Orbit modeling

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

Orbit modeling is the process of creating mathematical models to simulate motion of a massive body as it moves in orbit around another massive body due to gravity. Other forces such as gravitational attraction from tertiary bodies, air resistance, solar pressure, or thrust from a propulsion system are typically modeled as secondary effects. Directly modeling an orbit can push the limits of machine precision due to the need to model small perturbations to very large orbits. Because of this, perturbation methods are often used to model the orbit in order to achieve better accuracy.

Background

The study of orbital motion and mathematical modeling of orbits began with the first attempts to predict planetary motions in the sky, although in ancient times the causes remained a mystery. Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations, recognizing the complex difficulties of their calculation. Many of the great mathematicians since then have given attention to the various problems involved; throughout the 18th and 19th centuries there was demand for accurate tables of the position of the Moon and planets for purposes of navigation at sea.

The complex motions of orbits can be broken down. The hypothetical motion that the body follows under the gravitational effect of one other body only is typically a conic section, and can be readily modeled with the methods of geometry. This is called a two-body problem, or an unperturbed Keplerian orbit. The differences between the Keplerian orbit and the actual motion of the body are caused by perturbations. These perturbations are caused by forces other than the gravitational effect between the primary and secondary body and must be modeled to create an accurate orbit simulation. Most orbit modeling approaches model the two-body problem and then add models of these perturbing forces and simulate these models over time. Perturbing forces may include gravitational attraction from other bodies besides the primary, solar wind, drag, magnetic fields, and propulsive forces.

Analytical solutions (mathematical expressions to predict the positions and motions at any future time) for simple two-body and three-body problems exist; none have been found for the n-body problem except for certain special cases. Even the two-body problem becomes insoluble if one of the bodies is irregular in shape.

Due to the difficulty in finding analytic solutions to most problems of interest, computer modeling and simulation is typically used to analyze orbital motion. A wide variety of software is available to simulate orbits and trajectories of spacecraft.

Keplerian orbit model

Main article: Kepler orbit

In its simplest form, an orbit model can be created by assuming that only two bodies are involved, both behave as spherical point-masses, and that no other forces act on the bodies. For this case the model is simplified to a Kepler orbit.

Keplerian orbits follow conic sections. The mathematical model of the orbit which gives the distance between a central body and an orbiting body can be expressed as:

${\displaystyle r(\nu )=\frac{a(1-e^2)}{1+e\cos (\nu )}}$

Where:

${\displaystyle r}$ is the distance

${\displaystyle a}$ is the semi-major axis, which defines the size of the orbit

${\displaystyle e}$ is the eccentricity, which defines the shape of the orbit

${\displaystyle \nu }$ is the true anomaly, which is the angle between the current position of the orbiting object and the location in the orbit at it is closest to the central body (called the periapsis)

Alternately, the equation can be expressed as:

${\displaystyle r(\nu )=\frac{p}{1+e\cos (\nu )}}$

Where ${\displaystyle p}$ is called the semi-latus rectum of the curve. This form of the equation is particularly useful when dealing with parabolic trajectories, for which the semi-major axis is infinite.

An alternate approach uses Isaac Newton's law of universal gravitation as defined below:

${\displaystyle F=G\frac{m_1{m}_2}{r^2}}$

where:

${\displaystyle F}$ is the magnitude of the gravitational force between the two point masses

${\displaystyle G}$ is the gravitational constant

${\displaystyle m_1}$ is the mass of the first point mass

${\displaystyle m_2}$ is the mass of the second point mass

${\displaystyle r}$ is the distance between the two point masses

Making an additional assumption that the mass of the primary body is much greater than the mass of the secondary body and substituting in Newton's second law of motion, results in the following differential equation

${\displaystyle \ddot{\mathbf{r}}=\frac{G{m}_1}{r^2}\hat{\mathbf{r}}}$

Solving this differential equation results in Keplerian motion for an orbit. In practice, Keplerian orbits are typically only useful for first-order approximations, special cases, or as the base model for a perturbed orbit.

Orbit simulation methods

Main article: Perturbation (astronomy)

Orbit models are typically propagated in time and space using special perturbation methods. This is performed by first modeling the orbit as a Keplerian orbit. Then perturbations are added to the model to account for the various perturbations that affect the orbit. Special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small. Special perturbation methods are the basis of the most accurate machine-generated planetary ephemerides.

Cowell's method

Cowell's method. Forces from all perturbing bodies (black and gray) are summed to form the total force on body i (red), and this is numerically integrated starting from the initial position (the epoch of osculation).

Cowell's method is a special perturbation method; mathematically, for ${\displaystyle n}$ mutually interacting bodies, Newtonian forces on body ${\displaystyle i}$ from the other bodies ${\displaystyle j}$ are simply summed thus,

${\displaystyle {\ddot{\mathbf{r}}}_i=\sum _{\underset{j\ne i}{j=1}}^n\frac{G{m}_j({\mathbf{r}}_j-{\mathbf{r}}_i)}{r_{ij}^3}}$

where

${\displaystyle {\ddot{\mathbf{r}}}_i}$ is the acceleration vector of body ${\displaystyle i}$

${\displaystyle G}$ is the gravitational constant

${\displaystyle m_j}$ is the mass of body ${\displaystyle j}$

${\displaystyle {\mathbf{r}}_i}$ and ${\displaystyle {\mathbf{r}}_j}$ are the position vectors of objects ${\displaystyle i}$ and ${\displaystyle j}$

${\displaystyle r_{ij}}$ is the distance from object ${\displaystyle i}$ to object ${\displaystyle j}$

with all vectors being referred to the barycenter of the system. This equation is resolved into components in ${\displaystyle x}$, ${\displaystyle y}$, ${\displaystyle z}$ and these are integrated numerically to form the new velocity and position vectors as the simulation moves forward in time. The advantage of Cowell's method is ease of application and programming. A disadvantage is that when perturbations become large in magnitude (as when an object makes a close approach to another) the errors of the method also become large. Another disadvantage is that in systems with a dominant central body, such as the Sun, it is necessary to carry many significant digits in the arithmetic because of the large difference in the forces of the central body and the perturbing bodies.

Encke's method

Encke's method. Greatly exaggerated here, the small difference δr (blue) between the osculating, unperturbed orbit (black) and the perturbed orbit (red), is numerically integrated starting from the initial position (the epoch of osculation).

Encke's method begins with the osculating orbit as a reference and integrates numerically to solve for the variation from the reference as a function of time. Its advantages are that perturbations are generally small in magnitude, so the integration can proceed in larger steps (with resulting lesser errors), and the method is much less affected by extreme perturbations than Cowell's method. Its disadvantage is complexity; it cannot be used indefinitely without occasionally updating the osculating orbit and continuing from there, a process known as rectification.

Letting ${\displaystyle \mathit{\rho }}$ be the radius vector of the osculating orbit, ${\displaystyle \mathbf{r}}$ the radius vector of the perturbed orbit, and ${\displaystyle \delta \mathbf{r}}$ the variation from the osculating orbit,

${\displaystyle \delta \mathbf{r}=\mathbf{r}-\mathit{\rho },}$ and the equation of motion of ${\displaystyle \delta \mathbf{r}}$ is simply

(1)

${\displaystyle \ddot{\delta \mathbf{r}}=\ddot{\mathbf{r}}-\ddot{\mathit{\rho }}.}$

(2)

${\displaystyle \ddot{\mathbf{r}}}$ and ${\displaystyle \ddot{\mathit{\rho }}}$ are just the equations of motion of ${\displaystyle \mathbf{r}}$ and ${\displaystyle \mathit{\rho }}$,

${\displaystyle \ddot{\mathbf{r}}={\mathbf{a}}_{\text{per}}-\frac{\mu }{r^3}\mathbf{r}}$ for the perturbed orbit and

(3)

${\displaystyle \ddot{\mathit{\rho }}=-\frac{\mu }{{\rho }^3}\mathit{\rho }}$ for the unperturbed orbit,

(4)

where ${\displaystyle \mu =G(M+m)}$ is the gravitational parameter with ${\displaystyle M}$ and ${\displaystyle m}$ the masses of the central body and the perturbed body, ${\displaystyle {\mathbf{a}}_{\text{per}}}$ is the perturbing acceleration, and ${\displaystyle r}$ and ${\displaystyle \rho }$ are the magnitudes of ${\displaystyle \mathbf{r}}$ and ${\displaystyle \mathit{\rho }}$.

Substituting from equations (3) and (4) into equation (2),

${\displaystyle \ddot{\delta \mathbf{r}}={\mathbf{a}}_{\text{per}}+\mu \left(\frac{\mathit{\rho }}{{\rho }^3}-\frac{\mathbf{r}}{r^3}\right),}$

(5)

which, in theory, could be integrated twice to find ${\displaystyle \delta \mathbf{r}}$. Since the osculating orbit is easily calculated by two-body methods, ${\displaystyle \mathit{\rho }}$ and ${\displaystyle \delta \mathbf{r}}$ are accounted for and ${\displaystyle \mathbf{r}}$ can be solved. In practice, the quantity in the brackets, ${\displaystyle \frac{\mathit{\rho }}{{\rho }^3}-\frac{\mathbf{r}}{r^3}}$, is the difference of two nearly equal vectors, and further manipulation is necessary to avoid the need for extra significant digits.

Sperling–Burdet method

In 1991 Victor R. Bond and Michael F. Fraietta created an efficient and highly accurate method for solving the two-body perturbed problem. This method uses the linearized and regularized differential equations of motion derived by Hans Sperling and a perturbation theory based on these equations developed by C.A. Burdet in the year 1864. In 1973, Bond and Hanssen improved Burdet's set of differential equations by using the total energy of the perturbed system as a parameter instead of the two-body energy and by reducing the number of elements to 13. In 1989 Bond and Gottlieb embedded the Jacobian integral, which is a constant when the potential function is explicitly dependent upon time as well as position in the Newtonian equations. The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In this process, another element which is proportional to a component of the angular momentum is introduced. This brought the total number of elements back to 14. In 1991, Bond and Fraietta made further revisions by replacing the Laplace vector with another vector integral as well as another scalar integral which removed small secular terms which appeared in the differential equations for some of the elements.

The Sperling–Burdet method is executed in a 5 step process as follows:

Step 1: Initialization

Given an initial position, ${\displaystyle {\mathbf{r}}_0}$, an initial velocity, ${\displaystyle {\mathbf{v}}_0}$, and an initial time, ${\displaystyle t_0}$, the following variables are initialized:

${\displaystyle s=0}$

${\displaystyle r_0=({\mathbf{r}}_0\cdot {\mathbf{r}}_0{)}^{1/2}}$

${\displaystyle a=r_0}$

${\displaystyle b={\mathbf{r}}_0\cdot {\mathbf{v}}_0}$

${\displaystyle \tau =t_0}$

${\displaystyle \mathit{\alpha }={\mathbf{r}}_0}$

${\displaystyle \mathit{\beta }=a{\mathbf{v}}_0}$

Perturbations due to perturbing masses, defined as ${\displaystyle V_0}$ and ${\displaystyle [\frac{\mathrm{\partial }V}{\mathrm{\partial }\mathbf{r}}{]}_0}$, are evaluated

Perturbations due to other accelerations, defined as ${\displaystyle {\mathbf{P}}_0}$, are evaluated

${\displaystyle {\alpha }_J=\frac{2\mu }{r_0}-{\mathbf{v}}_0\cdot {\mathbf{v}}_0-2V_0}$

${\displaystyle \gamma =\mu -{\alpha }_{J}a}$

${\displaystyle \mathit{\delta }=-({\mathbf{v}}_0\cdot {\mathbf{v}}_0){\mathbf{r}}_0+({\mathbf{r}}_0\cdot {\mathbf{v}}_0){\mathbf{v}}_0+\frac{\mu }{r_0}{\mathbf{r}}_0-{\alpha }_J{\mathbf{r}}_0}$

${\displaystyle \sigma =0}$

Step 2: Transform elements to coordinates

${\displaystyle \mathbf{r}=\mathit{\alpha }+\mathit{\beta }s{c}_1+\mathit{\delta }{s}^2{c}_2}$

${\displaystyle {\mathbf{r}}^{\prime }=\mathit{\beta }{c}_0+\mathit{\delta }s{c}_1}$

${\displaystyle {\mathbf{x}}_3={\alpha }_J(\mathit{\alpha }-\mathbf{r})+\mathit{\delta }}$

${\displaystyle \gamma =\mu -{\alpha }_{J}a}$

${\displaystyle r=a+bs{c}_1+\gamma s^2{c}_2}$

${\displaystyle \mathbf{v}={\mathbf{r}}^{\prime }/r}$

${\displaystyle r^{\prime }=b{c}_0+\gamma s{c}_1}$

${\displaystyle t=\tau +as+b{s}^2{c}_2+\gamma s^3{c}_3}$

where ${\displaystyle c_0,c_1,c_2,c_3}$ are Stumpff functions

Step 3: Evaluate differential equations for the elements

${\displaystyle \mathbf{F}=\mathbf{P}-\frac{\mathrm{\partial }V}{\mathrm{\partial }\mathbf{r}}}$

${\displaystyle \mathbf{Q}=r^2\mathbf{F}+2\mathbf{r}(-V+\sigma )}$

${\displaystyle {\alpha }_J^{\prime }=2(-{\mathbf{r}}^{\prime }+r\mathit{\omega }\times \mathbf{r})\cdot \mathbf{P}}$

${\displaystyle \mu {\mathit{ϵ}}^{\prime }=2({\mathbf{r}}^{\prime }\cdot \mathbf{F})\mathbf{r}-(\mathbf{r}\cdot \mathbf{F}){\mathbf{r}}^{\prime }-(\mathbf{r}\cdot {\mathbf{r}}^{\prime })\mathbf{F}}$

${\displaystyle {\mathit{\alpha }}^{\prime }=-\mathbf{Q}s{c}_1-\mu {\mathit{ϵ}}^{\prime }{s}^2{c}_2-{\alpha }_J^{\prime }[\mathit{\alpha }{s}^2{c}_2+2\mathit{\beta }{s}^3{\overline{c}}_3+\frac{1}{2}\mathit{\delta }{s}^4{c}_2^2]}$

${\displaystyle {\mathit{\beta }}^{\prime }=\mathbf{Q}{c}_0+\mu {\mathit{ϵ}}^{\prime }s{c}_1+{\alpha }_J^{\prime }[\mathit{\alpha }s{c}_1+\mathit{\beta }{s}^2{\overline{c}}_2-\mathit{\delta }{s}^3(2{\overline{c}}_3-c_1{c}_2)]}$

${\displaystyle {\mathit{\delta }}^{\prime }=\mathbf{Q}{\alpha }_{J}s{c}_1-\mu {\mathit{ϵ}}^{\prime }{c}_0+{\alpha }_J^{\prime }[-\mathit{\alpha }{c}_0+2{\alpha }_J\mathit{\beta }{s}^3{\overline{c}}_3+\frac{1}{2}\mathit{\delta }{\alpha }_J{s}^4{c}_2^2]}$

${\displaystyle {\sigma }^{\prime }=r\mathit{\omega }\cdot \mathbf{r}\times \mathbf{F}}$

${\displaystyle a^{\prime }=-\frac{1}{r}\mathbf{r}\cdot \mathbf{Q}s{c}_1-{\alpha }_J^{\prime }[a{s}^2{c}_2+2b{s}^3{\overline{c}}_3+\frac{1}{2}\gamma s^4{c}_2^2]}$

${\displaystyle b^{\prime }=\frac{1}{r}\mathbf{r}\cdot \mathbf{Q}{c}_0+{\alpha }_J^{\prime }[as{c}_1+b{s}^2{\overline{c}}_2-\gamma s^3(2{\overline{c}}_3-c_1{c}_2)]}$

${\displaystyle {\gamma }^{\prime }=-\frac{1}{r}\mathbf{r}\cdot \mathbf{Q}{\alpha }_{J}s{c}_1+{\alpha }_J^{\prime }[-a{c}_0+2b{\alpha }_J{s}^3{\overline{c}}_3+\frac{1}{2}\gamma {\alpha }_J{s}^4{c}_2^2]}$

${\displaystyle {\tau }^{\prime }=\frac{1}{r}\mathbf{r}\cdot \mathbf{Q}{s}^2{c}_2+{\alpha }_J^{\prime }[a{s}^3{c}_3+\frac{1}{2}b{s}^4{c}_2^2-2\gamma s^5(c_5-4{\overline{c}}_5)]}$

Step 4: Integration

Here the differential equations are integrated over a period ${\displaystyle \mathrm{\Delta }s}$ to obtain the element value at ${\displaystyle s+\mathrm{\Delta }s}$

Step 5: Advance

Set ${\displaystyle s=s+\mathrm{\Delta }s}$ and return to step 2 until simulation stopping conditions are met.

Perturbations

Main articles: Orbit § Perturbations, and Perturbation (astronomy)

Perturbing forces cause orbits to become perturbed from a perfect Keplerian orbit. Models for each of these forces are created and executed during the orbit simulation so their effects on the orbit can be determined.

Non-spherical gravity

The Earth is not a perfect sphere nor is mass evenly distributed within the Earth. This results in the point-mass gravity model being inaccurate for orbits around the Earth, particularly Low Earth orbits. To account for variations in gravitational potential around the surface of the Earth, the gravitational field of the Earth is modeled with spherical harmonics which are expressed through the equation:

${\displaystyle \mathbf{f}=-\frac{\mu }{R^2}\hat{\mathbf{r}}+\sum _{n=2}^{\mathrm{\infty }}\sum _{m=0}^n{\mathbf{f}}_{n,m}}$

where

${\displaystyle \mu }$ is the gravitational parameter defined as the product of G, the universal gravitational constant, and the mass of the primary body.

${\displaystyle \hat{\mathbf{r}}}$ is the unit vector defining the distance between the primary and secondary bodies, with ${\displaystyle R}$ being the magnitude of the distance.

${\displaystyle {\mathbf{f}}_{n,m}}$ represents the contribution to ${\displaystyle \mathbf{f}}$ of the spherical harmonic of degree n and order m, which is defined as:

${\displaystyle \begin{array}{rl}{\mathbf{f}}_{n,m}& =\frac{\mu R_O^2}{R^{n+m+1}}\left(\frac{C_{n,m}{\mathcal{C}}_m+S_{n,m}{\mathcal{S}}_m}{R}(A_{n,m+1}{\hat{\mathbf{e}}}_3-\left(s_{\lambda }{A}_{n,m+1}+(n+m+1)A_{n,m}\right)\hat{\mathbf{r}}\right)\\ & +m{A}_{n,m}((C_{n,m}{\mathcal{C}}_{m-1}+S_{n,m}{\mathcal{S}}_{m-1}){\hat{\mathbf{e}}}_1+(S_{n,m}{\mathcal{C}}_{m-1}-C_{n,m}{\mathcal{S}}_{m-1}){\hat{\mathbf{e}}}_2))\end{array}}$

where:

${\displaystyle R_O}$ is the mean equatorial radius of the primary body.

${\displaystyle R}$ is the magnitude of the position vector from the center of the primary body to the center of the secondary body.

${\displaystyle C_{n,m}}$ and ${\displaystyle S_{n,m}}$ are gravitational coefficients of degree n and order m. These are typically found through gravimetry measurements.

The unit vectors ${\displaystyle {\hat{\mathbf{e}}}_1,{\hat{\mathbf{e}}}_2,{\hat{\mathbf{e}}}_3}$ define a coordinate system fixed on the primary body. For the Earth, ${\displaystyle {\hat{\mathbf{e}}}_1}$ lies in the equatorial plane parallel to a line intersecting Earth's geometric center and the Greenwich meridian,${\displaystyle {\hat{\mathbf{e}}}_3}$ points in the direction of the North polar axis, and ${\displaystyle {\hat{\mathbf{e}}}_2={\hat{\mathbf{e}}}_3\times {\hat{\mathbf{e}}}_1}$

${\displaystyle A_{n,m}}$ is referred to as a derived Legendre polynomial of degree n and order m. They are solved through the recurrence relation: ${\displaystyle A_{n,m}(u)=\frac{1}{n-m}((2n-1)u{A}_{n-1,m}(u)-(n+m-1)A_{n-2,m}(u))}$

${\displaystyle s_{\lambda }}$ is sine of the geographic latitude of the secondary body, which is ${\displaystyle \hat{\mathbf{r}}\cdot {\hat{\mathbf{e}}}_3}$.

${\displaystyle {\mathcal{C}}_m,{\mathcal{S}}_m}$ are defined with the following recurrence relation and initial conditions:${\displaystyle {\mathcal{C}}_m={\mathcal{C}}_1{\mathcal{C}}_{m-1}-{\mathcal{S}}_1{\mathcal{S}}_{m-1},{\mathcal{S}}_m={\mathcal{S}}_1{\mathcal{C}}_{m-1}+{\mathcal{C}}_1{\mathcal{S}}_{m-1},{\mathcal{S}}_0=0,{\mathcal{S}}_1=\mathbf{R}\cdot {\hat{\mathbf{e}}}_2,{\mathcal{C}}_0=1,{\mathcal{C}}_1=\mathbf{R}\cdot {\hat{\mathbf{e}}}_1}$

When modeling perturbations of an orbit around a primary body only the sum of the ${\displaystyle {\mathbf{f}}_{n,m}}$ terms need to be included in the perturbation since the point-mass gravity model is accounted for in the ${\displaystyle -\frac{\mu }{R^2}\hat{\mathbf{r}}}$ term

Third-body perturbations

Gravitational forces from third bodies can cause perturbations to an orbit. For example, the Sun and Moon cause perturbations to Orbits around the Earth. These forces are modeled in the same way that gravity is modeled for the primary body by means of direct gravitational N-body simulations. Typically, only a spherical point-mass gravity model is used for modeling effects from these third bodies. Some special cases of third-body perturbations have approximate analytic solutions. For example, perturbations for the right ascension of the ascending node and argument of perigee for a circular Earth orbit are:

${\displaystyle {\dot{\mathrm{\Omega }}}_{\mathrm{M}\mathrm{O}\mathrm{O}\mathrm{N}}=-0.00338(\cos (i))/n}$

${\displaystyle {\dot{\omega }}_{\mathrm{M}\mathrm{O}\mathrm{O}\mathrm{N}}=-0.00169(4-5{\sin }^2(i))/n}$

where:

${\displaystyle \dot{\mathrm{\Omega }}}$ is the change to the right ascension of the ascending node in degrees per day.

${\displaystyle \dot{\omega }}$ is the change to the argument of perigee in degrees per day.

${\displaystyle i}$ is the orbital inclination.

${\displaystyle n}$ is the number of orbital revolutions per day.

Solar radiation

Main article: Radiation pressure

Solar radiation pressure causes perturbations to orbits. The magnitude of acceleration it imparts to a spacecraft in Earth orbit is modeled using the equation below:

${\displaystyle a_R\approx -4.5\times {10}^{-6}(1+r)A/m}$

where:

${\displaystyle a_R}$ is the magnitude of acceleration in meters per second-squared.

${\displaystyle A}$ is the cross-sectional area exposed to the Sun in meters-squared.

${\displaystyle m}$ is the spacecraft mass in kilograms.

${\displaystyle r}$ is the reflection factor which depends on material properties. ${\displaystyle r=0}$ for absorption, ${\displaystyle r=1}$ for specular reflection, and ${\displaystyle r\approx 0.4}$ for diffuse reflection.

For orbits around the Earth, solar radiation pressure becomes a stronger force than drag above 800 km altitude.

Propulsion

Main article: Spacecraft propulsion

There are many different types of spacecraft propulsion. Rocket engines are one of the most widely used. The force of a rocket engine is modeled by the equation:

${\displaystyle F_n=\dot{m}{v}_{\text{e}}=\dot{m}{v}_{\text{e-act}}+A_{\text{e}}(p_{\text{e}}-p_{\text{amb}})}$

where:
${\displaystyle \dot{m}}$	=  exhaust gas mass flow
${\displaystyle v_{\text{e}}}$	=  effective exhaust velocity
${\displaystyle v_{\text{e-act}}}$	=  actual jet velocity at nozzle exit plane
${\displaystyle A_{\text{e}}}$	=  flow area at nozzle exit plane (or the plane where the jet leaves the nozzle if separated flow)
${\displaystyle p_{\text{e}}}$	=  static pressure at nozzle exit plane
${\displaystyle p_{\text{amb}}}$	=  ambient (or atmospheric) pressure

Another possible method is a solar sail. Solar sails use radiation pressure in a way to achieve a desired propulsive force. The perturbation model due to the solar wind can be used as a model of propulsive force from a solar sail.

Drag

Main article: Drag (physics)

The primary non-gravitational force acting on satellites in low Earth orbit is atmospheric drag. Drag will act in opposition to the direction of velocity and remove energy from an orbit. The force due to drag is modeled by the following equation:

${\displaystyle F_D=\frac{1}{2}\rho v^2{C}_{d}A,}$

where

${\displaystyle {\mathbf{F}}_D}$ is the force of drag,

${\displaystyle \rho }$ is the density of the fluid,

${\displaystyle v}$ is the velocity of the object relative to the fluid,

${\displaystyle C_d}$ is the drag coefficient (a dimensionless parameter, e.g. 2 to 4 for most satellites)

${\displaystyle A}$ is the reference area.

Orbits with an altitude below 120 km generally have such high drag that the orbits decay too rapidly to give a satellite a sufficient lifetime to accomplish any practical mission. On the other hand, orbits with an altitude above 600 km have relatively small drag so that the orbit decays slow enough that it has no real impact on the satellite over its useful life. Density of air can vary significantly in the thermosphere where most low Earth orbiting satellites reside. The variation is primarily due to solar activity, and thus solar activity can greatly influence the force of drag on a spacecraft and complicate long-term orbit simulation.

Magnetic fields

Magnetic fields can play a significant role as a source of orbit perturbation as was seen in the Long Duration Exposure Facility. Like gravity, the magnetic field of the Earth can be expressed through spherical harmonics as shown below:

${\displaystyle \mathbf{B}=\sum _{n=1}^{\mathrm{\infty }}\sum _{m=0}^n{\mathbf{B}}_{n,m}}$

where

${\displaystyle \mathbf{B}}$ is the magnetic field vector at a point above the Earth's surface.

${\displaystyle {\mathbf{B}}_{n,m}}$ represents the contribution to ${\displaystyle \mathbf{B}}$ of the spherical harmonic of degree n and order m, defined as:

${\displaystyle \begin{array}{rl}{\mathbf{B}}_{n,m}=& \frac{K_{n,m}{a}^{n+2}}{R^{n+m+1}}\left[\frac{g_{n,m}{\mathcal{C}}_m+h_{n,m}{\mathcal{S}}_m}{R}((s_{\lambda }{A}_{n,m+1}+(n+m+1)A_{n,m})\hat{\mathbf{r}})-A_{n,m+1}{\hat{\mathbf{e}}}_3\right]\\ & -m{A}_{n,m}((g_{n,m}{\mathcal{C}}_{m-1}+h_{n,m}{\mathcal{S}}_{m-1}){\hat{\mathbf{e}}}_1+(h_{n,m}{\mathcal{C}}_{m-1}-g_{n,m}{\mathcal{S}}_{m-1}){\hat{\mathbf{e}}}_2))\end{array}}$

where:

${\displaystyle a}$ is the mean equatorial radius of the primary body.

${\displaystyle R}$ is the magnitude of the position vector from the center of the primary body to the center of the secondary body.

${\displaystyle \hat{\mathbf{r}}}$ is a unit vector in the direction of the secondary body with its origin at the center of the primary body.

${\displaystyle g_{n,m}}$ and ${\displaystyle h_{n,m}}$ are Gauss coefficients of degree n and order m. These are typically found through magnetic field measurements.

The unit vectors ${\displaystyle {\hat{\mathbf{e}}}_1,{\hat{\mathbf{e}}}_2,{\hat{\mathbf{e}}}_3}$ define a coordinate system fixed on the primary body. For the Earth, ${\displaystyle {\hat{\mathbf{e}}}_1}$ lies in the equatorial plane parallel to a line intersecting Earth's geometric center and the Greenwich meridian,${\displaystyle {\hat{\mathbf{e}}}_3}$ points in the direction of the North polar axis, and ${\displaystyle {\hat{\mathbf{e}}}_2={\hat{\mathbf{e}}}_3\times {\hat{\mathbf{e}}}_1}$

${\displaystyle A_{n,m}}$ is referred to as a derived Legendre polynomial of degree n and order m. They are solved through the recurrence relation: ${\displaystyle A_{n,m}(u)=\frac{1}{n-m}((2n-1)u{A}_{n-1,m}(u)-(n+m-1)A_{n-2,m}(u))}$

${\displaystyle K_{n,m}}$ is defined as: 1 if m = 0, ${\displaystyle [\frac{n-m}{n+m}{]}^{0.5}{K}_{n-1,m}}$ for ${\displaystyle n\ge (m+1)}$ and ${\displaystyle m=[1\dots \mathrm{\infty }]}$ , and ${\displaystyle [(n+m)(n-m+1){]}^{-0.5}{K}_{n,m-1}}$ for ${\displaystyle n\ge m}$ and ${\displaystyle m=[2\dots \mathrm{\infty }]}$

${\displaystyle s_{\lambda }}$ is sine of the geographic latitude of the secondary body, which is ${\displaystyle \hat{\mathbf{r}}\cdot {\hat{\mathbf{e}}}_3}$.

${\displaystyle {\mathcal{C}}_m,{\mathcal{S}}_m}$ are defined with the following recurrence relation and initial conditions:${\displaystyle {\mathcal{C}}_m={\mathcal{C}}_1{\mathcal{C}}_{m-1}-{\mathcal{S}}_1{\mathcal{S}}_{m-1},{\mathcal{S}}_m={\mathcal{S}}_1{\mathcal{C}}_{m-1}+{\mathcal{C}}_1{\mathcal{S}}_{m-1},{\mathcal{S}}_0=0,{\mathcal{S}}_1=\mathbf{R}\cdot {\hat{\mathbf{e}}}_2,{\mathcal{C}}_0=1,{\mathcal{C}}_1=\mathbf{R}\cdot {\hat{\mathbf{e}}}_1}$

Interstellar object

From Wikipedia, the free encyclopedia

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

2I/Borisov comet, the second confirmed interstellar object, photographed in late-2019 beside a distant galaxy

An interstellar object is an astronomical object (such as an asteroid, a comet, or a rogue planet, but not a star) in interstellar space that is not gravitationally bound to a star. This term can also be applied to an object that is on an interstellar trajectory but is temporarily passing close to a star, such as certain asteroids and comets (including exocomets). In the latter case, the object may be called an interstellar interloper.

The first interstellar objects discovered were rogue planets, planets ejected from their original stellar system (e.g., OTS 44 or Cha 110913−773444), though they are difficult to distinguish from sub-brown dwarfs, planet-mass objects that formed in interstellar space as stars do.

The first interstellar object which was discovered traveling through the Solar System was 1I/ʻOumuamua in 2017. The second was 2I/Borisov in 2019. They both possess significant hyperbolic excess velocity, indicating they did not originate in the Solar System. The discovery of ʻOumuamua inspired the identification of CNEOS 2014-01-08, also known as the Manus Island fireball, as an interstellar object that impacted the Earth. This was confirmed by the U.S. Space Command in 2022 based on the object's velocity relative to the Sun. In May 2023, astronomers reported the possible capture of other interstellar objects in Near Earth Orbit (NEO) over the years.

Nomenclature

With the first discovery of an interstellar object in the Solar System, the IAU has proposed a new series of small-body designations for interstellar objects, the I numbers, similar to the comet numbering system. The Minor Planet Center will assign the numbers. Provisional designations for interstellar objects will be handled using the C/ or A/ prefix (comet or asteroid), as appropriate.

Overview

Interstellar velocity inbound (${\displaystyle v_{\mathrm{\infty }}}$)

Object	Velocity
C/2012 S1 (ISON) (weakly hyperbolic Oort Cloud comet)	0.2 km/s 0.04 au/yr
Voyager 1 (For comparison)	16.9 km/s 3.57 au/yr
1I/2017 U1 (ʻOumuamua)	26.33 km/s 5.55 au/yr
2I/Borisov	32.1 km/s 6.77 au/yr
2014Jan08 bolide (in peer review)	43.8 km/s 9.24 au/yr

Astronomers estimate that several interstellar objects of extrasolar origin (like ʻOumuamua) pass inside the orbit of Earth each year, and that 10,000 are passing inside the orbit of Neptune on any given day.

Interstellar comets occasionally pass through the inner Solar System and approach with random velocities, mostly from the direction of the constellation Hercules because the Solar System is moving in that direction, called the solar apex. Until the discovery of 'Oumuamua, the fact that no comet with a speed greater than the Sun's escape velocity had been observed was used to place upper limits to their density in interstellar space. A paper by Torbett indicated that the density was no more than 10¹³ (10 trillion) comets per cubic parsec. Other analyses, of data from LINEAR, set the upper limit at 4.5×10⁻⁴/AU³, or 10¹² (1 trillion) comets per cubic parsec. A more recent estimate by David C. Jewitt and colleagues, following the detection of 'Oumuamua, predicts that "The steady-state population of similar, ~100 m scale interstellar objects inside the orbit of Neptune is ~1×10⁴, each with a residence time of ~10 years."

Current models of Oort cloud formation predict that more comets are ejected into interstellar space than are retained in the Oort cloud, with estimates varying from 3 to 100 times as many. Other simulations suggest that 90–99% of comets are ejected. There is no reason to believe comets formed in other star systems would not be similarly scattered. Amir Siraj and Avi Loeb demonstrated that the Oort Cloud could have been formed from ejected planetesimals from other stars in the Sun's birth cluster.

It is possible for objects orbiting a star to be ejected due to interaction with a third massive body, thereby becoming interstellar objects. Such a process was initiated in the early 1980s when C/1980 E1, initially gravitationally bound to the Sun, passed near Jupiter and was accelerated sufficiently to reach escape velocity from the Solar System. This changed its orbit from elliptical to hyperbolic and made it the most eccentric known object at the time, with an eccentricity of 1.057. It is heading for interstellar space.

Comet Machholz 1 (96P/Machholz) as viewed by STEREO-A (April 2007)

Due to present observational difficulties, an interstellar object can usually only be detected if it passes through the Solar System, where it can be distinguished by its strongly hyperbolic trajectory and hyperbolic excess velocity of more than a few km/s, proving that it is not gravitationally bound to the Sun. In contrast, gravitationally bound objects follow elliptic orbits around the Sun. (There are a few objects whose orbits are so close to parabolic that their gravitationally bound status is unclear.)

An interstellar comet can probably, on rare occasions, be captured into a heliocentric orbit while passing through the Solar System. Computer simulations show that Jupiter is the only planet massive enough to capture one, and that this can be expected to occur once every sixty million years. Comets Machholz 1 and Hyakutake C/1996 B2 are possible examples of such comets. They have atypical chemical makeups for comets in the Solar System.

Amir Siraj and Avi Loeb proposed a search for ʻOumuamua-like objects which are trapped in the Solar System as a result of losing orbital energy through a close encounter with Jupiter. They identified centaur candidates, such as 2017 SV₁₃ and 2018 TL₆, as captured interstellar objects that could be visited by dedicated missions. The authors pointed out that future sky surveys, such as Vera C. Rubin Observatory, should find many candidates.

Recent research suggests that asteroid 514107 Kaʻepaokaʻawela may be a former interstellar object, captured some 4.5 billion years ago, as evidenced by its co-orbital motion with Jupiter and its retrograde orbit around the Sun. In addition, comet C/2018 V1 (Machholz-Fujikawa-Iwamoto) has a significant probability (72.6%) of having an extrasolar provenance although an origin in the Oort cloud cannot be excluded. Harvard astronomers suggest that matter—and potentially dormant spores—can be exchanged across vast distances. The detection of ʻOumuamua crossing the inner Solar System confirms the possibility of a material link with exoplanetary systems.

Interstellar visitors in the Solar System cover the whole range of sizes – from kilometer large objects down to submicron particles. Also, interstellar dust and meteoroids carry with them valuable information from their parent systems. Detection of these objects along the continuum of sizes is, however, not evident.

Interstellar visitors in the Solar System cover the whole range of sizes – from kilometer large objects down to submicron particles. Also, interstellar dust and meteoroids carry with them valuable information from their parent systems. Detection of these objects along the continuum of sizes is, however, not evident (see Figure). The smallest interstellar dust particles are filtered out of the solar system by electromagnetic forces, while the largest ones are too sparse to obtain good statistics from in situ spacecraft detectors. Discrimination between interstellar and interplanetary populations can be a challenge for intermediate (0.1–1 micrometer) sizes. These can vary widely in velocity and directionality. The identification of interstellar meteoroids, observed in the Earth's atmosphere as meteors, is highly challenging and requires high accuracy measurements and appropriate error examinations. Otherwise, measurement errors can transfer near-parabolic orbits over the parabolic limit and create an artificial population of hyperbolic particles, often interpreted as of interstellar origin. Large interstellar visitors like asteroids and comets were detected the first time in the solar system in 2017 (1I/'Oumuamua) and 2019 (2I/Borisov) and are expected to be detected more frequently with new telescopes, e.g. the Vera Rubin Observatory. Amir Siraj and Avi Loeb have predicted that the Vera C. Rubin Observatory will be capable of detecting an anisotropy in the distribution of interstellar objects due to the Sun's motion relative to the Local Standard of Rest and identify the characteristic ejection speed of interstellar objects from their parent stars.

In May 2023, astronomers reported the possible capture of other interstellar objects in Near Earth Orbit (NEO) over the years.

In July 2023, Harvard astronomer Avi Loeb reported the possibility of finding interstellar material.

Confirmed objects

1I/2017 U1 (ʻOumuamua)

Main article: ʻOumuamua

Path of the hyperbolic, extrasolar object ʻOumuamua, the first confirmed interstellar object, discovered in 2017

A dim object was discovered on October 19, 2017, by the Pan-STARRS telescope, at an apparent magnitude of 20. The observations showed that it follows a strongly hyperbolic trajectory around the Sun at a speed greater than the solar escape velocity, in turn meaning that it is not gravitationally bound to the Solar System and likely to be an interstellar object. It was initially named C/2017 U1 because it was assumed to be a comet, and was renamed to A/2017 U1 after no cometary activity was found on October 25. After its interstellar nature was confirmed, it was renamed to 1I/ʻOumuamua – "1" because it is the first such object to be discovered, "I" for interstellar, and "‘Oumuamua" is a Hawaiian word meaning "a messenger from afar arriving first".

The lack of cometary activity from ʻOumuamua suggests an origin from the inner regions of whatever stellar system it came from, losing all surface volatiles within the frost line, much like the rocky asteroids, extinct comets and damocloids we know from the Solar System. This is only a suggestion, as ʻOumuamua might very well have lost all surface volatiles to eons of cosmic radiation exposure in interstellar space, developing a thick crust layer after it was expelled from its parent system.

ʻOumuamua has an eccentricity of 1.199, which was the highest eccentricity ever observed for any object in the Solar System by a wide margin prior to the discovery of comet 2I/Borisov in August 2019.

In September 2018, astronomers described several possible home star systems from which ʻOumuamua may have begun its interstellar journey.

2I/Borisov

Main article: 2I/Borisov

The object was discovered on 30 August 2019 at MARGO, Nauchnyy, Crimea by Gennadiy Borisov using his custom-built 0.65-meter telescope. On 13 September 2019, the Gran Telescopio Canarias obtained a low-resolution visible spectrum of 2I/Borisov that revealed that this object has a surface composition not too different from that found in typical Oort Cloud comets. The IAU Working Group for Small Body Nomenclature kept the name Borisov, giving the comet the interstellar designation of 2I/Borisov. On 12 March 2020, astronomers reported observational evidence of "ongoing nucleus fragmentation" from Borisov.

Candidates

Comet Hyakutake (C/1996 B2) might be a former interstellar object captured by the Solar System

In 2007, Afanasiev et al. reported the likely detection of a multi-centimeter intergalactic meteor hitting the atmosphere above the Special Astrophysical Observatory of the Russian Academy of Sciences on July 28, 2006.

In November 2018, Harvard astronomers Amir Siraj and Avi Loeb reported that there should be hundreds of 'Oumuamua-size interstellar objects in the Solar System, based on calculated orbital characteristics, and presented several centaur candidates such as 2017 SV₁₃ and 2018 TL₆. These are all orbiting the Sun, but may have been captured in the distant past.

Amir Siraj and Avi Loeb have proposed methods for increasing the discovery rate of interstellar objects that include stellar occultations, optical signatures from impacts with the moon or the Earth's atmosphere, and radio flares from collisions with neutron stars.

2014 interstellar meteor

Main article: CNEOS 2014-01-08

CNEOS 2014-01-08 (also known as Interstellar meteor 1; IM1), a meteor with a mass of 0.46 tons and width of 0.45 m (1.5 ft), burned up in the Earth's atmosphere on January 8, 2014. A 2019 preprint suggested this meteor had been of interstellar origin. It had a heliocentric speed of 60 km/s (37 mi/s) and an asymptotic speed of 42.1 ± 5.5 km/s (26.2 ± 3.4 mi/s), and it exploded at 17:05:34 UTC near Papua New Guinea at an altitude of 18.7 km (61,000 ft). After declassifying the data in April 2022, the U.S. Space Command, based on information collected from its planetary defense sensors, confirmed the velocity of the potential interstellar meteor. In 2023, The Galileo Project completed an expedition to retrieve small fragments of the apparently peculiar meteor. Claims about their findings have been doubted by their peers according to a report in The New York Times. Further related studies were reported on 1 September 2023.

Other astronomers doubt the interstellar origin because the meteoroid catalog used does not report uncertainties on the incoming velocity. The validity of any single data point (especially for smaller meteoroids) remains questionable. In November 2022, a paper was published, claiming the anomalous properties (including its high strength and strongly hyperbolic trajectory) of CNEOS 2014-01-08 are better described as measurement error rather than genuine parameters. Successful retrieval of any meteoroid fragments is highly unlikely. Common micrometeorites would be indistinguishable from one another.

2017 interstellar meteor

CNEOS 2017-03-09 (aka Interstellar meteor 2; IM2), a meteor with a mass of roughly 6.3 tons, burned up in the Earth's atmosphere on March 9, 2017. Similar to IM1, it has a high mechanical strength.

In September 2022, astronomers Amir Siraj and Avi Loeb reported the discovery of a candidate interstellar meteor, CNEOS 2017-03-09 (aka Interstellar meteor 2; IM2), that impacted Earth in 2017 and is considered, based in part on the high material strength of the meteor, to be a possible interstellar object.

Hypothetical missions

With current space technology, close visits and orbital missions are challenging due to their high speeds, though not impossible.

The Initiative for Interstellar Studies (i4is) launched in 2017 Project Lyra to assess the feasibility of a mission to ʻOumuamua. Several options for sending a spacecraft to ʻOumuamua within a time-frame of 5 to 25 years were suggested. One option is using first a Jupiter flyby followed by a close solar flyby at 3 solar radii (2.1×10⁶ km; 1.3×10⁶ mi) in order to take advantage of the Oberth effect. Different mission durations and their velocity requirements were explored with respect to the launch date, assuming direct impulsive transfer to the intercept trajectory.

The Comet Interceptor spacecraft by ESA and JAXA, planned to launch in 2029, will be positioned at the Sun-Earth L₂ point to wait for a suitable long-period comet to intercept and flyby for study. In case that no suitable comet is identified during its 3-year wait, the spacecraft could be tasked to intercept an interstellar object in short notice, if reachable.

Sensory processing

From Wikipedia, the free encyclopedia

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

Sensory processing is the process that organizes and distinguishes sensation (sensory information) from one's own body and the environment, thus making it possible to use the body effectively within the environment. Specifically, it deals with how the brain processes multiple sensory modality inputs, such as proprioception, vision, auditory system, tactile, olfactory, vestibular system, interoception, and taste into usable functional outputs.

It has been believed for some time that inputs from different sensory organs are processed in different areas in the brain. The communication within and among these specialized areas of the brain is known as functional integration. Newer research has shown that these different regions of the brain may not be solely responsible for only one sensory modality, but could use multiple inputs to perceive what the body senses about its environment. Multisensory integration is necessary for almost every activity that we perform because the combination of multiple sensory inputs is essential for us to comprehend our surroundings.

Overview

It has been believed for some time that inputs from different sensory organs are processed in different areas in the brain, relating to systems neuroscience. Using functional neuroimaging, it can be seen that sensory-specific cortices are activated by different inputs. For example, regions in the occipital cortex are tied to vision and those on the superior temporal gyrus are recipients of auditory inputs. There exist studies suggesting deeper multisensory convergences than those at the sensory-specific cortices, which were listed earlier. This convergence of multiple sensory modalities is known as multisensory integration.

Sensory processing deals with how the brain processes sensory input from multiple sensory modalities. These include the five classic senses of vision (sight), audition (hearing), tactile stimulation (touch), olfaction (smell), and gustation (taste). Other sensory modalities exist, for example the vestibular sense (balance and the sense of movement) and proprioception (the sense of knowing one's position in space) Along with Time (The sense of knowing where one is in time or activities). It is important that the information of these different sensory modalities must be relatable. The sensory inputs themselves are in different electrical signals, and in different contexts. Through sensory processing, the brain can relate all sensory inputs into a coherent percept, upon which our interaction with the environment is ultimately based.

Basic structures involved

The different senses were always thought to be controlled by separate lobes of the brain, called projection areas. The lobes of the brain are the classifications that divide the brain both anatomically and functionally. These lobes are the Frontal lobe, responsible for conscious thought, Parietal lobe, responsible for visuospatial processing, the Occipital lobe, responsible for the sense of sight, and the temporal lobe, responsible for the senses of smell and sound. From the earliest times of neurology, it has been thought that these lobes are solely responsible for their one sensory modality input. However, newer research has shown that that may not entirely be the case.

Problems

Main article: Sensory processing disorder

See also: Sensory processing sensitivity

Sometimes there can be a problem with the encoding of the sensory information. This disorder is known as Sensory processing disorder (SPD). This disorder can be further classified into three main types.

• Sensory modulation disorder, in which patients seek sensory stimulation due to an over or under response to sensory stimuli.
• Sensory based motor disorder. Patients have incorrect processing of motor information that leads to poor motor skills.
• Sensory processing disorder or sensory discrimination disorder, which is characterized by postural control problems, lack of attentiveness, and disorganization.

There are several therapies used to treat SPD. Anna Jean Ayres claimed that a child needs a healthy "sensory diet," which is all of the activities that children engage in, that gives them the necessary sensory inputs that they need to get their brain into improving sensory processing.

History

In the 1930s, Wilder Penfield was conducting a very bizarre operation at the Montreal Neurological Institute. Penfield "pioneered the incorporation of neurophysiological principles in the practice of neurosurgery. Penfield was interested in determining a solution to solve the epileptic seizure problems that his patients were having. He used an electrode to stimulate different regions of the brain's cortex, and would ask his still conscious patient what he or she felt. This process led to the publication of his book, The Cerebral Cortex of Man. The "mapping" of the sensations his patients felt led Penfield to chart out the sensations that were triggered by stimulating different cortical regions. Mrs. H. P. Cantlie was the artist Penfield hired to illustrate his findings. The result was the conception of the first sensory Homonculus.

The Homonculus is a visual representation of the intensity of sensations derived from different parts of the body. Wilder Penfield and his colleague Herbert Jasper developed the Montreal procedure using an electrode to stimulate different parts of the brain to determine which parts were the cause of the epilepsy. This part could then be surgically removed or altered in order to regain optimal brain performance. While performing these tests, they discovered that the functional maps of the sensory and motor cortices were similar in all patients. Because of their novelty at the time, these Homonculi were hailed as the "E=mc² of Neuroscience".

Current research

There are still no definitive answers to the questions regarding the relationship between functional and structural asymmetries in the brain. There are a number of asymmetries in the human brain including how language is processed mainly in the left hemisphere of the brain. There have been some cases, however, in which individuals have comparable language skills to someone who uses his left hemisphere to process language, yet they mainly use their right or both hemispheres. These cases pose the possibility that function may not follow structure in some cognitive tasks. Current research in the fields of sensory processing and multisensory integration is aiming to hopefully unlock the mysteries behind the concept of brain lateralization.

Research on sensory processing has much to offer towards understanding the function of the brain as a whole. The primary task of multisensory integration is to figure out and sort out the vast quantities of sensory information in the body through multiple sensory modalities. These modalities not only are not independent, but they are also quite complementary. Where one sensory modality may give information on one part of a situation, another modality can pick up other necessary information. Bringing this information together facilitates the better understanding of the physical world around us.

It may seem redundant that we are being provided with multiple sensory inputs about the same object, but that is not necessarily the case. This so-called "redundant" information is in fact verification that what we are experiencing is in fact happening. Perceptions of the world are based on models that we build of the world. Sensory information informs these models, but this information can also confuse the models. Sensory illusions occur when these models do not match up. For example, where our visual system may fool us in one case, our auditory system can bring us back to a ground reality. This prevents sensory misrepresentations, because through the combination of multiple sensory modalities, the model that we create is much more robust and gives a better assessment of the situation. Thinking about it logically, it is far easier to fool one sense than it is to simultaneously fool two or more senses.

Examples

One of the earliest sensations is the olfactory sensation. Evolutionary, gustation and olfaction developed together. This multisensory integration was necessary for early humans in order to ensure that they were receiving proper nutrition from their food, and also to make sure that they were not consuming poisonous materials. There are several other sensory integrations that developed early on in the human evolutionary time line. The integration between vision and audition was necessary for spatial mapping. Integration between vision and tactile sensations developed along with our finer motor skills including better hand-eye coordination. While humans developed into bipedal organisms, balance became exponentially more essential to survival. The multisensory integration between visual inputs, vestibular (balance) inputs, and proprioception inputs played an important role in our development into upright walkers.

Audiovisual system

Perhaps one of the most studied sensory integrations is the relationship between vision and audition. These two senses perceive the same objects in the world in different ways, and by combining the two, they help us understand this information better. Vision dominates our perception of the world around us. This is because visual spatial information is one of the most reliable sensory modalities. Visual stimuli are recorded directly onto the retina, and there are few, if any, external distortions that provide incorrect information to the brain about the true location of an object. Other spatial information is not as reliable as visual spatial information. For example, consider auditory spatial input. The location of an object can sometimes be determined solely on its sound, but the sensory input can easily be modified or altered, thus giving a less reliable spatial representation of the object. Auditory information therefore is not spatially represented unlike visual stimuli. But once one has the spatial mapping from the visual information, multisensory integration helps bring the information from both the visual and auditory stimuli together to make a more robust mapping.

There have been studies done that show that a dynamic neural mechanism exists for matching the auditory and visual inputs from an event that stimulates multiple senses. One example of this that has been observed is how the brain compensates for target distance. When you are speaking with someone or watching something happen, auditory and visual signals are not being processed concurrently, but they are perceived as being simultaneous. This kind of multisensory integration can lead to slight misperceptions in the visual-auditory system in the form of the ventriloquism effect. An example of the ventriloquism effect is when a person on the television appears to have his voice coming from his mouth, rather than the television's speakers. This occurs because of a pre-existing spatial representation within the brain which is programmed to think that voices come from another human's mouth. This then makes it so the visual response to the audio input is spatially misrepresented, and therefore misaligned.

Sensorimotor system

Hand eye coordination is one example of sensory integration. In this case, we require a tight integration of what we visually perceive about an object, and what we tactilely perceive about that same object. If these two senses were not combined within the brain, then one would have less ability to manipulate an object. Eye–hand coordination is the tactile sensation in the context of the visual system. The visual system is very static, in that it does not move around much, but the hands and other parts used in tactile sensory collection can freely move around. This movement of the hands must be included in the mapping of both the tactile and visual sensations, otherwise one would not be able to comprehend where they were moving their hands, and what they were touching and looking at. An example of this happening is looking at an infant. The infant picks up objects and puts them in his mouth, or touches them to his feet or face. All of these actions are culminating to the formation of spatial maps in the brain and the realization that "Hey, that thing that's moving this object is actually a part of me." Seeing the same thing that they are feeling is a major step in the mapping that is required for infants to begin to realize that they can move their arms and interact with an object. This is the earliest and most explicit way of experiencing sensory integration.

Further research

In the future, research on sensory integration will be used to better understand how different sensory modalities are incorporated within the brain to help us perform even the simplest of tasks. For example, we do not currently have the understanding needed to comprehend how neural circuits transform sensory cues into changes in motor activities. More research done on the sensorimotor system can help understand how these movements are controlled. This understanding can potentially be used to learn more about how to make better prosthetics, and eventually help patients who have lost the use of a limb. Also, by learning more about how different sensory inputs can combine can have profound effects on new engineering approaches using robotics. The robot's sensory devices may take in inputs of different modalities, but if we understand multisensory integration better, we might be able to program these robots to convey these data into a useful output to better serve our purposes.

Depolarization

From Wikipedia, the free encyclopedia

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

In biology, depolarization or hypopolarization is a change within a cell, during which the cell undergoes a shift in electric charge distribution, resulting in less negative charge inside the cell compared to the outside. Depolarization is essential to the function of many cells, communication between cells, and the overall physiology of an organism.

Action potential in a neuron, showing depolarization, in which the cell's internal charge becomes less negative (more positive), and repolarization, where the internal charge returns to a more negative value.

Most cells in higher organisms maintain an internal environment that is negatively charged relative to the cell's exterior. This difference in charge is called the cell's membrane potential. In the process of depolarization, the negative internal charge of the cell temporarily becomes more positive (less negative). This shift from a negative to a more positive membrane potential occurs during several processes, including an action potential. During an action potential, the depolarization is so large that the potential difference across the cell membrane briefly reverses polarity, with the inside of the cell becoming positively charged.

The change in charge typically occurs due to an influx of sodium ions into a cell, although it can be mediated by an influx of any kind of cation or efflux of any kind of anion. The opposite of a depolarization is called a hyperpolarization.

Usage of the term "depolarization" in biology differs from its use in physics, where it refers to situations in which any form of polarity ( i.e. the presence of any electrical charge, whether positive or negative) changes to a value of zero.

Depolarization is sometimes referred to as "hypopolarization" (as opposed to hyperpolarization).

Physiology

The process of depolarization is entirely dependent upon the intrinsic electrical nature of most cells. When a cell is at rest, the cell maintains what is known as a resting potential. The resting potential generated by nearly all cells results in the interior of the cell having a negative charge compared to the exterior of the cell. To maintain this electrical imbalance, ions are transported across the cell's plasma membrane. The transport of the ions across the plasma membrane is accomplished through several different types of transmembrane proteins embedded in the cell's plasma membrane that function as pathways for ions both into and out of the cell, such as ion channels, sodium potassium pumps, and voltage-gated ion channels.

Resting potential

The resting potential must be established within a cell before the cell can be depolarized. There are many mechanisms by which a cell can establish a resting potential, however there is a typical pattern of generating this resting potential that many cells follow. The cell uses ion channels, ion pumps, and voltage-gated ion channels to generate a negative resting potential within the cell. However, the process of generating the resting potential within the cell also creates an environment outside the cell that favors depolarization. The sodium potassium pump is largely responsible for the optimization of conditions on both the interior and the exterior of the cell for depolarization. By pumping three positively charged sodium ions (Na⁺) out of the cell for every two positively charged potassium ions (K⁺) pumped into the cell, not only is the resting potential of the cell established, but an unfavorable concentration gradient is created by increasing the concentration of sodium outside the cell and increasing the concentration of potassium within the cell. Although there is an excessive amount of potassium in the cell and sodium outside the cell, the generated resting potential keeps the voltage-gated ion channels in the plasma membrane closed, preventing the ions that have been pumped across the plasma membrane from diffusing to an area of lower concentration. Additionally, despite the high concentration of positively-charged potassium ions, most cells contain internal components (of negative charge), which accumulate to establish a negative inner-charge.

Depolarization

Voltage-gated sodium channel. Open channel (top) carries an influx of Na⁺ ions, giving rise to depolarization. As the channel becomes closed/inactivated (bottom), the depolarization ends.

After a cell has established a resting potential, that cell has the capacity to undergo depolarization. During depolarization, the membrane potential rapidly shifts from negative to positive. For this rapid change to take place within the interior of the cell, several events must occur along the plasma membrane of the cell. While the sodium–potassium pump continues to work, the voltage-gated sodium and calcium channels that had been closed while the cell was at resting potential are opened in response to an initial change in voltage. As the sodium ions rush back into the cell, they add positive charge to the cell interior, and change the membrane potential from negative to positive. Once the interior of the cell becomes more positively charged, depolarization of the cell is complete, and the channels close again.

Repolarization

After a cell has been depolarized, it undergoes one final change in internal charge. Following depolarization, the voltage-gated sodium ion channels that had been open while the cell was undergoing depolarization close again. The increased positive charge within the cell now causes the potassium channels to open. Potassium ions (K⁺) begin to move down the electrochemical gradient (in favor of the concentration gradient and the newly established electrical gradient). As potassium moves out of the cell the potential within the cell decreases and approaches its resting potential once more. The sodium potassium pump works continuously throughout this process.

Hyperpolarization

The process of repolarization causes an overshoot in the potential of the cell. Potassium ions continue to move out of the axon so much so that the resting potential is exceeded and the new cell potential becomes more negative than the resting potential. The resting potential is ultimately re-established by the closing of all voltage-gated ion channels and the activity of the sodium potassium ion pump.

Neurons

Structure of a neuron

Depolarization is essential to the functions of many cells in the human body, which is exemplified by the transmission of stimuli both within a neuron and between two neurons. The reception of stimuli, neural integration of those stimuli, and the neuron's response to stimuli all rely upon the ability of neurons to utilize depolarization to transmit stimuli either within a neuron or between neurons.

Response to stimulus

Stimuli to neurons can be physical, electrical, or chemical, and can either inhibit or excite the neuron being stimulated. An inhibitory stimulus is transmitted to the dendrite of a neuron, causing hyperpolarization of the neuron. The hyperpolarization following an inhibitory stimulus causes a further decrease in voltage within the neuron below the resting potential. By hyperpolarizing a neuron, an inhibitory stimulus results in a greater negative charge that must be overcome for depolarization to occur. Excitation stimuli, on the other hand, increases the voltage in the neuron, which leads to a neuron that is easier to depolarize than the same neuron in the resting state. Regardless of it being excitatory or inhibitory, the stimulus travels down the dendrites of a neuron to the cell body for integration.

Integration of stimuli

Summation of stimuli at an axon hillock

Once the stimuli have reached the cell body, the nerve must integrate the various stimuli before the nerve can respond. The stimuli that have traveled down the dendrites converge at the axon hillock, where they are summed to determine the neuronal response. If the sum of the stimuli reaches a certain voltage, known as the threshold potential, depolarization continues from the axon hillock down the axon.

Response

The surge of depolarization traveling from the axon hillock to the axon terminal is known as an action potential. Action potentials reach the axon terminal, where the action potential triggers the release of neurotransmitters from the neuron. The neurotransmitters that are released from the axon continue on to stimulate other cells such as other neurons or muscle cells. After an action potential travels down the axon of a neuron, the resting membrane potential of the axon must be restored before another action potential can travel the axon. This is known as the recovery period of the neuron, during which the neuron cannot transmit another action potential.

Rod cells of the eye

The importance and versatility of depolarization within cells can be seen in the relationship between rod cells in the eye and their associated neurons. When rod cells are in the dark, they are depolarized. In the rod cells, this depolarization is maintained by ion channels that remain open due to the higher voltage of the rod cell in the depolarized state. The ion channels allow calcium and sodium to pass freely into the cell, maintaining the depolarized state. Rod cells in the depolarized state constantly release neurotransmitters which in turn stimulate the nerves associated with rod cells. This cycle is broken when rod cells are exposed to light; the absorption of light by the rod cell causes the channels that had facilitated the entry of sodium and calcium into the rod cell to close. When these channels close, the rod cells produce fewer neurotransmitters, which is perceived by the brain as an increase in light. Therefore, in the case of rod cells and their associated neurons, depolarization actually prevents a signal from reaching the brain as opposed to stimulating the transmission of the signal.^{[7][page needed]}

Vascular endothelium

Endothelium is a thin layer of simple squamous epithelial cells that line the interior of both blood and lymph vessels. The endothelium that lines blood vessels is known as vascular endothelium, which is subject to and must withstand the forces of blood flow and blood pressure from the cardiovascular system. To withstand these cardiovascular forces, endothelial cells must simultaneously have a structure capable of withstanding the forces of circulation while also maintaining a certain level of plasticity in the strength of their structure. This plasticity in the structural strength of the vascular endothelium is essential to overall function of the cardiovascular system. Endothelial cells within blood vessels can alter the strength of their structure to maintain the vascular tone of the blood vessel they line, prevent vascular rigidity, and even help to regulate blood pressure within the cardiovascular system. Endothelial cells accomplish these feats by using depolarization to alter their structural strength. When an endothelial cell undergoes depolarization, the result is a marked decrease in the rigidity and structural strength of the cell by altering the network of fibers that provide these cells with their structural support. Depolarization in vascular endothelium is essential not only to the structural integrity of endothelial cells, but also to the ability of the vascular endothelium to aid in the regulation of vascular tone, prevention of vascular rigidity, and the regulation of blood pressure.

Heart

Electrocardiogram

Depolarization occurs in the four chambers of the heart: both atria first, and then both ventricles.

1. The sinoatrial (SA) node on the wall of the right atrium initiates depolarization in the right and left atria, causing contraction, which corresponds to the P wave on an electrocardiogram.
2. The SA node sends the depolarization wave to the atrioventricular (AV) node which—with about a 100 ms delay to let the atria finish contracting—then causes contraction in both ventricles, seen in the QRS wave. At the same time, the atria re-polarize and relax.
3. The ventricles are re-polarized and relaxed at the T wave.

This process continues regularly, unless there is a problem in the heart.

Depolarization blockers

There are drugs, called depolarization blocking agents, that cause prolonged depolarization by opening channels responsible for depolarization and not allowing them to close, preventing repolarization. Examples include the nicotinic agonists, suxamethonium and decamethonium.

Common carotid artery

From Wikipedia, the free encyclopedia

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

 

Common carotid artery
The common carotid artery arises directly from the aorta on the left and as a branch of the brachiocephalic trunk on the right.
The common carotid artery and its main branches
Details
Precursor	aortic arch 3
Source	aortic arch, brachiocephalic artery
Branches	internal carotid artery, external carotid artery
Vein	internal jugular vein
Supplies	head and neck

In anatomy, the left and right common carotid arteries (carotids) (English: /kəˈrɒtɪd/) are arteries that supply the head and neck with oxygenated blood; they divide in the neck to form the external and internal carotid arteries.

Structure

The common carotid arteries are present on the left and right sides of the body. These arteries originate from different arteries but follow symmetrical courses. The right common carotid originates in the neck from the brachiocephalic trunk; the left from the aortic arch in the thorax. These split into the external and internal carotid arteries at the upper border of the thyroid cartilage, at around the level of the fourth cervical vertebra.

The left common carotid artery can be thought of as having two parts: a thoracic (chest) part and a cervical (neck) part. The right common carotid originates in or close to the neck and contains only a small thoracic portion. There are studies in the bioengineering literature that have looked into characterizing the geometric structure of the common carotid artery from both qualitative and mathematical (quantitative) standpoints.

The average diameters of the common carotids in adult males and females are 6.5 mm and 6.1 mm respectively.

In the chest

Only the left common carotid artery has a substantial presence in the thorax. It originates directly from the aortic arch, and travels upward through the superior mediastinum to the level of the left sternoclavicular joint.

During the thoracic part of its course, the left common carotid artery is related to the following structures: In front, it is separated from the manubrium of the sternum by the sternohyoid and sternothyroid muscles, the anterior portions of the left pleura and lung, the left brachiocephalic vein, and the remains of the thymus; behind, it lies on the trachea, esophagus, left recurrent laryngeal nerve, and thoracic duct.

To its right side below is the brachiocephalic trunk, and above, the trachea, the inferior thyroid veins, and the remains of the thymus; to its left side are the left vagus and phrenic nerves, left pleura, and lung. The left subclavian artery is posterior and slightly lateral to it.

In the neck

Arteries of the neck. The right common carotid artery – labeled Common caroti in the figure – divides into the right internal carotid artery and external carotid artery.

The cervical portions of the common carotids resemble each other so closely that one description will apply to both.

Each vessel passes obliquely upward, from behind the sternoclavicular joint to the level of the upper border of the thyroid cartilage, where it divides.

At the lower neck the two common carotid arteries are separated from each other by a very narrow interval which contains the trachea; but at the upper part, the thyroid gland, the larynx and pharynx separate the two arteries.

The common carotid artery is contained in a sheath known as the carotid sheath, which is derived from the deep cervical fascia and encloses also the internal jugular vein and vagus nerve, the vein lying lateral to the artery, and the nerve between the artery and vein, on a plane posterior to both. On opening the sheath, each of these three structures is seen to have a separate fibrous cover.

At approximately the level of the fourth cervical vertebra, the common carotid artery splits ("bifurcates" in literature) into an internal carotid artery (ICA) and an external carotid artery (ECA). While both branches travel upward, the internal carotid takes a deeper (more internal) path, eventually travelling up into the skull to supply the brain. The external carotid artery travels more closely to the surface, and sends off numerous branches that supply the neck and face.

Superficial dissection of the right side of the neck, showing the carotid and subclavian arteries

At the lower part of the neck the common carotid artery is very deeply seated, being covered by the integument, superficial fascia, the platysma muscle, deep cervical fascia, the sternocleidomastoid muscle, the sternohyoid, sternothyroid, and the omohyoid; in the upper part of its course it is more superficial, being covered merely by the integument, the superficial fascia, the platysma, deep cervical fascia, and medial margin of the sternocleidomastoid.

When the sternocleidomastoid muscle is drawn backward, the artery is seen to be contained in a triangular space known as the carotid triangle. This space is bounded behind by the sternocleidomastoid, above by the stylohyoid and the posterior belly of the digastric muscle, and below by the superior belly of the omohyoid.

This part of the artery is crossed obliquely, from its medial to its lateral side, by the sternocleidomastoid branch of the superior thyroid artery; it is also crossed by the superior and middle thyroid veins (which end in the internal jugular vein); descending in front of its sheath is the descending branch of the hypoglossal nerve, this filament being joined by one or two branches from the cervical nerves, which cross the vessel obliquely.

Sometimes the descending branch of the hypoglossal nerve is contained within the sheath.

The superior thyroid vein crosses the artery near its termination, and the middle thyroid vein a little below the level of the cricoid cartilage; the anterior jugular vein crosses the artery just above the clavicle, but is separated from it by the sternohyoid and sternothyroid.

Behind, the artery is separated from the transverse processes of the cervical vertebrae by the longus colli and longus capitis muscles, the sympathetic trunk being interposed between it and the muscles. The inferior thyroid artery crosses behind the lower part of the vessel.

Medially, it is in relation with the esophagus, trachea, and thyroid gland (which overlaps it), the inferior thyroid artery and recurrent laryngeal nerve being interposed; higher up, with the larynx and pharynx. Lateral to the artery, inside the carotid sheath with the common carotid, are the internal jugular vein and vagus nerve.

At the lower part of the neck, on the right side of the body, the right recurrent laryngeal nerve crosses obliquely behind the artery; the right internal jugular vein diverges from the artery. On the left side, however, the left internal jugular vein approaches and often overlaps the lower part of the artery.

Behind the angle of bifurcation of the common carotid artery is a reddish-brown oval body known as the carotid body. It is similar in structure to the coccygeal body which is situated on the median sacral artery.

The relations of the cervical region of the common carotid artery may be discussed in two points:

• Internal relations of organs present inside the carotid sheath
• two external relations of carotid sheath

Collateral circulation

The chief communications outside the skull take place between the superior and inferior thyroid arteries, and the deep cervical artery and the descending branch of the occipital artery; the vertebral artery takes the place of the internal carotid artery within the cranium.

Variation

Origin

The right common carotid may rise above the level of the upper border of the sternoclavicular joint; this variation occurs in about 12 percent of cases.

In other cases, the artery on the right side may arise as a separate branch from the arch of the aorta, or in conjunction with the left carotid.

The left common carotid varies in its origin more than the right.

In the majority of abnormal cases it arises with the brachiocephalic trunk; if that artery is absent, the two carotids arise usually by a single trunk.

It is rarely joined with the left subclavian artery, except in cases of transposition of the aortic arch.

Point of division

In the majority of abnormal cases, the bifurcation occurs higher than usual, the artery dividing opposite or even above the hyoid bone; more rarely, it occurs below, opposite the middle of the larynx, or the lower border of the cricoid cartilage. In at least one reported case, the artery was only 4 cm in length and divided at the root of the neck.

Very rarely, the common carotid artery ascends in the neck without any subdivision, either the external or the internal carotid being absent; and in a few cases the common carotid has itself been found to be absent, the external and internal carotids arising directly from the arch of the aorta.

This peculiarity existed on both sides in some instances, on one side in others.

Occasional branches

The common carotid usually gives off no branch previous to its bifurcation, but it occasionally gives origin to the superior thyroid artery or its laryngeal branch, the ascending pharyngeal artery, the inferior thyroid artery, or, more rarely, the vertebral artery.

Clinical significance

The common carotid artery is often used in measuring the pulse, especially in patients who are in shock and who lack a detectable pulse in the more peripheral arteries of the body. The pulse is taken by palpating the artery just deep to the anterior border of the sternocleidomastoid muscle at the level of the superior border of the thyroid cartilage.

Presence of a carotid pulse has been estimated to indicate a systolic blood pressure of more than 40 mmHg, as given by the 50% percentile.

Carotidynia is a syndrome marked by soreness of the carotid artery near the bifurcation.

Carotid stenosis may occur in patients with atherosclerosis.

The intima-media thickness of the carotid artery wall is a marker of subclinical atherosclerosis, it increases with age and with long-term exposure to particulate air pollution.