Specific orbital energy

From Wikipedia, the free encyclopedia

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

In the gravitational two-body problem, the specific orbital energy ${\displaystyle \epsilon }$ (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy (${\displaystyle {\epsilon }_p}$) and their total kinetic energy (${\displaystyle {\epsilon }_k}$), divided by the reduced mass. According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time:

$${\displaystyle \begin{array}{rl}\epsilon & ={\epsilon }_k+{\epsilon }_p\\ & =\frac{v^2}{2}-\frac{\mu }{r}=-\frac{1}{2}\frac{{\mu }^2}{h^2}\left(1-e^2\right)=-\frac{\mu }{2a}\end{array}}$$

where

• ${\displaystyle v}$ is the relative orbital speed;
• ${\displaystyle r}$ is the orbital distance between the bodies;
• ${\displaystyle \mu =G(m_1+m_2)}$ is the sum of the standard gravitational parameters of the bodies;
• ${\displaystyle h}$ is the specific relative angular momentum in the sense of relative angular momentum divided by the reduced mass;
• ${\displaystyle e}$ is the orbital eccentricity;
• ${\displaystyle a}$ is the semi-major axis.

It is typically expressed in ${\displaystyle \frac{\text{MJ}}{\text{kg}}}$ (megajoule per kilogram) or ${\displaystyle \frac{{\text{km}}^2}{{\text{s}}^2}}$ (squared kilometer per squared second). For an elliptic orbit the specific orbital energy is the negative of the additional energy required to accelerate a mass of one kilogram to escape velocity (parabolic orbit). For a hyperbolic orbit, it is equal to the excess energy compared to that of a parabolic orbit. In this case the specific orbital energy is also referred to as characteristic energy.

Equation forms for different orbits

For an elliptic orbit, the specific orbital energy equation, when combined with conservation of specific angular momentum at one of the orbit's apsides, simplifies to:

$${\displaystyle \epsilon =-\frac{\mu }{2a}}$$

where

• ${\displaystyle \mu =G\left(m_1+m_2\right)}$ is the standard gravitational parameter;
• ${\displaystyle a}$ is semi-major axis of the orbit.

Proof

For an elliptic orbit with specific angular momentum h given by

$${\displaystyle h^2=\mu p=\mu a\left(1-e^2\right)}$$

we use the general form of the specific orbital energy equation,

$${\displaystyle \epsilon =\frac{v^2}{2}-\frac{\mu }{r}}$$

with the relation that the relative velocity at periapsis is

$${\displaystyle v_p^2=\frac{h^2}{r_p^2}=\frac{h^2}{a^2(1-e{)}^2}=\frac{\mu a\left(1-e^2\right)}{a^2(1-e{)}^2}=\frac{\mu \left(1-e^2\right)}{a(1-e{)}^2}}$$

Thus our specific orbital energy equation becomes

$${\displaystyle \epsilon =\frac{\mu }{a}\left[\frac{1-e^2}{2(1-e{)}^2}-\frac{1}{1-e}\right]=\frac{\mu }{a}\left[\frac{(1-e)(1+e)}{2(1-e{)}^2}-\frac{1}{1-e}\right]=\frac{\mu }{a}\left[\frac{1+e}{2(1-e)}-\frac{2}{2(1-e)}\right]=\frac{\mu }{a}\left[\frac{e-1}{2(1-e)}\right]}$$

and finally with the last simplification we obtain:

$${\displaystyle \epsilon =-\frac{\mu }{2a}}$$

For a parabolic orbit this equation simplifies to

$${\displaystyle \epsilon =0.}$$

For a hyperbolic trajectory this specific orbital energy is either given by

$${\displaystyle \epsilon =\frac{\mu }{2a}.}$$

or the same as for an ellipse, depending on the convention for the sign of a.

In this case the specific orbital energy is also referred to as characteristic energy (or ${\displaystyle C_3}$) and is equal to the excess specific energy compared to that for a parabolic orbit.

It is related to the hyperbolic excess velocity ${\displaystyle v_{\mathrm{\infty }}}$ (the orbital velocity at infinity) by

$${\displaystyle 2\epsilon =C_3=v_{\mathrm{\infty }}^2.}$$

It is relevant for interplanetary missions.

Thus, if orbital position vector (${\displaystyle \mathbf{r}}$) and orbital velocity vector (${\displaystyle \mathbf{v}}$) are known at one position, and ${\displaystyle \mu }$ is known, then the energy can be computed and from that, for any other position, the orbital speed.

Rate of change

For an elliptic orbit the rate of change of the specific orbital energy with respect to a change in the semi-major axis is

$${\displaystyle \frac{\mu }{2a^2}}$$

where

• ${\displaystyle \mu =G(m_1+m_2)}$ is the standard gravitational parameter;
• ${\displaystyle a}$ is semi-major axis of the orbit.

In the case of circular orbits, this rate is one half of the gravitation at the orbit. This corresponds to the fact that for such orbits the total energy is one half of the potential energy, because the kinetic energy is minus one half of the potential energy.

Additional energy

If the central body has radius R, then the additional specific energy of an elliptic orbit compared to being stationary at the surface is

$${\displaystyle -\frac{\mu }{2a}+\frac{\mu }{R}=\frac{\mu (2a-R)}{2aR}}$$

The quantity ${\displaystyle 2a-R}$ is the height the ellipse extends above the surface, plus the periapsis distance (the distance the ellipse extends beyond the center of the Earth). For the Earth and ${\displaystyle a}$ just little more than ${\displaystyle R}$ the additional specific energy is ${\displaystyle (gR/2)}$; which is the kinetic energy of the horizontal component of the velocity, i.e. $\frac{1}{2}{V}^2=\frac{1}{2}gR$, ${\displaystyle V=\sqrt{gR}}$.

Examples

ISS

The International Space Station has an orbital period of 91.74 minutes (5504 s), hence by Kepler's Third Law the semi-major axis of its orbit is 6,738 km.

The specific orbital energy associated with this orbit is −29.6 MJ/kg: the potential energy is −59.2 MJ/kg, and the kinetic energy 29.6 MJ/kg. Compare with the potential energy at the surface, which is −62.6 MJ/kg. The extra potential energy is 3.4 MJ/kg, the total extra energy is 33.0 MJ/kg. The average speed is 7.7 km/s, the net delta-v to reach this orbit is 8.1 km/s (the actual delta-v is typically 1.5–2.0 km/s more for atmospheric drag and gravity drag).

The increase per meter would be 4.4 J/kg; this rate corresponds to one half of the local gravity of 8.8 m/s².

For an altitude of 100 km (radius is 6471 km):

The energy is −30.8 MJ/kg: the potential energy is −61.6 MJ/kg, and the kinetic energy 30.8 MJ/kg. Compare with the potential energy at the surface, which is −62.6 MJ/kg. The extra potential energy is 1.0 MJ/kg, the total extra energy is 31.8 MJ/kg.

The increase per meter would be 4.8 J/kg; this rate corresponds to one half of the local gravity of 9.5 m/s². The speed is 7.8 km/s, the net delta-v to reach this orbit is 8.0 km/s.

Taking into account the rotation of the Earth, the delta-v is up to 0.46 km/s less (starting at the equator and going east) or more (if going west).

Voyager 1

For Voyager 1, with respect to the Sun:

• ${\displaystyle \mu =GM}$ = 132,712,440,018 km³⋅s⁻² is the standard gravitational parameter of the Sun
• r = 17 billion kilometers
• v = 17.1 km/s

Hence:

$${\displaystyle \epsilon ={\epsilon }_k+{\epsilon }_p=\frac{v^2}{2}-\frac{\mu }{r}=146\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}-8\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}=138\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}}$$

Thus the hyperbolic excess velocity (the theoretical orbital velocity at infinity) is given by

$${\displaystyle v_{\mathrm{\infty }}=16.6\mathrm{k}\mathrm{m}/\mathrm{s}}$$

However, Voyager 1 does not have enough velocity to leave the Milky Way. The computed speed applies far away from the Sun, but at such a position that the potential energy with respect to the Milky Way as a whole has changed negligibly, and only if there is no strong interaction with celestial bodies other than the Sun.

Applying thrust

Assume:

• a is the acceleration due to thrust (the time-rate at which delta-v is spent)
• g is the gravitational field strength
• v is the velocity of the rocket

Then the time-rate of change of the specific energy of the rocket is ${\displaystyle \mathbf{v}\cdot \mathbf{a}}$: an amount ${\displaystyle \mathbf{v}\cdot (\mathbf{a}-\mathbf{g})}$ for the kinetic energy and an amount ${\displaystyle \mathbf{v}\cdot \mathbf{g}}$ for the potential energy.

The change of the specific energy of the rocket per unit change of delta-v is

$${\displaystyle \frac{\mathbf{v}\cdot \mathbf{a}}{|\mathbf{a}|}}$$

which is |v| times the cosine of the angle between v and a.

Thus, when applying delta-v to increase specific orbital energy, this is done most efficiently if a is applied in the direction of v, and when |v| is large. If the angle between v and g is obtuse, for example in a launch and in a transfer to a higher orbit, this means applying the delta-v as early as possible and at full capacity. See also gravity drag. When passing by a celestial body it means applying thrust when nearest to the body. When gradually making an elliptic orbit larger, it means applying thrust each time when near the periapsis.

When applying delta-v to decrease specific orbital energy, this is done most efficiently if a is applied in the direction opposite to that of v, and again when |v| is large. If the angle between v and g is acute, for example in a landing (on a celestial body without atmosphere) and in a transfer to a circular orbit around a celestial body when arriving from outside, this means applying the delta-v as late as possible. When passing by a planet it means applying thrust when nearest to the planet. When gradually making an elliptic orbit smaller, it means applying thrust each time when near the periapsis.

If a is in the direction of v:

$${\displaystyle \mathrm{\Delta }\epsilon =\int vd(\mathrm{\Delta }v)=\int vadt}$$

Tidal locking

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

Tidal locking results in the Moon rotating about its axis in about the same time it takes to orbit Earth. Except for libration, this results in the Moon keeping the same face turned toward Earth, as seen in the left figure. The Moon is shown in polar view, and is not drawn to scale. If the Moon were not rotating at all, it would alternately show its near and far sides to Earth, while moving around Earth in orbit, as shown in the right figure.

A side view of the Pluto–Charon system. Pluto and Charon are tidally locked to each other. Charon is massive enough that the barycenter of Pluto's system lies outside of Pluto; thus, Pluto and Charon are sometimes considered to be a binary system.

Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon, as well as for Eris and Dysnomia. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking.

The effect arises between two bodies when their gravitational interaction slows a body's rotation until it becomes tidally locked. Over many millions of years, the interaction forces changes to their orbits and rotation rates as a result of energy exchange and heat dissipation. When one of the bodies reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit, it is said to be tidally locked. The object tends to stay in this state because leaving it would require adding energy back into the system. The object's orbit may migrate over time so as to undo the tidal lock, for example, if a giant planet perturbs the object.

Not every case of tidal locking involves synchronous rotation. With Mercury, for example, this tidally locked planet completes three rotations for every two revolutions around the Sun, a 3:2 spin–orbit resonance. In the special case where an orbit is nearly circular and the body's rotation axis is not significantly tilted, such as the Moon, tidal locking results in the same hemisphere of the revolving object constantly facing its partner. However, in this case the exact same portion of the body does not always face the partner on all orbits. There can be some shifting due to variations in the locked body's orbital velocity and the inclination of its rotation axis.

Mechanism

Further information: Centers of gravity in non-uniform fields

If the tidal bulges on a body (green) are misaligned with the major axis (red), the tidal forces (blue) exert a net torque on that body that twists the body toward the direction of realignment.

Consider a pair of co-orbiting objects, A and B. The change in rotation rate necessary to tidally lock body B to the larger body A is caused by the torque applied by A's gravity on bulges it has induced on B by tidal forces.

The gravitational force from object A upon B will vary with distance, being greatest at the nearest surface to A and least at the most distant. This creates a gravitational gradient across object B that will distort its equilibrium shape slightly. The body of object B will become elongated along the axis oriented toward A, and conversely, slightly reduced in dimension in directions orthogonal to this axis. The elongated distortions are known as tidal bulges. (For the solid Earth, these bulges can reach displacements of up to around 0.4 m or 1 ft 4 in.) When B is not yet tidally locked, the bulges travel over its surface due to orbital motions, with one of the two "high" tidal bulges traveling close to the point where body A is overhead. For large astronomical bodies that are nearly spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid, i.e. an axially symmetric ellipsoid that is elongated along its major axis. Smaller bodies also experience distortion, but this distortion is less regular.

The material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time is required to reshape B to the gravitational equilibrium shape, by which time the forming bulges have already been carried some distance away from the A–B axis by B's rotation. Seen from a vantage point in space, the points of maximum bulge extension are displaced from the axis oriented toward A. If B's rotation period is shorter than its orbital period, the bulges are carried forward of the axis oriented toward A in the direction of rotation, whereas if B's rotation period is longer, the bulges instead lag behind.

Because the bulges are now displaced from the A–B axis, A's gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, whereas the "back" bulge, which faces away from A, acts in the opposite sense. However, the bulge on the A-facing side is closer to A than the back bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational force and torque. The net resulting torque from both bulges, then, is always in the direction that acts to synchronize B's rotation with its orbital period, leading eventually to tidal locking.

Orbital changes

In (1), a satellite orbits in the same direction as (but slower than) its parent body's rotation. The nearer tidal bulge (red) attracts the satellite more than the farther bulge (blue), slowing the parent's rotation while imparting a net positive force (dotted arrows showing forces resolved into their components) in the direction of orbit, lifting it into a higher orbit (tidal acceleration).
In (2) with the rotation reversed, the net force opposes the satellite's direction of orbit, lowering it (tidal deceleration).

If rotational frequency is larger than orbital frequency, a small torque counteracting the rotation arises, eventually locking the frequencies (situation depicted in green)

The angular momentum of the whole A–B system is conserved in this process, so that when B slows down and loses rotational angular momentum, its orbital angular momentum is boosted by a similar amount (there are also some smaller effects on A's rotation). This results in a raising of B's orbit about A in tandem with its rotational slowdown. For the other case where B starts off rotating too slowly, tidal locking both speeds up its rotation, and lowers its orbit.

Locking of the larger body

See also: Synchronous orbit

The tidal locking effect is also experienced by the larger body A, but at a slower rate because B's gravitational effect is weaker due to B's smaller mass. For example, Earth's rotation is gradually being slowed by the Moon, by an amount that becomes noticeable over geological time as revealed in the fossil record. Current estimations are that this (together with the tidal influence of the Sun) has helped lengthen the Earth day from about 6 hours to the current 24 hours (over ≈ ⁠4½ billion years). Currently, atomic clocks show that Earth's day lengthens, on average, by about 2.3 milliseconds per century. Given enough time, this would create a mutual tidal locking between Earth and the Moon. The length of the Earth's day would increase and the length of a lunar month would also increase. The Earth's sidereal day would eventually have the same length as the Moon's orbital period, about 47 times the length of the Earth's day at present. However, Earth is not expected to become tidally locked to the Moon before the Sun becomes a red giant and engulfs Earth and the Moon.

For bodies of similar size the effect may be of comparable size for both, and both may become tidally locked to each other on a much shorter timescale. An example is the dwarf planet Pluto and its satellite Charon. They have already reached a state where Charon is visible from only one hemisphere of Pluto and vice versa.

Eccentric orbits

A widely spread misapprehension is that a tidally locked body permanently turns one side to its host.

— Heller et al. (2011)

For orbits that do not have an eccentricity close to zero, the rotation rate tends to become locked with the orbital speed when the body is at periapsis, which is the point of strongest tidal interaction between the two objects. If the orbiting object has a companion, this third body can cause the rotation rate of the parent object to vary in an oscillatory manner. This interaction can also drive an increase in orbital eccentricity of the orbiting object around the primary – an effect known as eccentricity pumping.

In some cases where the orbit is eccentric and the tidal effect is relatively weak, the smaller body may end up in a so-called spin–orbit resonance, rather than being tidally locked. Here, the ratio of the rotation period of a body to its own orbital period is some simple fraction different from 1:1. A well known case is the rotation of Mercury, which is locked to its own orbit around the Sun in a 3:2 resonance. This results in the rotation speed roughly matching the orbital speed around perihelion.

Many exoplanets (especially the close-in ones) are expected to be in spin–orbit resonances higher than 1:1. A Mercury-like terrestrial planet can, for example, become captured in a 3:2, 2:1, or 5:2 spin–orbit resonance, with the probability of each being dependent on the orbital eccentricity.

Occurrence

Moons

Due to tidal locking, the inhabitants of the central body will never be able to see the satellite's green area.

All twenty known moons in the Solar System that are large enough to be round are tidally locked with their primaries, because they orbit very closely and tidal force increases rapidly (as a cubic function) with decreasing distance. On the other hand, the irregular outer satellites of the gas giants (e.g. Phoebe), which orbit much farther away than the large well-known moons, are not tidally locked.

Pluto and Charon are an extreme example of a tidal lock. Charon is a relatively large moon in comparison to its primary and also has a very close orbit. This results in Pluto and Charon being mutually tidally locked. Pluto's other moons are not tidally locked; Styx, Nix, Kerberos, and Hydra all rotate chaotically due to the influence of Charon. Similarly, Eris and Dysnomia are mutually tidally locked. Orcus and Vanth might also be mutually tidally locked, but the data is not conclusive.

The tidal locking situation for asteroid moons is largely unknown, but closely orbiting binaries are expected to be tidally locked, as well as contact binaries.

Earth's Moon

Libration causes variability in the portion of the Moon visible from Earth.

Earth's Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth, the same hemisphere of the Moon is always seen. Most of the far side of the Moon was not seen until 1959, when photographs of most of the far side were transmitted from the Soviet spacecraft Luna 3.

When the Earth is observed from the Moon, the Earth does not appear to move across the sky. It remains in the same place while showing nearly all its surface as it rotates on its axis.

Despite the Moon's rotational and orbital periods being exactly locked, about 59 percent of the Moon's total surface may be seen with repeated observations from Earth, due to the phenomena of libration and parallax. Librations are primarily caused by the Moon's varying orbital speed due to the eccentricity of its orbit: this allows up to about 6° more along its perimeter to be seen from Earth. Parallax is a geometric effect: at the surface of Earth observers are offset from the line through the centers of Earth and Moon, and because of this about 1° more can be seen around the side of the Moon when it is on the local horizon.

Planets

It was thought for some time that Mercury was in synchronous rotation with the Sun. This was because whenever Mercury was best placed for observation, the same side faced inward. Radar observations in 1965 demonstrated instead that Mercury has a 3:2 spin–orbit resonance, rotating three times for every two revolutions around the Sun, which results in the same positioning at those observation points. Modeling has demonstrated that Mercury was captured into the 3:2 spin–orbit state very early in its history, probably within 10–20 million years after its formation.

The 583.92-day interval between successive close approaches of Venus to Earth is equal to 5.001444 Venusian solar days, making approximately the same face visible from Earth at each close approach. Whether this relationship arose by chance or is the result of some kind of tidal locking with Earth is unknown.

The exoplanet Proxima Centauri b discovered in 2016 which orbits around Proxima Centauri, is almost certainly tidally locked, expressing either synchronized rotation or a 3:2 spin–orbit resonance like that of Mercury.

One form of hypothetical tidally locked exoplanets are eyeball planets, which in turn are divided into "hot" and "cold" eyeball planets.

Stars

Close binary stars throughout the universe are expected to be tidally locked with each other, and extrasolar planets that have been found to orbit their primaries extremely closely are also thought to be tidally locked to them. An unusual example, confirmed by MOST, may be Tau Boötis, a star that is probably tidally locked by its planet Tau Boötis b. If so, the tidal locking is almost certainly mutual.

Timescale

An estimate of the time for a body to become tidally locked can be obtained using the following formula:

${\displaystyle t_{\text{lock}}\approx \frac{\omega a^{6}IQ}{3G{m}_p^2{k}_2{R}^5}}$

where

• ${\displaystyle \omega }$ is the initial spin rate expressed in radians per second,
• ${\displaystyle a}$ is the semi-major axis of the motion of the satellite around the planet (given by the average of the periapsis and apoapsis distances),
• ${\displaystyle I}$ ${\displaystyle \approx 0.4m_s{R}^2}$ is the moment of inertia of the satellite, where ${\displaystyle m_s}$ is the mass of the satellite and ${\displaystyle R}$ is the mean radius of the satellite,
• ${\displaystyle Q}$ is the dissipation function of the satellite,
• ${\displaystyle G}$ is the gravitational constant,
• ${\displaystyle m_p}$ is the mass of the planet (i.e., the object being orbited), and
• ${\displaystyle k_2}$ is the tidal Love number of the satellite.

${\displaystyle Q}$ and ${\displaystyle k_2}$ are generally very poorly known except for the Moon, which has ${\displaystyle k_2/Q=0.0011}$. For a really rough estimate it is common to take ${\displaystyle Q\approx 100}$ (perhaps conservatively, giving overestimated locking times), and

${\displaystyle k_2\approx \frac{1.5}{1+\frac{19\mu }{2\rho gR}},}$

where

• ${\displaystyle \rho }$ is the density of the satellite
• ${\displaystyle g\approx G{m}_s/R^2}$ is the surface gravity of the satellite
• ${\displaystyle \mu }$ is the rigidity of the satellite. This can be roughly taken as 3×10¹⁰ N·m⁻² for rocky objects and 4×10⁹ N·m⁻² for icy ones.

Even knowing the size and density of the satellite leaves many parameters that must be estimated (especially ω, Q, and μ), so that any calculated locking times obtained are expected to be inaccurate, even to factors of ten. Further, during the tidal locking phase the semi-major axis ${\displaystyle a}$ may have been significantly different from that observed nowadays due to subsequent tidal acceleration, and the locking time is extremely sensitive to this value.

Because the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one. By assuming that the satellite is spherical, ${\displaystyle k_2\ll 1,Q=100}$, and it is sensible to guess one revolution every 12 hours in the initial non-locked state (most asteroids have rotational periods between about 2 hours and about 2 days)

${\displaystyle t_{\text{lock}}\approx 6\frac{a^{6}R\mu }{m_s{m}_p^2}\times {10}^{10}\text{years},}$

with masses in kilograms, distances in meters, and ${\displaystyle \mu }$ in newtons per meter squared; ${\displaystyle \mu }$ can be roughly taken as 3×10¹⁰ N·m⁻² for rocky objects and 4×10⁹ N·m⁻² for icy ones.

There is an extremely strong dependence on semi-major axis ${\displaystyle a}$.

For the locking of a primary body to its satellite as in the case of Pluto, the satellite and primary body parameters can be swapped.

One conclusion is that, other things being equal (such as ${\displaystyle Q}$ and ${\displaystyle \mu }$), a large moon will lock faster than a smaller moon at the same orbital distance from the planet because ${\displaystyle m_s}$ grows as the cube of the satellite radius ${\displaystyle R}$. A possible example of this is in the Saturn system, where Hyperion is not tidally locked, whereas the larger Iapetus, which orbits at a greater distance, is. However, this is not clear cut because Hyperion also experiences strong driving from the nearby Titan, which forces its rotation to be chaotic.

The above formulae for the timescale of locking may be off by orders of magnitude, because they ignore the frequency dependence of ${\displaystyle k_2/Q}$. More importantly, they may be inapplicable to viscous binaries (double stars, or double asteroids that are rubble), because the spin–orbit dynamics of such bodies is defined mainly by their viscosity, not rigidity.

List of known tidally locked bodies

Solar System

Parent body	Tidally-locked satellites
Sun	Mercury (3:2 spin–orbit resonance) Note: planet is tidally-locked in non-synchronized rotation, per the attached refs
Earth	Moon (Synchronous rotation; a special case of tidal locking)
Mars	Phobos · Deimos
Jupiter	Metis · Adrastea · Amalthea · Thebe · Io · Europa · Ganymede · Callisto
Saturn	Pan · Atlas · Prometheus · Pandora · Epimetheus · Janus · Mimas · Enceladus · Telesto · Tethys · Calypso · Dione · Rhea · Titan · Iapetus
Uranus	Miranda · Ariel · Umbriel · Titania · Oberon
Neptune	Proteus · Triton
Pluto	Charon (Pluto is itself locked to Charon)
Eris	Dysnomia (Eris is itself locked to Dysnomia)

Extra-solar

• The most successful detection methods of exoplanets (transits and radial velocities) suffer from a clear observational bias favoring the detection of planets near the star; thus, 85% of the exoplanets detected are inside the tidal locking zone, which makes it difficult to estimate the true incidence of this phenomenon. Tau Boötis is known to be locked to the close-orbiting giant planet Tau Boötis b.

Bodies likely to be locked

Solar System

Based on comparison between the likely time needed to lock a body to its primary, and the time it has been in its present orbit (comparable with the age of the Solar System for most planetary moons), a number of moons are thought to be locked. However their rotations are not known or not known enough. These are:

Probably locked to Saturn

• Daphnis
• Aegaeon
• Methone
• Anthe
• Pallene
• Helene
• Polydeuces

Probably locked to Uranus

• Cordelia
• Ophelia
• Bianca
• Cressida
• Desdemona
• Juliet
• Portia
• Rosalind
• Cupid
• Belinda
• Perdita
• Puck
• Mab

Probably locked to Neptune

• Naiad
• Thalassa
• Despina
• Galatea
• Larissa

Probably mutually tidally locked

• Orcus and Vanth

Extrasolar

Gliese 581c, Gliese 581g, Gliese 581b, and Gliese 581e may be tidally locked to their parent star Gliese 581. Gliese 581d is almost certainly captured either into the 2:1 or the 3:2 spin–orbit resonance with the same star.

All planets in the TRAPPIST-1 system are likely to be tidally locked.

Multiple drug resistance

From Wikipedia, the free encyclopedia

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

Multiple drug resistance (MDR), multidrug resistance or multiresistance is antimicrobial resistance shown by a species of microorganism to at least one antimicrobial drug in three or more antimicrobial categories. Antimicrobial categories are classifications of antimicrobial agents based on their mode of action and specific to target organisms. The MDR types most threatening to public health are MDR bacteria that resist multiple antibiotics; other types include MDR viruses, parasites (resistant to multiple antifungal, antiviral, and antiparasitic drugs of a wide chemical variety).

Recognizing different degrees of MDR in bacteria, the terms extensively drug-resistant (XDR) and pandrug-resistant (PDR) have been introduced. Extensively drug-resistant (XDR) is the non-susceptibility of one bacteria species to all antimicrobial agents except in two or less antimicrobial categories. Within XDR, pandrug-resistant (PDR) is the non-susceptibility of bacteria to all antimicrobial agents in all antimicrobial categories. The definitions were published in 2011 in the journal Clinical Microbiology and Infection and are openly accessible.

Common multidrug-resistant organisms (MDROs)

Common multidrug-resistant organisms are usually bacteria:

• Vancomycin-Resistant Enterococci (VRE)
• Methicillin-resistant Staphylococcus aureus (MRSA)
• Extended-spectrum β-lactamase (ESBLs) producing Gram-negative bacteria
• Klebsiella pneumoniae carbapenemase (KPC) producing Gram-negatives
• Multidrug-resistant Gram negative rods (MDR GNR) MDRGN bacteria such as Enterobacter species, E.coli, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa
• Multi-drug-resistant tuberculosis

Overlapping with MDRGN, a group of Gram-positive and Gram-negative bacteria of particular recent importance have been dubbed as the ESKAPE group (Enterococcus faecium, Staphylococcus aureus, Klebsiella pneumoniae, Acinetobacter baumannii, Pseudomonas aeruginosa and Enterobacter species).

Bacterial resistance to antibiotics

Main article: Antibiotic resistance

Various microorganisms have survived for thousands of years by their ability to adapt to antimicrobial agents. They do so via spontaneous mutation or by DNA transfer. This process enables some bacteria to oppose the action of certain antibiotics, rendering the antibiotics ineffective. These microorganisms employ several mechanisms in attaining multi-drug resistance:

• No longer relying on a glycoprotein cell wall
• Enzymatic deactivation of antibiotics
• Decreased cell wall permeability to antibiotics
• Altered target sites of antibiotic
• Efflux mechanisms to remove antibiotics
• Increased mutation rate as a stress response

Many different bacteria now exhibit multi-drug resistance, including staphylococci, enterococci, gonococci, streptococci, salmonella, as well as numerous other Gram-negative bacteria and Mycobacterium tuberculosis. Antibiotic resistant bacteria are able to transfer copies of DNA that code for a mechanism of resistance to other bacteria even distantly related to them, which then are also able to pass on the resistance genes and so generations of antibiotics resistant bacteria are produced. This process is called horizontal gene transfer and is mediated through cell-cell conjugation.

Bacterial resistance to bacteriophages

Phage-resistant bacteria variants have been observed in human studies. As for antibiotics, horizontal transfer of phage resistance can be acquired by plasmid acquisition.

Antifungal resistance

Yeasts such as Candida species can become resistant under long-term treatment with azole preparations, requiring treatment with a different drug class. Lomentospora prolificans infections are often fatal because of their resistance to multiple antifungal agents.

Antiviral resistance

HIV is the prime example of MDR against antivirals, as it mutates rapidly under monotherapy. Influenza virus has become increasingly MDR; first to amantadines, then to neuraminidase inhibitors such as oseltamivir, (2008-2009: 98.5% of Influenza A tested resistant), also more commonly in people with weak immune systems. Cytomegalovirus can become resistant to ganciclovir and foscarnet under treatment, especially in immunosuppressed patients. Herpes simplex virus rarely becomes resistant to acyclovir preparations, mostly in the form of cross-resistance to famciclovir and valacyclovir, usually in immunosuppressed patients.

Antiparasitic resistance

The prime example for MDR against antiparasitic drugs is malaria. Plasmodium vivax has become chloroquine and sulfadoxine-pyrimethamine resistant a few decades ago, and as of 2012 artemisinin-resistant Plasmodium falciparum has emerged in western Cambodia and western Thailand. Toxoplasma gondii can also become resistant to artemisinin, as well as atovaquone and sulfadiazine, but is not usually MDR Antihelminthic resistance is mainly reported in the veterinary literature, for example in connection with the practice of livestock drenching and has been recent focus of FDA regulation.

Preventing the emergence of antimicrobial resistance

To limit the development of antimicrobial resistance, it has been suggested to:

• Use the appropriate antimicrobial for an infection; e.g. no antibiotics for viral infections
• Identify the causative organism whenever possible
• Select an antimicrobial which targets the specific organism, rather than relying on a broad-spectrum antimicrobial
• Complete an appropriate duration of antimicrobial treatment (not too short and not too long)
• Use the correct dose for eradication; subtherapeutic dosing is associated with resistance, as demonstrated in food animals.
• More thorough education of and by prescribers on their actions' implications globally.

The medical community relies on education of its prescribers, and self-regulation in the form of appeals to voluntary antimicrobial stewardship, which at hospitals may take the form of an antimicrobial stewardship program. It has been argued that depending on the cultural context government can aid in educating the public on the importance of restrictive use of antibiotics for human clinical use, but unlike narcotics, there is no regulation of its use anywhere in the world at this time. Antibiotic use has been restricted or regulated for treating animals raised for human consumption with success, in Denmark for example.

Infection prevention is the most efficient strategy of prevention of an infection with a MDR organism within a hospital, because there are few alternatives to antibiotics in the case of an extensively resistant or panresistant infection; if an infection is localized, removal or excision can be attempted (with MDR-TB the lung for example), but in the case of a systemic infection only generic measures like boosting the immune system with immunoglobulins may be possible. The use of bacteriophages (viruses which kill bacteria) is a developing area of possible therapeutic treatments.

It is necessary to develop new antibiotics over time since the selection of resistant bacteria cannot be prevented completely. This means with every application of a specific antibiotic, the survival of a few bacteria which already got a resistance gene against the substance is promoted, and the concerning bacterial population amplifies. Therefore, the resistance gene is farther distributed in the organism and the environment, and a higher percentage of bacteria means they no longer respond to a therapy with this specific antibiotic. In addition to developing new antibiotics, new strategies entirely must be implemented in order to keep the public safe from the event of total resistance. New strategies are being tested such as UV light treatments and bacteriophage utilization, however more resources must be dedicated to this cause.