Celestial Movements/Mechanics Flashcards
Lidov-Kozai mechanism:
refers to the orbit of a satellite that is perturbed by another body orbiting farther out. Due to the perturbation, the orbit of the satellite experiences libration (oscillation about a constant value) of its argument of pericenter. As the orbit librates, there is a periodic exchange between its inclination and its eccentricity.
Jacobi’s integral:
the only known conserved quantity for the circular restricted three-body problem problem; unlike in the two-body problem, the energy and momentum of the system are not conserved separately and a general analytical solution is not possible. The integral has been used to derive numerous solutions in special cases.
Tisserand’s Criterion
is used to determine whether or not an observed orbiting body, such as a comet or an asteroid, is the same as a previously observed orbiting body.
While all the orbital parameters of an object orbiting the Sun during the close encounter with another massive body (e.g. Jupiter) can be changed dramatically, the value of a function of these parameters, called Tisserand’s relation (due to Félix Tisserand) is approximately conserved, making possible to recognise the orbit after the encounter.
beta angle
a measurement that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft in low Earth orbit (LEO) spends in direct sunlight, absorbing solar energy.
Kepler orbit (Keplerian orbit)
describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. (A Kepler orbit can also form a straight line.) It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on. It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parametrized into six orbital elements in various ways.
Orbital inclination change
an orbital maneuver aimed at changing the inclination of an orbiting body’s orbit. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector (delta v) at the orbital nodes (i.e. the point where the initial and desired orbits intersect, the line of orbital nodes is defined by the intersection of the two orbital planes).
In general, inclination changes can take a very large amount of delta v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This is typically achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize any inclination change required over the duration of the spacecraft life. Planetary flybys are the most efficient way to achieve large inclination changes, but they are only effective for interplanetary missions.
Axial tilt
known to astronomers as obliquity, is the angle between an object’s rotational axis, and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. It differs from orbital inclination.
Orbital inclination
the angle between a reference plane and another plane or axis of direction.
Azimuth
an angular measurement in a spherical coordinate system. The vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane; the angle between the projected vector and a reference vector on the reference plane is called the azimuth.
An example of an azimuth is the measurement of the position of a star in the sky. The star is the point of interest, the reference plane is the horizon or the surface of the sea, and the reference vector points to the north. The azimuth is the angle between the north vector and the perpendicular projection of the star down onto the horizon.
Laplace’s invariable plane of a planetary system
the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector. In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four jovian planets (Jupiter, Saturn, Uranus, and Neptune). The invariable plane is within 0.5° of the orbital plane of Jupiter, and may be regarded as the weighted average of all planetary orbital and rotational planes.
The ecliptic
the apparent path of the Sun on the celestial sphere, and is the basis for the ecliptic coordinate system. It also refers to the plane of this path, which is coplanar with both the orbit of the Earth around the Sun and the apparent orbit of the Sun around the Earth. The path of the Sun is not normally noticeable from the Earth’s surface because the Earth rotates, carrying the observer through the cycle of sunrise and sunset, obscuring the apparent motion of the Sun with respect to the stars.
Protoplanetary disk
a rotating circumstellar disk of dense gas surrounding a young newly formed star, a T Tauri star, or Herbig Ae/Be star. The protoplanetary disk may be considered an accretion disc because gaseous material may be falling from the inner edge of the disk onto the surface of the star, but this process should not be confused with the accretion process thought to build up the planets themselves. Externally illuminated photo-evaporating protoplanetary disks are called proplyds.
Protostars:
typically form from molecular clouds consisting primarily of molecular hydrogen. When a portion of a molecular cloud reaches a critical size, mass, or density, it begins to collapse under its own gravity. As this collapsing cloud, called a solar nebula, becomes denser, random gas motions originally present in the cloud average out in favor of the direction of the nebula’s net angular momentum. Conservation of angular momentum causes the rotation to increase as the nebula radius decreases. This rotation causes the cloud to flatten out—much like forming a flat pizza out of dough—and take the form of a disk. The initial collapse takes about 100,000 years. After that time the star reaches a surface temperature similar to that of a main sequence star of the same mass and becomes visible. It is now a T Tauri star. Accretion of gas onto the star continues for another 10 million years, before the disk disappears, perhaps being blown away by the young star’s solar wind, or perhaps simply ceasing to emit radiation after accretion has ended. The oldest protoplanetary disk ever discovered is 25 million years old.
Accretion disc (often a circumstellar disk)
formed by diffuse material in orbital motion around a central body. The central body is typically a star. Gravity causes material in the disc to spiral inward towards the central body. Gravitational forces compress the material causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object. Accretion discs of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of accretion discs is called diskoseismology.
Laplace plane:
a mean or reference plane about whose axis the instantaneous orbital plane of a satellite precesses.
Laplace’s name is sometimes applied to the invariable plane, which is the plane perpendicular to a system’s mean angular momentum vector, but the two should not be confused. They are equivalent only in the case where all perturbers and resonances are far from the precessing body.
Astronomical precession
refers to any of several gravity-induced, slow and continuous changes in an astronomical body’s rotational axis or orbital path. Precession of the equinoxes, perihelion precession, changes in the tilt of the Earth’s axis to its orbit, and the eccentricity of its orbit over tens of thousands of years are all important parts of the astronomical theory of ice ages.
Axial precession is the movement of the rotational axis of an astronomical body, whereby the axis slowly traces out a cone.
Nutation
a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism. If it is not caused by forces external to the body, it is called free nutation or Euler nutation.
Protostar
a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years. It starts with a core of increased density in a molecular cloud and ends with the formation of a T Tauri star, which then develops into a main sequence star. This is heralded by the T Tauri wind, a type of super solar wind that marks the change from the star accreting mass into radiating energy.
Interstellar medium (ISM)
the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space. The energy that occupies the same volume, in the form of electromagnetic radiation, is the interstellar radiation field.
The interstellar medium is composed of multiple phases, distinguished by whether matter is ionic, atomic, or molecular, and the temperature and density of the matter. The thermal pressures of these phases are in rough equilibrium with one another. Magnetic fields and turbulent motions also provide pressure in the ISM, and are typically more important dynamically than the thermal pressure is.
Molecular cloud:
sometimes called a stellar nursery if star formation is occurring within, is a type of interstellar cloud whose density and size permits the formation of molecules, most commonly molecular hydrogen (H2). This is in contrast to other areas of the interstellar medium that contain predominately ionized gas.
Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is CO (carbon monoxide). The ratio between CO luminosity and H2 mass is thought to be constant, although there are reasons to doubt this assumption in observations of some other galaxies.
Within our own galaxy, molecular gas clouds accounts for less than one percent of the volume of the interstellar medium (ISM), yet it is also the densest part of the medium comprising roughly one-half of the total gas mass interior to the Sun’s galactic orbit. The bulk of the molecular gas is contained in a ring between 3.5 and 7.5 kiloparsecs (11,000 and 24,000 ly) from the center of the galaxy (the Sun is about 8.5 kpc from the center). Large scale carbon monoxide maps of the galaxy show that the position of this gas correlates with the spiral arms of the galaxy. That molecular gas occurs predominantly in the spiral arms argues that molecular clouds must form and dissociate on a timescale shorter than 10 million years—the time it takes for material to pass through the arm region.
