Resonance Book Two: Against Darker Days

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The elongated distortions are known as tidal bulges. For the solid Earth, these bulges can reach displacements of up to around 0. For large astronomical bodies that are nearly spherical due to self-gravitation, the tidal distortion produces a slightly prolate spheroid , i. 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.

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. 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. Currently, atomic clocks show that Earth's day lengthens, on average, by about 15 microseconds every year. 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. A widely spread misapprehension is that a tidally locked body permanently turns one side to its host.

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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.

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Here, the ratio of the rotation period of a body to its own orbital period is some simple fraction different from A well known case is the rotation of Mercury , which is locked to its own orbit around the Sun in a resonance. Many exoplanets especially the close-in ones are expected to be in spin—orbit resonances higher than A Mercury-like terrestrial planet can, for example, become captured in a , , or spin—orbit resonance, with the probability of each being dependent on the orbital eccentricity.

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. 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.

The 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. The far side of the Moon was not seen until , 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 translate across the sky but appears to remain in the same place, rotating on its own axis.

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 demonstrated instead that Mercury has a 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 spin—orbit state very early in its history, within 20 and more likely even 10 million years after its formation.

Venus 's Whether this relationship arose by chance or is the result of some kind of tidal locking with Earth is unknown. Proxima Centauri b , the "Earth-like planet" discovered in that orbits around the star Proxima Centauri is tidally locked, either in synchronized rotation, [18] or otherwise expresses a spin—orbit resonance like that of Mercury. One form of hypothetical tidal locked exoplanets are eyeball planets , that in turn are divided into "hot" and "cold" eyeball planets. 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 estimate of the time for a body to become tidally locked can be obtained using the following formula: [24]. Because the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one. 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. 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. 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.

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:.

From Wikipedia, the free encyclopedia. See also: Synchronous orbit. Naiad Thalassa Despina Galatea Larissa. Universe Today. Formation and Evolution of Exoplanets. April Physics and Chemistry of the Solar System. Academic Press. Geophysical Research Letters. Comfortable positioning of the patient with arms by the side or above the head. Metal artifact Ferromagnetic iron, nickel, cobalt and non-ferromagnetic titanium metals have higher magnetic susceptibility. Metallic objects such as biopsy clips, jewelry, skin tattoos, metallic snaps on clothing, deposits from core biopsy needle or electrocautery devices produce field inhomogeneity which presents as signal void along with distortion of the image.

MRI of the post-surgical breast for local recurrence remains challenging due to the metal artifact. Fix: Thorough examination of the patient with the removal of any metallic objects is required; using a lower field strength scanner such as 1. Zipper artifact Zipper artifact, also known as radiofrequency interference occurs when there is an external radio-frequency RF signal that is not consistent with the phase encoding gradient. The images have a noisy background which manifests as alternating dark and bright bands across the image. The source of the external RF signal can be within the imaging unit or outside such as television, radio, or patient monitoring equipment.

The imaging unit has a metal shield called the Faraday cage that normally prevents the external RF signal from entering the unit. Breach in this metal shield result in zipper artifact. Ensure the door to the scan room is closed correctly. Wrap-around artifact When the FOV is smaller than the signal producing tissue, it results in a wrap-around artifact.

The signal generated by the tissue outside the FOV gets superimposed on the contralateral side of the image. Wrap-around artifact, also known as aliasing, occurs along the phase-encoding direction. Fix: Aliasing can be reduced by increasing the FOV or by phase oversampling.

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Saturation bands can also be used to suppress the signal from excited tissues outside the FOV. Chemical shift artifactThere are two kinds of chemical shift artifact. This type always occurs in the frequency encoding direction. The second kind of chemical shift artifact occurs on gradient-echo images, where the water and fat protons move in and out of phase at fixed time points, depending on the strength of the magnet 1.

Fix : Chemical shift artifact first kind can be reduced by increasing the bandwidth per pixel. Use of fat suppression technique, longer TE and changing the frequency encoding direction also can reduce this artifact.


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Moire fringes or Zebra artifact Zebra artifact is a combination of wrap-around artifact and field inhomogeneity. It can also occur when a body coil is used instead of the breast coil. Fix: Selecting appropriate FOV to reduce aliasing or phase oversampling.

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Shimming of the magnet to reduce field inhomogeneities. It is essential to understand the importance of breast MRI and its indications for screening and diagnostic purposes which aids in timely diagnosis, management, and better patient outcome. Identifying the potential artifacts related to the technique and ways to overcome them will yield good quality images and avoid unnecessary interventions. Annual screening mammography is recommended to every woman starting at age MRI of the breast is an ideal complementary imaging study to mammography and ultrasound for the evaluation of breast disease.

The primary care provider and nurse practitioner must be aware of the screening recommendations and indications for breast MRI. To access free multiple choice questions on this topic, click here.

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This book is distributed under the terms of the Creative Commons Attribution 4. Turn recording back on. National Center for Biotechnology Information , U. StatPearls [Internet]. Search term. Indications The most common indication for obtaining breast MRI in clinical practice is to evaluate for breast cancer.

Screening of contralateral breast in conditions where there is an increased risk of bilaterality such as lobular carcinoma. Technique A 1. Technical factors: 1. Clinical Significance It is essential to understand the importance of breast MRI and its indications for screening and diagnostic purposes which aids in timely diagnosis, management, and better patient outcome.

Questions To access free multiple choice questions on this topic, click here. References 1. Screening for Breast Cancer. North Am. Magnetic Resonance Imaging of the Breast. Clin Obstet Gynecol. Clinical role of breast MRI now and going forward. Clin Radiol. Eur Radiol.


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Breast MRI ordering practices in a large health care network. Breast J.


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