Sir Thomas More for his 1516 book ''Utopia (book), Utopia'', describing a fictional ...
are also observed to have significant crustal thinning,
with the center of Isidis basins believed to have the thinnest crust on Mars.
Crust redistribution by impacting and viscous relaxation
![Evolution of topographic profile of large impact craters with viscous relaxation taking place](https://upload.wikimedia.org/wikipedia/commons/a/a5/Evolution_of_topographic_profile_of_large_impact_craters_with_viscous_relaxation_taking_place.png)
Crustal thinning is believed to have taken place underneath almost all the major impact craters.
Crustal excavation, modification through emplacement of volcanic material and crustal flow taking place in the weak lithosphere are the possible causes.
With the pre-impact crust excavated, gravitational restoration would take place through central mantle uplift, so that the mass deficit of cavity could be compensated by the mass of the uplifted denser material.
Giant impact basins Utopia, Hellas, Argyre and Isidis are some of the most prominent examples.
Utopia
A utopia ( ) typically describes an imaginary community or society that possesses highly desirable or nearly perfect qualities for its members. It was coined by Sir Thomas More for his 1516 book ''Utopia (book), Utopia'', describing a fictional ...
, an impact basin located in northern lowland, is filled by light and water-deposited sedimentary material and has slightly thickened crust at the center.
This is potentially due to large resurfacing process in the northern lowland.
While for
Hellas,
Argyre and
Isidis basins, they have great Moho uplifted relief and exhibit annuli of diffuse thickened crust beyond the crustal rim.
But on the contrary, almost all the Martian basins with diameter of 275 km
< ''D''
< 1000 km are associated with low amplitude surface and low amplitude Moho relief.
Many are even found to have negative
free air gravity anomaly, though evidence has shown that all of them should have experienced gravity high (positive free air gravity anomaly).
These have been suggested not caused by erosion and burial alone, as the adding of material into the basin would in fact increase the gravity strength rather than decrease it.
Thus
viscous relaxation should have been taking place.
High heat flux and high water content in the early Martian crust favored viscous relaxation.
These two factors have made the crust more ductile. The basin topography of the craters would be subjected to greater stress due to self-gravitation. Such stress would drive crustal flow and therefore decay of relief. The giant impact basins are the exceptions that have not experienced viscous relaxation, as crustal thinning has made the crust too thin to sustain sub-solidus crustal flow.
Low bulk crustal density
The most recent
crustal density model RM1 developed in 2017 gives the
bulk crustal density to be 2582 ± 209 kg m
−3 for Mars,
which represents a global average value.
Lateral variation of the crustal density should exist.
For example, over the volcanic complexes, local density is expected to be as high as 3231 ± 95 kg m
−3,
which matched the meteorite data and previous estimations. In addition, the density of the northern hemisphere is in general higher than that of the southern hemisphere,
which may imply that the latter is more porous than the former.
To achieve the bulk value,
porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
could play an important role. If the mineral grain density is chosen to be 3100 kg m
−3,
10% to 23% porosity could give a 200 kg m
−3 drop in the bulk density.
If the pore spaces are filled with water or ice, bulk density decrease is also expected.
A further drop in bulk density could be explained by increasing density with depth,
with the surface layer more porous than the deeper Mars, and the increase of density with depth also has geographical variation.
Engineering and scientific applications
Areoid
The areoid is a
planetary geoid that represents the gravitational and rotational equipotential figure of Mars, analogous to the concept of
geoid
The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
("
sea level
Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardised g ...
") on Earth.
This has been set as the reference frame for developing the MOLA
Mission Experiment Gridded Data Records
Mission (from Latin ''missio'' "the act of sending out") may refer to:
Organised activities Religion
*Christian mission, an organized effort to spread Christianity
*Mission (LDS Church), an administrative area of The Church of Jesus Christ of ...
(MEGDRs),
which is a global topography model. The topography model is important in mapping the geomorphological features and understanding different kinds of processes on Mars.
To derive the areoid, two parts of works are required. First, as gravity data is essential for identifying the position of the center of mass of the planet,
which is largely affected by the distribution of the mass of the interior, radio tracking data of spacecraft is necessary.
This was largely done by the
Mars Global Surveyor
''Mars Global Surveyor'' (MGS) was an American robotic space probe developed by NASA's Jet Propulsion Laboratory and launched November 1996. MGS was a global mapping mission that examined the entire planet, from the ionosphere down through t ...
(MGS).
Then, the
MOLA 2 instrument aboard the MGS, which operates at 400-km elevation orbit, could measure the range (distance) between the spacecraft and the ground surface through counting the round-trip time of flight of the pulse from the instrument.
Combination of these two works allows the areoid as well as the MEGDRs to be constructed.
Based on the above, the areoid has taken the radius as the mean radius of the planet at the equator as 3396 km.
Surface landing
As there is a large distance between Mars and Earth, immediate command to the lander is almost impossible and the landing relies highly on its autonomous system. It has been recognized that to avoid failure, precise understanding of the gravity field of Mars is essential for the landing projects, so that offsetting factors and uncertainties of gravitational effects could be minimized, allowing for a smooth landing progress.
[Balaram, J., Austin, R., Banerjee, P., Bentley, T., Henriquez, D., Martin, B., ... & Sohl, G. (2002). Dsends-a high-fidelity dynamics and spacecraft simulator for entry, descent and surface landing. In ''Aerospace Conference Proceedings, 2002. IEEE'' (Vol. 7, pp. 7–7). IEEE.] The first ever man-made object landing on Mars, the
Mars 2
The Mars 2 was an uncrewed space probe of the Mars program, a series of uncrewed Mars landers and orbiters launched by the Soviet Union beginning 19 May 1971. The Mars 2 and Mars 3 missions consisted of identical spacecraft, each with an orbi ...
lander, crashed for an unknown reason. Since the surface environment of Mars is complex, composed of laterally varying morphological patterns, in order to avoid rock hazard the landing progress should be further assisted by employment of
LIDAR
Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be ...
on site in determining the exact landing position and other protective measures.
References
{{Portal bar, Physics, Astronomy, Stars, Spaceflight, Outer space, Science
Gravimetry of objects
Gravity
Mars