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Saturday, September 30, 2023

Wind shear

From Wikipedia, the free encyclopedia

Wind shear (or windshear), sometimes referred to as wind gradient, is a difference in wind speed and/or direction over a relatively short distance in the atmosphere. Atmospheric wind shear is normally described as either vertical or horizontal wind shear. Vertical wind shear is a change in wind speed or direction with a change in altitude. Horizontal wind shear is a change in wind speed with a change in lateral position for a given altitude.

Wind shear is a microscale meteorological phenomenon occurring over a very small distance, but it can be associated with mesoscale or synoptic scale weather features such as squall lines and cold fronts. It is commonly observed near microbursts and downbursts caused by thunderstorms, fronts, areas of locally higher low-level winds referred to as low-level jets, near mountains, radiation inversions that occur due to clear skies and calm winds, buildings, wind turbines, and sailboats. Wind shear has significant effects on the control of an aircraft, and it has been the sole or a contributing cause of many aircraft accidents.

Sound movement through the atmosphere is affected by wind shear, which can bend the wave front, causing sounds to be heard where they normally would not. Strong vertical wind shear within the troposphere also inhibits tropical cyclone development but helps to organize individual thunderstorms into longer life cycles which can then produce severe weather. The thermal wind concept explains how differences in wind speed at different heights are dependent on horizontal temperature differences and explains the existence of the jet stream.

Definition

Wind shear refers to the variation of wind velocity over either horizontal or vertical distances. Airplane pilots generally regard significant wind shear to be a horizontal change in airspeed of 30 knots (15 m/s) for light aircraft, and near 45 knots (23 m/s) for airliners at flight altitude. Vertical speed changes greater than 4.9 knots (2.5 m/s) also qualify as significant wind shear for aircraft. Low-level wind shear can affect aircraft airspeed during takeoff and landing in disastrous ways, and airliner pilots are trained to avoid all microburst wind shear (headwind loss in excess of 30 knots [15 m/s]). The rationale for this additional caution includes:

microburst intensity can double in a minute or less,
the winds can shift to excessive crosswinds,
40–50 knots (21–26 m/s) is the threshold for survivability at some stages of low-altitude operations, and
several of the historical wind shear accidents involved 35–45 knots (18–23 m/s) microbursts.

Wind shear is also a key factor in the formation of severe thunderstorms. The additional hazard of turbulence is often associated with wind shear.

Occurrence

Microburst schematic from NASA. The direction of travel is downward until the air current hits ground level, at which point it spreads outward in all directions. The wind regime in a microburst is completely opposite to a tornado.

Weather situations where shear is observed include:

Weather fronts. Significant shear is observed when the temperature difference across the front is 5 °C (9 °F) or more, and the front moves at 30 knots (15 m/s) or faster. Because fronts are three-dimensional phenomena, frontal shear can be observed at any altitude between surface and tropopause, and can therefore be seen both horizontally and vertically. Vertical wind shear above warm fronts is more of an aviation concern than near and behind cold fronts due to their greater duration.
Upper-level jet streams. Associated with upper-level jet streams is a phenomenon known as clear air turbulence (CAT), caused by vertical and horizontal wind shear connected to the wind gradient at the edge of the jet streams. The CAT is strongest on the anticyclonic shear side of the jet, usually next to or just below the axis of the jet.
Low-level jet streams. When a nocturnal low-level jet forms overnight above Earth's surface ahead of a cold front, significant low-level vertical wind shear can develop near the lower portion of the low-level jet. This is also known as non-convective wind shear as it is not due to nearby thunderstorms.
Mountains.
Inversions. When on a clear and calm night, a radiation inversion is formed near the ground, the friction does not affect wind above the top of the inversion layer. The change in wind can be 90 degrees in direction and 40 knots (21 m/s) in speed. Even a nocturnal (overnight) low-level jet can sometimes be observed. It tends to be strongest towards sunrise. Density differences cause additional problems to aviation.
Downbursts. When an outflow boundary forms due to a shallow layer of rain-cooled air spreading out near ground level from the parent thunderstorm, both speed and directional wind shear can result at the leading edge of the three-dimensional boundary. The stronger the outflow boundary is, the stronger the resultant vertical wind shear will become.

Horizontal component

Weather fronts

Weather fronts are boundaries between two masses of air of different densities, or different temperature and moisture properties, which normally are convergence zones in the wind field and are the principal cause of significant weather. Within surface weather analyses, they are depicted using various colored lines and symbols. The air masses usually differ in temperature and may also differ in humidity. Wind shear in the horizontal occurs near these boundaries. Cold fronts feature narrow bands of thunderstorms and severe weather and may be preceded by squall lines and dry lines. Cold fronts are sharper surface boundaries with more significant horizontal wind shear than warm fronts. When a front becomes stationary, it can degenerate into a line that separates regions of differing wind speed, known as a shear line, though the wind direction across the front normally remains constant. In the tropics, tropical waves move from east to west across the Atlantic and eastern Pacific basins. Directional and speed shear can occur across the axis of stronger tropical waves, as northerly winds precede the wave axis and southeast winds are seen behind the wave axis. Horizontal wind shear can also occur along the local land breeze and sea breeze boundaries.

Near coastlines

The magnitude of winds offshore is nearly double the wind speed observed onshore. This is attributed to the differences in friction between landmasses and offshore waters. Sometimes, there are even directional differences, particularly if local sea breezes change the wind on shore during daylight hours.

Vertical component

Thermal wind

Thermal wind is a meteorological term not referring to an actual wind, but a difference in the geostrophic wind between two pressure levels $p 1$ and $p 0$ , with $p 1 < p 0$ ; in essence, wind shear. It is only present in an atmosphere with horizontal changes in temperature (or in an ocean with horizontal gradients of density), i.e., baroclinicity. In a barotropic atmosphere, where temperature is uniform, the geostrophic wind is independent of height. The name stems from the fact that this wind flows around areas of low (and high) temperature in the same manner as the geostrophic wind flows around areas of low (and high) pressure.

The thermal wind equation is

f v_{T} = k \times \nabla (φ_{1} - φ_{0}),

where the $φ$ are geopotential height fields with $φ 1 > φ 0$ , $f$ is the Coriolis parameter, and $k$ is the upward-pointing unit vector in the vertical direction. The thermal wind equation does not determine the wind in the tropics. Since $f$ is small or zero, such as near the equator, the equation reduces to stating that $\nabla(φ 1 - φ 0)$ is small.

This equation basically describes the existence of the jet stream, a westerly current of air with maximum wind speeds close to the tropopause which is (even though other factors are also important) the result of the temperature contrast between equator and pole.

Effects on tropical cyclones

Strong wind shear in the high troposphere forms the anvil-shaped top of this mature cumulonimbus cloud, or thunderstorm.

Tropical cyclones are, in essence, heat engines that are fueled by the temperature gradient between the warm tropical ocean surface and the colder upper atmosphere. Tropical cyclone development requires relatively low values of vertical wind shear so that their warm core can remain above their surface circulation center, thereby promoting intensification. Vertical wind shear tears up the "machinery" of the heat engine causing it to break down. Strongly sheared tropical cyclones weaken as the upper circulation is blown away from the low-level center.

Effects on thunderstorms and severe weather

Severe thunderstorms, which can spawn tornadoes and hailstorms, require wind shear to organize the storm in such a way as to maintain the thunderstorm for a longer period. This occurs as the storm's inflow becomes separated from its rain-cooled outflow. An increasing nocturnal, or overnight, low-level jet can increase the severe weather potential by increasing the vertical wind shear through the troposphere. Thunderstorms in an atmosphere with virtually no vertical wind shear weaken as soon as they send out an outflow boundary in all directions, which then quickly cuts off its inflow of relatively warm, moist air and causes the thunderstorm to dissipate.

Planetary boundary layer

The atmospheric effect of surface friction with winds aloft forces surface winds to slow and back counterclockwise near the surface of Earth blowing inward across isobars (lines of equal pressure) when compared to the winds in frictionless flow well above Earth's surface. This layer where friction slows and changes the wind is known as the planetary boundary layer, sometimes the Ekman layer, and it is thickest during the day and thinnest at night. Daytime heating thickens the boundary layer as winds at the surface become increasingly mixed with winds aloft due to insolation, or solar heating. Radiative cooling overnight further enhances wind decoupling between the winds at the surface and the winds above the boundary layer by calming the surface wind which increases wind shear. These wind changes force wind shear between the boundary layer and the wind aloft and are most emphasized at night.

Effects on flight

Gliding

In gliding, wind gradients just above the surface affect the takeoff and landing phases of the flight of a glider. Wind gradient can have a noticeable effect on ground launches, also known as winch launches or wire launches. If the wind gradient is significant or sudden, or both, and the pilot maintains the same pitch attitude, the indicated airspeed will increase, possibly exceeding the maximum ground launch tow speed. The pilot must adjust the airspeed to deal with the effect of the gradient.

When landing, wind shear is also a hazard, particularly when the winds are strong. As the glider descends through the wind gradient on final approach to landing, airspeed decreases while sink rate increases, and there is insufficient time to accelerate prior to ground contact. The pilot must anticipate the wind gradient and use a higher approach speed to compensate for it.

Wind shear is also a hazard for aircraft making steep turns near the ground. It is a particular problem for gliders which have a relatively long wingspan, which exposes them to a greater wind speed difference for a given bank angle. The different airspeed experienced by each wing tip can result in an aerodynamic stall on one wing, causing a loss of control accident.

Parachuting

Wind shear or wind gradients are a threat to parachutists, particularly to BASE jumping and wingsuit flying. Skydivers have been pushed off of their course by sudden shifts in wind direction and speed, and have collided with bridges, cliffsides, trees, other skydivers, the ground, and other obstacles. Skydivers routinely make adjustments to the position of their open canopies to compensate for changes in direction while making landings to prevent accidents such as canopy collisions and canopy inversion.

Soaring

Soaring related to wind shear, also called dynamic soaring, is a technique used by soaring birds like albatrosses, who can maintain flight without wing flapping. If the wind shear is of sufficient magnitude, a bird can climb into the wind gradient, trading ground speed for height, while maintaining airspeed. By then turning downwind, and diving through the wind gradient, they can also gain energy. It has also been used by glider pilots on rare occasions.

Wind shear can also produce wave. This occurs when an atmospheric inversion separates two layers with a marked difference in wind direction. If the wind encounters distortions in the inversion layer caused by thermals coming up from below, it will produce significant shear waves that can be used for soaring.

Impact on passenger aircraft

Effect of wind shear on aircraft trajectory. Note how merely correcting for the initial gust front can have dire consequences.

Windshear can be extremely dangerous for aircraft, especially during takeoff and landing. Sudden changes in wind velocity can cause rapid decreases in airspeed, leading to the aircraft being unable to maintain altitude. Windshear has been responsible for several deadly accidents, including Eastern Air Lines Flight 66, Pan Am Flight 759, Delta Air Lines Flight 191, and USAir Flight 1016.

Windshear can be detected using Doppler radar. Airports can be fitted with low-level windshear alert systems or Terminal Doppler Weather Radar, and aircraft can be fitted with airborne wind shear detection and alert systems. Following the 1985 crash of Delta Air Lines Flight 191, in 1988 the U.S. Federal Aviation Administration mandated that all commercial aircraft have airborne wind shear detection and alert systems by 1993. The installation of high-resolution Terminal Doppler Weather Radar stations at many U.S. airports that are commonly affected by windshear has further aided the ability of pilots and ground controllers to avoid wind shear conditions.

Sailing

Wind shear affects sailboats in motion by presenting a different wind speed and direction at different heights along the mast. The effect of low-level wind shear can be factored into the selection of sail twist in the sail design, but this can be difficult to predict since wind shear may vary widely in different weather conditions. Sailors may also adjust the trim of the sail to account for low-level wind shear, for example using a boom vang.

Sound propagation

Wind shear can have a pronounced effect upon sound propagation in the lower atmosphere, where waves can be "bent" by refraction phenomenon. The audibility of sounds from distant sources, such as thunder or gunshots, is very dependent on the amount of shear. The result of these differing sound levels is key in noise pollution considerations, for example from roadway noise and aircraft noise, and must be considered in the design of noise barriers. This phenomenon was first applied to the field of noise pollution study in the 1960s, contributing to the design of urban highways as well as noise barriers.

The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, producing an acoustic shadow at some distance from the source. In 1862, during the American Civil War Battle of Iuka, an acoustic shadow, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle, because they could not hear the sounds of battle only six miles downwind.

Effects on architecture

Wind engineering is a field of engineering devoted to the analysis of wind effects on the natural and built environment. It includes strong winds which may cause discomfort as well as extreme winds such as tornadoes, hurricanes, and storms which may cause widespread destruction. Wind engineering draws upon meteorology, aerodynamics, and several specialist engineering disciplines. The tools used include climate models, atmospheric boundary layer wind tunnels, and numerical models. It involves, among other topics, how wind impacting buildings must be accounted for in engineering.

Wind turbines are affected by wind shear. Vertical wind-speed profiles result in different wind speeds at the blades nearest to the ground level compared to those at the top of blade travel, and this, in turn, affects the turbine operation. This low-level wind shear can cause a large bending moment in the shaft of a two-bladed turbine when the blades are vertical. The reduced wind shear over water means shorter and less expensive wind turbine towers can be used in shallow seas.

Earth's outer core

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Earth%27s_outer_core

Earth's outer core is a fluid layer about 2,260 km (1,400 mi) thick, composed of mostly iron and nickel that lies above Earth's solid inner core and below its mantle. The outer core begins approximately 2,889 km (1,795 mi) beneath Earth's surface at the core-mantle boundary and ends 5,150 km (3,200 mi) beneath Earth's surface at the inner core boundary.

Properties

Unlike Earth's solid, inner core, its outer core is liquid. Evidence for a fluid outer core includes seismology which shows that seismic shear-waves are not transmitted through the outer core. Although having a composition similar to Earth's solid inner core, the outer core remains liquid as there is not enough pressure to keep it in a solid state.

Seismic inversions of body waves and normal modes constrain the radius of the outer core to be 3483 km with an uncertainty of 5 km, while that of the inner core is 1220±10 km.

Estimates for the temperature of the outer core are about 3,000–4,500 K (2,700–4,200 °C; 4,900–7,600 °F) in its outer region and 4,000–8,000 K (3,700–7,700 °C; 6,700–14,000 °F) near the inner core. Modeling has shown that the outer core, because of its high temperature, is a low-viscosity fluid that convects turbulently. The dynamo theory sees eddy currents in the nickel-iron fluid of the outer core as the principal source of Earth's magnetic field. The average magnetic field strength in Earth's outer core is estimated to be 2.5 millitesla, 50 times stronger than the magnetic field at the surface.

As Earth's core cools, the liquid at the inner core boundary freezes, causing the solid inner core to grow at the expense of the outer core, at an estimated rate of 1 mm per year. This is approximately 80,000 tonnes of iron per second.

Light elements of Earth's outer core

Composition

Earth's outer core cannot be entirely constituted of iron or iron-nickel alloy because their densities are higher than geophysical measurements of the density of Earth's outer core.In fact, Earth's outer core is approximately 5 to 10 percent lower density than iron at Earth's core temperatures and pressures. Hence it has been proposed that light elements with low atomic numbers comprise part of Earth's outer core, as the only feasible way to lower its density. Although Earth's outer core is inaccessible to direct sampling, the composition of light elements can be meaningfully constrained by high-pressure experiments, calculations based on seismic measurements, models of Earth's accretion, and carbonaceous chondrite meteorite comparisons with bulk silicate Earth (BSE). Recent estimates are that Earth's outer core is composed of iron along with 0 to 0.26 percent hydrogen, 0.2 percent carbon, 0.8 to 5.3 percent oxygen, 0 to 4.0 percent silicon, 1.7 percent sulfur, and 5 percent nickel by weight, and the temperature of the core-mantle boundary and the inner core boundary ranges from 4,137 to 4,300 K and from 5,400 to 6,300 K respectively.

Constraints

Accretion

The variety of light elements present in Earth's outer core is constrained in part by Earth's accretion. Namely, the light elements contained must have been abundant during Earth's formation, must be able to partition into liquid iron at low pressures, and must not volatilize and escape during Earth's accretionary process.

CI chondrites

CI chondritic meteorites are believed to contain the same planet-forming elements in the same proportions as in the early Solar System, so differences between CI meteorites and BSE can provide insights into the light element composition of Earth's outer core. For instance, the depletion of silicon in BSE compared to CI meteorites may indicate that silicon was absorbed into Earth's core; however, a wide range of silicon concentrations in Earth's outer and inner core is still possible.

Implications for Earth's accretion and core formation history

Tighter constraints on the concentrations of light elements in Earth's outer core would provide a better understanding of Earth's accretion and core formation history.

Consequences for Earth's accretion

Models of Earth's accretion could be better tested if we had better constraints on light element concentrations in Earth's outer core. For example, accretionary models based on core-mantle element partitioning tend to support proto-Earths constructed from reduced, condensed, and volatile-free material, despite the possibility that oxidized material from the outer Solar System was accreted towards the conclusion of Earth's accretion. If we could better constrain the concentrations of hydrogen, oxygen, and silicon in Earth's outer core, models of Earth's accretion that match these concentrations would presumably better constrain Earth’s formation.

Consequences for Earth's core formation

The depletion of siderophile elements in Earth's mantle compared to chondritic meteorites is attributed to metal-silicate reactions during formation of Earth's core. These reactions are dependent on oxygen, silicon, and sulfur, so better constraints on concentrations of these elements in Earth's outer core will help elucidate the conditions of formation of Earth's core.

In another example, the possible presence of hydrogen in Earth's outer core suggests that the accretion of Earth’s water was not limited to the final stages of Earth's accretion and that water may have been absorbed into core-forming metals through a hydrous magma ocean.

Implications for Earth's magnetic field

Earth's magnetic field is driven by thermal convection and also by chemical convection, the exclusion of light elements from the inner core, which float upward within the fluid outer core while denser elements sink. This chemical convection releases gravitational energy that is then available to power the geodynamo that produces Earth's magnetic field. Carnot efficiencies with large uncertainties suggest that compositional and thermal convection contribute about 80 percent and 20 percent respectively to the power of Earth's geodynamo. Traditionally it was thought that prior to the formation of Earth's inner core, Earth's geodynamo was mainly driven by thermal convection. However, recent claims that the thermal conductivity of iron at core temperatures and pressures is much higher than previously thought imply that core cooling was largely by conduction not convection, limiting the ability of thermal convection to drive the geodynamo.This conundrum is known as the new "core paradox." An alternative process that could have sustained Earth's geodynamo requires Earth's core to have initially been hot enough to dissolve oxygen, magnesium, silicon, and other light elements. As the Earth's core began to cool, it would become supersaturated in these light elements that would then precipitate into the lower mantle forming oxides leading to a different variant of chemical convection.

Internal structure of Earth

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Internal_structure_of_Earth

The internal structure of Earth is the solid portion of the Earth, excluding its atmosphere and hydrosphere. The structure consists of an outer silicate solid crust, a highly viscous asthenosphere and solid mantle, a liquid outer core whose flow generates the Earth's magnetic field, and a solid inner core.

Scientific understanding of the internal structure of Earth is based on observations of topography and bathymetry, observations of rock in outcrop, samples brought to the surface from greater depths by volcanoes or volcanic activity, analysis of the seismic waves that pass through Earth, measurements of the gravitational and magnetic fields of Earth, and experiments with crystalline solids at pressures and temperatures characteristic of Earth's deep interior.

Global properties

Measurements of the force exerted by Earth's gravity can be used to calculate its mass. Astronomers can also calculate Earth's mass by observing the motion of orbiting satellites. Earth's average density can be determined through gravimetric experiments, which have historically involved pendulums. The mass of Earth is about 6×10²⁴ kg. The average density of the Earth is 5.515 g/cm³.

Layers

The structure of Earth can be defined in two ways: by mechanical properties such as rheology, or chemically. Mechanically, it can be divided into lithosphere, asthenosphere, mesospheric mantle, outer core, and the inner core. Chemically, Earth can be divided into the crust, upper mantle, lower mantle, outer core, and inner core. The geologic component layers of Earth are at increasing depths below the surface.

Crust and lithosphere

The Earth's crust ranges from 5–70 kilometres (3.1–43.5 mi) in depth and is the outermost layer. The thin parts are the oceanic crust, which underlie the ocean basins (5–10 km) and is mafic-rich (dense iron-magnesium silicate mineral or igneous rock). The thicker crust is the continental crust, which is less dense and is felsic-rich (igneous rocks rich in elements that form feldspar and quartz). The rocks of the crust fall into two major categories – sial (aluminium silicate) and sima (magnesium silicate). It is estimated that sima starts about 11 km below the Conrad discontinuity, though the discontinuity is not distinct and can be absent in some continental regions.

The Earth's lithosphere consists of the crust and the uppermost mantle. The crust-mantle boundary occurs as two physically different phenomena. The Mohorovičić discontinuity is a distinct change of seismic wave velocity. This is caused by a change in the rock's density – Immediately above the Moho, the velocities of primary seismic waves (P wave) are consistent with those through basalt (6.7–7.2 km/s), and below they are similar to those through peridotite or dunite (7.6–8.6 km/s). Second, in oceanic crust, there is a chemical discontinuity between ultramafic cumulates and tectonized harzburgites, which has been observed from deep parts of the oceanic crust that have been obducted onto the continental crust and preserved as ophiolite sequences.

Many rocks making up Earth's crust formed less than 100 million years ago; however, the oldest known mineral grains are about 4.4 billion years old, indicating that Earth has had a solid crust for at least 4.4 billion years.

Mantle

Earth's mantle extends to a depth of 2,890 km (1,800 mi), making it the planet's thickest layer. [This is 45% of the 6,371 km (3,959 mi) radius, and 83.7% of the volume - 0.6% of the volume is the crust]. The mantle is divided into upper and lower mantle separated by a transition zone. The lowest part of the mantle next to the core-mantle boundary is known as the D″ (D-double-prime) layer. The pressure at the bottom of the mantle is ≈140 GPa (1.4 Matm). The mantle is composed of silicate rocks richer in iron and magnesium than the overlying crust. Although solid, the mantle's extremely hot silicate material can flow over very long timescales. Convection of the mantle propels the motion of the tectonic plates in the crust. The source of heat that drives this motion is the decay of radioactive isotopes in the Earth's crust and mantle combined with the initial heat from the planet's formation.

Due to increasing pressure deeper in the mantle, the lower part flows less easily, though chemical changes within the mantle may also be important. The viscosity of the mantle ranges between 10²¹ and 10²⁴ pascal-second, increasing with depth. In comparison, the viscosity of water at 300 K (27 °C; 80 °F) is 0.89 pascal-second and pitch is (2.3 ± 0.5)⁸ pascal-second.

Core

Earth's outer core is a fluid layer about 2,400 km (1,500 mi) in diameter [19% of the Earth's diameter, 15.6% of the volume] and composed of mostly iron and nickel that lies above Earth's solid inner core and below its mantle. Its outer boundary lies 2,890 km (1,800 mi) beneath Earth's surface. The transition between the inner core and outer core is located approximately 5,150 km (3,200 mi) beneath the Earth's surface. Earth's inner core is the innermost geologic layer of the planet Earth. It is primarily a solid ball with a radius of about 1,220 km (760 mi), which is about 19% of Earth's radius [0.7% of volume] or 70% of the Moon's radius.

The inner core was discovered in 1936 by Inge Lehmann and is generally composed primarily of iron and some nickel. Since this layer is able to transmit shear waves (transverse seismic waves), it must be solid. Experimental evidence has at times been inconsistent with current crystal models of the core. Other experimental studies show a discrepancy under high pressure: diamond anvil (static) studies at core pressures yield melting temperatures that are approximately 2000 K below those from shock laser (dynamic) studies. The laser studies create plasma, and the results are suggestive that constraining inner core conditions will depend on whether the inner core is a solid or is a plasma with the density of a solid. This is an area of active research.

In early stages of Earth's formation about 4.6 billion years ago, melting would have caused denser substances to sink toward the center in a process called planetary differentiation (see also the iron catastrophe), while less-dense materials would have migrated to the crust. The core is thus believed to largely be composed of iron (80%), along with nickel and one or more light elements, whereas other dense elements, such as lead and uranium, either are too rare to be significant or tend to bind to lighter elements and thus remain in the crust (see felsic materials). Some have argued that the inner core may be in the form of a single iron crystal.

Under laboratory conditions a sample of iron–nickel alloy was subjected to the corelike pressures by gripping it in a vise between 2 diamond tips (diamond anvil cell), and then heating to approximately 4000 K. The sample was observed with x-rays, and strongly supported the theory that Earth's inner core was made of giant crystals running north to south.

The composition of the Earth bears strong similarities to that of certain chondrite meteorites, and even to some elements in the outer portion of the Sun. Beginning as early as 1940, scientists, including Francis Birch, built geophysics upon the premise that Earth is like ordinary chondrites, the most common type of meteorite observed impacting Earth. This ignores the less abundant enstatite chondrites, which formed under extremely limited available oxygen, leading to certain normally oxyphile elements existing either partially or wholly in the alloy portion that corresponds to the core of Earth.

Dynamo theory suggests that convection in the outer core, combined with the Coriolis effect, gives rise to Earth's magnetic field. The solid inner core is too hot to hold a permanent magnetic field (see Curie temperature) but probably acts to stabilize the magnetic field generated by the liquid outer core. The average magnetic field in Earth's outer core is estimated to measure 2.5 mT (25 G), 50 times stronger than the magnetic field at the surface.

Seismology

The layering of Earth has been inferred indirectly using the time of travel of refracted and reflected seismic waves created by earthquakes. The core does not allow shear waves to pass through it, while the speed of travel (seismic velocity) is different in other layers. The changes in seismic velocity between different layers causes refraction owing to Snell's law, like light bending as it passes through a prism. Likewise, reflections are caused by a large increase in seismic velocity and are similar to light reflecting from a mirror.

Gravity assist

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Gravity_assist

Animation of Voyager 1's trajectory from 5 September 1977 to 30 December 1981
Voyager 1 · Earth · Jupiter · Saturn · Sun

Animation of Voyager 2's trajectory from 20 August 1977 to 30 December 2000
Voyager 2 · Earth · Jupiter · Saturn · Uranus · Neptune · Sun

A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.

Gravity assistance can be used to accelerate a spacecraft, that is, to increase or decrease its speed or redirect its path. The "assist" is provided by the motion of the gravitating body as it pulls on the spacecraft. Any gain or loss of kinetic energy and linear momentum by a passing spacecraft is correspondingly lost or gained by the gravitational body, in accordance with Newton's Third Law. The gravity assist maneuver was first used in 1959 when the Soviet probe Luna 3 photographed the far side of Earth's Moon and it was used by interplanetary probes from Mariner 10 onward, including the two Voyager probes' notable flybys of Jupiter and Saturn.

Explanation

Example encounter.
In the planet's frame of reference, the space probe leaves with the exact same speed at which it had arrived. But when observed in the reference frame of the Solar System (fixed to the Sun), the benefit of this maneuver becomes apparent. Here it can be seen how the probe gains speed by tapping energy from the speed of the planet as it orbits the Sun. (If the trajectory is designed to pass in front of the planet instead of behind it, the gravity assist can be used as a braking maneuver rather than accelerating.) Because the mass of the probe is many orders of magnitude smaller than that of the planet, while the result on the probe is quite significant, the deceleration reaction experienced by the planet, according to Newton's third law, is utterly imperceptible.

Possible outcomes of a gravity assist maneuver depending on the velocity vector and flyby position of the incoming spacecraft

A gravity assist around a planet changes a spacecraft's velocity (relative to the Sun) by entering and leaving the gravitational sphere of influence of a planet. The spacecraft's speed increases as it approaches the planet and decreases as it leaves the planet. To increase speed, the spacecraft approaches the planet in the same direction the planet is orbiting the Sun, and departs in the opposite direction. To decrease speed, the spacecraft approaches the planet traveling the opposite direction from planet's orbital velocity. In both types of maneuver the energy transfer compared to the planet's total orbital energy is negligible. The sum of the kinetic energies of both bodies remains constant (see elastic collision). A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun.

A close terrestrial analogy is provided by a tennis ball bouncing off the front of a moving train. Imagine standing on a train platform, and throwing a ball at 30 km/h toward a train approaching at 50 km/h. The driver of the train sees the ball approaching at 80 km/h and then departing at 80 km/h after the ball bounces elastically off the front of the train. Because of the train's motion, however, that departure is at 130 km/h relative to the train platform; the ball has added twice the train's velocity to its own.

Translating this analogy into space: in the planet reference frame, the spaceship has a vertical velocity of v relative to the planet. After the slingshot occurs the spaceship is leaving on a course 90 degrees to that which it arrived on. It will still have a velocity of v, but in the horizontal direction. In the Sun reference frame, the planet has a horizontal velocity of v, and by using the Pythagorean Theorem, the spaceship initially has a total velocity of √2v. After the spaceship leaves the planet, it will have a velocity of v + v = 2v, gaining approximately 0.6v.

This oversimplified example is impossible to refine without additional details regarding the orbit, but if the spaceship travels in a path which forms a hyperbola, it can leave the planet in the opposite direction without firing its engine. This example is one of many trajectories and gains of speed the spaceship can experience.

This explanation might seem to violate the conservation of energy and momentum, apparently adding velocity to the spacecraft out of nothing, but the spacecraft's effects on the planet must also be taken into consideration to provide a complete picture of the mechanics involved. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, so the spacecraft gains velocity and the planet loses velocity. However, the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small even when compared to the orbital perturbations planets undergo due to interactions with other celestial bodies on astronomically short timescales. For example, one metric ton is a typical mass for an interplanetary space probe whereas Jupiter has a mass of almost 2 x 10²⁴ metric tons. Therefore, a one-ton spacecraft passing Jupiter will theoretically cause the planet to lose approximately 5 x 10⁻²⁵ km/s of orbital velocity for every km/s of velocity relative to the Sun gained by the spacecraft. For all practical purposes the effects on the planet can be ignored in the calculation.

Realistic portrayals of encounters in space require the consideration of three dimensions. The same principles apply as above except adding the planet's velocity to that of the spacecraft requires vector addition as shown below.

Due to the reversibility of orbits, gravitational slingshots can also be used to reduce the speed of a spacecraft. Both Mariner 10 and MESSENGER performed this maneuver to reach Mercury.

If more speed is needed than available from gravity assist alone, a rocket burn near the periapsis (closest planetary approach) uses the least fuel. A given rocket burn always provides the same change in velocity (Δv), but the change in kinetic energy is proportional to the vehicle's velocity at the time of the burn. Therefore the maximum kinetic energy is obtained when the burn occurs at the vehicle's maximum velocity (periapsis). The Oberth effect describes this technique in more detail.

Historical origins

In his paper "To those who will be reading in order to build" ("Тем, кто будет читать, чтобы строить"), published in 1938 but dated 1918–1919, Yuri Kondratyuk suggested that a spacecraft traveling between two planets could be accelerated at the beginning and end of its trajectory by using the gravity of the two planets' moons. The portion of his manuscript considering gravity-assists received no later development and was not published until the 1960s. In his 1925 paper "Problems of flight by jet propulsion: interplanetary flights" ("Проблема полета при помощи реактивных аппаратов: межпланетные полеты"), Friedrich Zander showed a deep understanding of the physics behind the concept of gravity assist and its potential for the interplanetary exploration of the solar system.

Italian engineer Gaetano Crocco was first to calculate an interplanetary journey considering multiple gravity-assists.

The gravity assist maneuver was first attempted in 1959 when the Soviet probe Luna 3 photographed the far side of the Moon. The maneuver relied on research performed under the direction of Mstislav Keldysh at the Keldysh Institute of Applied Mathematics.

In 1961, Michael Minovitch, UCLA graduate student who worked at NASA's Jet Propulsion Laboratory (JPL), developed a gravity assist technique, that would later be used for the Gary Flandro's Planetary Grand Tour idea.

During the summer of 1964 at the NASA JPL, Gary Flandro was assigned the task of studying techniques for exploring the outer planets of the solar system. In this study he discovered the rare alignment of the outer planets (Jupiter, Saturn, Uranus, and Neptune) and conceived the Planetary Grand Tour multi-planet mission utilizing gravity assist to reduce mission duration from forty years to less than ten.

Purpose

A spacecraft traveling from Earth to an inner planet will increase its relative speed because it is falling toward the Sun, and a spacecraft traveling from Earth to an outer planet will decrease its speed because it is leaving the vicinity of the Sun.

Although the orbital speed of an inner planet is greater than that of the Earth, a spacecraft traveling to an inner planet, even at the minimum speed needed to reach it, is still accelerated by the Sun's gravity to a speed notably greater than the orbital speed of that destination planet. If the spacecraft's purpose is only to fly by the inner planet, then there is typically no need to slow the spacecraft. However, if the spacecraft is to be inserted into orbit about that inner planet, then there must be some way to slow it down.

Similarly, while the orbital speed of an outer planet is less than that of the Earth, a spacecraft leaving the Earth at the minimum speed needed to travel to some outer planet is slowed by the Sun's gravity to a speed far less than the orbital speed of that outer planet. Therefore, there must be some way to accelerate the spacecraft when it reaches that outer planet if it is to enter orbit about it.

Rocket engines can certainly be used to increase and decrease the speed of the spacecraft. However, rocket thrust takes propellant, propellant has mass, and even a small change in velocity (known as Δv, or "delta-v", the delta symbol being used to represent a change and "v" signifying velocity) translates to a far larger requirement for propellant needed to escape Earth's gravity well. This is because not only must the primary-stage engines lift the extra propellant, they must also lift the extra propellant beyond that which is needed to lift that additional propellant. The liftoff mass requirement increases exponentially with an increase in the required delta-v of the spacecraft.

Because additional fuel is needed to lift fuel into space, space missions are designed with a tight propellant "budget", known as the "delta-v budget". The delta-v budget is in effect the total propellant that will be available after leaving the earth, for speeding up, slowing down, stabilization against external buffeting (by particles or other external effects), or direction changes, if it cannot acquire more propellant. The entire mission must be planned within that capability. Therefore, methods of speed and direction change that do not require fuel to be burned are advantageous, because they allow extra maneuvering capability and course enhancement, without spending fuel from the limited amount which has been carried into space. Gravity assist maneuvers can greatly change the speed of a spacecraft without expending propellant, and can save significant amounts of propellant, so they are a very common technique to save fuel.

Limits

The main practical limit to the use of a gravity assist maneuver is that planets and other large masses are seldom in the right places to enable a voyage to a particular destination. For example, the Voyager missions which started in the late 1970s were made possible by the "Grand Tour" alignment of Jupiter, Saturn, Uranus and Neptune. A similar alignment will not occur again until the middle of the 22nd century. That is an extreme case, but even for less ambitious missions there are years when the planets are scattered in unsuitable parts of their orbits.

Another limitation is the atmosphere, if any, of the available planet. The closer the spacecraft can approach, the faster its periapsis speed as gravity accelerates the spacecraft, allowing for more kinetic energy to be gained from a rocket burn. However, if a spacecraft gets too deep into the atmosphere, the energy lost to drag can exceed that gained from the planet's gravity. On the other hand, the atmosphere can be used to accomplish aerobraking. There have also been theoretical proposals to use aerodynamic lift as the spacecraft flies through the atmosphere. This maneuver, called an aerogravity assist, could bend the trajectory through a larger angle than gravity alone, and hence increase the gain in energy.

Even in the case of an airless body, there is a limit to how close a spacecraft may approach. The magnitude of the achievable change in velocity depends on the spacecraft's approach velocity and the planet's escape velocity at the point of closest approach (limited by either the surface or the atmosphere.)

Interplanetary slingshots using the Sun itself are not possible because the Sun is at rest relative to the Solar System as a whole. However, thrusting when near the Sun has the same effect as the powered slingshot described as the Oberth effect. This has the potential to magnify a spacecraft's thrusting power enormously, but is limited by the spacecraft's ability to resist the heat.

A rotating black hole might provide additional assistance, if its spin axis is aligned the right way. General relativity predicts that a large spinning mass produces frame-dragging—close to the object, space itself is dragged around in the direction of the spin. Any ordinary rotating object produces this effect. Although attempts to measure frame dragging about the Sun have produced no clear evidence, experiments performed by Gravity Probe B have detected frame-dragging effects caused by Earth. General relativity predicts that a spinning black hole is surrounded by a region of space, called the ergosphere, within which standing still (with respect to the black hole's spin) is impossible, because space itself is dragged at the speed of light in the same direction as the black hole's spin. The Penrose process may offer a way to gain energy from the ergosphere, although it would require the spaceship to dump some "ballast" into the black hole, and the spaceship would have had to expend energy to carry the "ballast" to the black hole.

Another potential application of gravity assist is alteration of the Earth's orbital distance from the Sun to reduce increasing global temperatures.

Tisserand parameter and gravity assists

The use of gravity assists is constrained by a conserved quantity called the Tisserand parameter (or invariant). This is an approximation to the Jacobi constant of the restricted three-body problem. Considering the case of a comet orbiting the Sun and the effects a Jupiter encounter would have, Félix Tisserand showed that

T_{P} = \frac{a_{J}}{a} + 2 \cdot \sqrt{\frac{a}{a_{J}} (1 - e^{2})} \cos i

will remain constant (where $a$ is the comet's semi-major axis, $e$ its eccentricity, $i$ its inclination, and $a_{J}$ is the semi-major axis of Jupiter).

This applies when the comet is sufficiently far from Jupiter to have well-defined orbital elements and to the extent that Jupiter is much less massive than the Sun and on a circular orbit.

This quantity is conserved for any system of three objects, one of which has negligible mass, and another of which is of intermediate mass and on a circular orbit. Examples are the Sun, Earth and a spacecraft, or Saturn, Titan and the Cassini spacecraft (using the semi-major axis of the perturbing body instead of $a_{J}$ ). This imposes a constraint on how a gravity assist may be used to alter a spacecraft's orbit.

The Tisserand parameter will change if the spacecraft makes a propulsive maneuver or a gravity assist of some fourth object, which is one reason that many spacecraft frequently combine Earth and Venus (or Mars) gravity assists or also perform large deep space maneuvers.

Notable examples of use

Luna 3

The gravity assist maneuver was first attempted in 1959 for Luna 3, to photograph the far side of the Moon. The satellite did not gain speed, but its orbit was changed that allowed successful transmission of the photos.

Pioneer 10

NASA's Pioneer 10 is a space probe launched in 1972 that completed the first mission to the planet Jupiter. Thereafter, Pioneer 10 became the first of five artificial objects to achieve the escape velocity needed to leave the Solar System. In December 1973, Pioneer 10 spacecraft was the first one to use the gravitational slingshot effect to reach escape velocity to leave Solar System.

Pioneer 11

Pioneer 11 was launched by NASA in 1973, to study the asteroid belt, the environment around Jupiter and Saturn, solar winds, and cosmic rays. It was the first probe to encounter Saturn, the second to fly through the asteroid belt, and the second to fly by Jupiter. To get to Saturn, the spacecraft got a gravity assist on Jupiter.

Mariner 10

The Mariner 10 probe was the first spacecraft to use the gravitational slingshot effect to reach another planet, passing by Venus on 5 February 1974 on its way to becoming the first spacecraft to explore Mercury.

Voyager 1

Voyager 1 was launched by NASA on September 5, 1977. It gained the energy to escape the Sun's gravity by performing slingshot maneuvers around Jupiter and Saturn. Having operated for 46 years and 22 days as of September 28, 2023 UTC, the spacecraft still communicates with the Deep Space Network to receive routine commands and to transmit data to Earth. Real-time distance and velocity data is provided by NASA and JPL. At a distance of 152.2 AU (22.8 billion km; 14.1 billion mi) from Earth as of January 12, 2020, it is the most distant human-made object from Earth.

Voyager 2

Voyager 2 was launched by NASA on August 20, 1977, to study the outer planets. Its trajectory took longer to reach Jupiter and Saturn than its twin spacecraft but enabled further encounters with Uranus and Neptune.

Galileo

The Galileo spacecraft was launched by NASA in 1989 and on its route to Jupiter get three gravity assists, one from Venus (February 10, 1990), and two from Earth (December 8, 1990 and December 8, 1992). Spacecraft reached Jupiter in December 1995. Gravity assists also allowed Galileo to flyby two asteroids, 243 Ida and 951 Gaspra.

Ulysses

In 1990, NASA launched the ESA spacecraft Ulysses to study the polar regions of the Sun. All the planets orbit approximately in a plane aligned with the equator of the Sun. Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane. It was achieved by a gravity assist from Jupiter on February 8, 1992.

MESSENGER

The MESSENGER mission (launched in August 2004) made extensive use of gravity assists to slow its speed before orbiting Mercury. The MESSENGER mission included one flyby of Earth, two flybys of Venus, and three flybys of Mercury before finally arriving at Mercury in March 2011 with a velocity low enough to permit orbit insertion with available fuel. Although the flybys were primarily orbital maneuvers, each provided an opportunity for significant scientific observations.

Cassini

The Cassini–Huygens spacecraft was launched from Earth on 15 October 1997, followed by gravity assist flybys of Venus (26 April 1998 and 21 June 1999), Earth (18 August 1999), and Jupiter (30 December 2000). Transit to Saturn took 6.7 years, the spacecraft arrived at 1 July 2004. Its trajectory was called "the Most Complex Gravity-Assist Trajectory Flown to Date" in 2019.

Cassini interplanetary trajectory

Animation of Cassini's trajectory from 15 October 1997 to 4 May 2008
Cassini–Huygens · Jupiter · Saturn · Earth · Venus · Mars

Cassini's speed relative to the Sun. Gravity assists form peaks to the left, while periodic variations on the right are caused by the spacecraft's orbit around Saturn.

After entering orbit around Saturn, the Cassini spacecraft used multiple Titan gravity assists to achieve significant changes in the inclination of its orbit as well so that instead of staying nearly in the equatorial plane, the spacecraft's flight path was inclined well out of the plane of the rings. A typical Titan encounter changed the spacecraft's velocity by 0.75 km/s, and the spacecraft made 127 Titan encounters. These encounters enabled an orbital tour with a wide range of periapsis and apoapsis distances, various alignments of the orbit with respect to the Sun, and orbital inclinations from 0° to 74°. The multiple flybys of Titan also allowed Cassini to flyby other moons, such as Rhea and Enceladus.

Rosetta

The Rosetta probe, launched in March 2004, used four gravity assist maneuvers (including one just 250 km from the surface of Mars, and three assists from Earth) to accelerate throughout the inner Solar System. That enabled it to flyby the asteroids 21 Lutetia and 2867 Šteins as well as eventually match the velocity of the 67P/Churyumov–Gerasimenko comet at the rendezvous point in August 2014.

New Horizons

New Horizons was launched by NASA in 2006, and reached Pluto in 2015. In 2007 it performed a gravity assist on Jupiter.

Juno

The Juno spacecraft was launched on August 5, 2011 (UTC). The trajectory used a gravity assist speed boost from Earth, accomplished by an Earth flyby in October 2013, two years after its launch on August 5, 2011. In that way Juno changed its orbit (and speed) toward its final goal, Jupiter, after only five years.

Parker Solar Probe

Parker Solar Probe, launched by NASA in 2018, has seven planned Venus gravity assists. Each gravity assist bring Parker Solar Probe progressively closer to the Sun. As of 2022, the spacecraft performed five of its seven assists. Parker Solar Probe's mission will make the closest approach to the Sun by any space mission.

Solar Orbiter

Solar Orbiter was launched by ESA in 2020. In its initial cruise phase, which lasts until November 2021, Solar Orbiter performed two gravity-assist manoeuvres around Venus and one around Earth to alter the spacecraft's trajectory, guiding it towards the innermost regions of the Solar System. The first close solar pass will take place on 26 March 2022 at around a third of Earth's distance from the Sun.

BepiColombo

BepiColombo is a joint mission of the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA) to the planet Mercury. It was launched on 20 October 2018. It will use the gravity assist technique with Earth once, with Venus twice, and six times with Mercury. It will arrive in 2025. BepiColombo is named after Giuseppe (Bepi) Colombo who was a pioneer thinker with this way of maneuvers.

Lucy

Lucy was launched by NASA on 16 October 2021. It gained one gravity assist from Earth on the 16th of October, 2022, and after a flyby of the main-belt asteroid 152830 Dinkinesh it will gain another in 2024. In 2025, it will fly by the inner main-belt asteroid 52246 Donaldjohanson. In 2027, it will arrive at the L₄ Trojan cloud (the Greek camp of asteroids that orbits about 60° ahead of Jupiter), where it will fly by four Trojans, 3548 Eurybates (with its satellite), 15094 Polymele, 11351 Leucus, and 21900 Orus. After these flybys, Lucy will return to Earth in 2031 for another gravity assist toward the L₅ Trojan cloud (the Trojan camp which trails about 60° behind Jupiter), where it will visit the binary Trojan 617 Patroclus with its satellite Menoetius in 2033.

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