Astrolabe 1

Αστρολάβος , المقنطرة ou اسطرلاب

Un astrolabe se compose d'un disque gradué en degrés (rapporteur) avec un bras tournant attaché à son centre, l'alidade. La marque 0° sur le cercle est alignée avec l'horizon. L'alidade pivote sur son axe et est pointée vers le soleil ou une étoile afin de lire l'angle représentant la hauteur du soleil ou d'une étoile majeure connue par rapport à l'horizon, sur les repères du disque. L'astrolabe se tient verticalement à la main par un anneau ; les astres sont visés en tournant le viseur jusqu'à ce que l'un d'eux soit vu par les deux bouts. La valeur en degrés obtenue par le viseur sur l'arc peut être convertie en degrés de latitude du point d'observation. Si une étoile, ou tout autre corps céleste, est visé à l'extrémité du bras mobile, la position de l'étoile peut être lue (« prise ») sur le cercle gradué. L'étymologie grecque du nom provient de cette action : astro = étoile, labe = prendre.
Cette fonction est la seule réalisée par les « astrolabes nautiques », utilisés pour la navigation maritime, et qui ne présentent pas la partie centrale.

Le centre de l'astrolabe est un abaque permettant de déterminer l'heure à partir de la hauteur de l'astre, et de là, sa direction.
Sur le plateau (mater) sont gravées des lignes qui représentent la projection stéréographique de la sphère céleste, uniquement valides pour une latitude géographique donnée.
Sur cette grille de coordonnées tourne le rete, qui est un cadre avec des points représentant les étoiles fixes.
Quand le rete tourne en fonction du temps local, la position des étoiles qu'il matérialise se déplace sur le plateau mater, où peuvent être lues les hauteurs et les directions. Réciproquement, l'instrument peut être ajusté à la position mesurée, le temps pouvant alors être lu sur l'échelle.
La hauteur de l'astre visée étant connue, on fait tourner le rete jusqu'à ce que le repère du rete correspondant à l'astre coïncide avec la graduation de la hauteur sur la mater. Dans cette position, l'astrolabe est réglé à l'heure locale, et la direction de l'axe peut être lue sur l'autre famille de graduation de la mater. Pour une lecture correcte, il faut savoir si l'astre visé est ascendant (à l'orient) ou descendant (à l'occident), ce qui ne pose guère de problème à l'observateur entraîné.

Gravitation 7

High-precision test of general relativity by the Cassini space probe (artist's impression): radio signals sent between the Earth and the probe (green wave) are delayed by the warping of space and time (blue lines) due to the Sun's mass.

Einstein modified his original field equations to include a cosmological term proportional to the metric

The constant Λ is called the cosmological constant. Since Λ is constant, the energy conservation law is unaffected.
The cosmological constant term was originally introduced by Einstein to allow for a static universe (i.e., one that is not expanding or contracting). This effort was unsuccessful for two reasons: the static universe described by this theory was unstable, and observations of distant galaxies by Hubble a decade later confirmed that our universe is, in fact, not static but expanding. So Λ was abandoned, with Einstein calling it the "biggest blunder [he] ever made".[3] For many years the cosmological constant was almost universally considered to be 0.
Despite Einstein's misguided motivation for introducing the cosmological constant term, there is nothing inconsistent with the presence of such a term in the equations. Indeed, recent improved astronomical techniques have found that a positive value of Λ is needed to explain some observations.
Einstein thought of the cosmological constant as an independent parameter, but its term in the field equation can also be moved algebraically to the other side, written as part of the stress-energy tensor:

The constant

is called the vacuum energy. The existence of a cosmological constant is equivalent to the existence of a non-zero vacuum energy. The terms are now used interchangeably in general relativity.

Gravitation 6

Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star

Precession of apsides

In general relativity, the apsides of any orbit (the point of the orbiting body's closest approach to the system's center of mass) will precess—the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a test particle. For him, the fact that his theory gave a straightforward explanation of the anomalous perihelion shift of the planet Mercury, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.
The effect can also be derived by using either the exact Schwarzschild metric (describing spacetime around a spherical mass) or the much more general post-Newtonian formalism. It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body's gravity (encoded in the nonlinearity of Einstein's equations). Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus and the Earth), as well as in binary pulsar systems, where it is larger by five orders of magnitude.

A representation of the geodetic effect.

Geodetic precession and frame-dragging

Several relativistic effects are directly related to the relativity of direction. One is geodetic precession: the axis direction of a gyroscope in free fall in curved spacetime will change when compared, for instance, with the direction of light received from distant stars—even though such a gyroscope represents the way of keeping a direction as stable as possible ("parallel transport"). For the Moon-Earth-system, this effect has been measured with the help of lunar laser ranging. More recently, it has been measured for test masses aboard the satellite Gravity Probe B to a precision of better than 1 percent.
Near a rotating mass, there are so-called gravitomagnetic or frame-dragging effects. A distant observer will determine that objects close to the mass get "dragged around". This is most extreme for rotating black holes where, for any object entering a zone known as the ergosphere, rotation is inevitable. Such effects can again be tested through their influence on the orientation of gyroscopes in free fall. Somewhat controversial tests have been performed using the LAGEOS satellites, confirming the relativistic prediction. A precision measurement is the main aim of the Gravity Probe B mission, with the results expected in September 2008.

Gravitation 5

Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray)

General relativity predicts that the path of light is bent in a gravitational field; light passing a massive body is deflected towards that body. This effect has been confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun.

This and related predictions follow from the fact that light follows what is called a light-like or null geodesic—a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity. As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion), several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light, the angle of deflection resulting from such calculations is only half the value given by general relativity.
Closely related to light deflection is the gravitational time delay (or Shapiro effect), the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction. In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on the geometry of space.

Gravitation 4

Schematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body

Assuming that the equivalence principle holds, gravity influences the passage of time. Light sent down into a gravity well is blueshifted, whereas light sent in the opposite direction (i.e., climbing out of the gravity well) is redshifted; collectively, these two effects are known as the gravitational frequency shift. More generally, processes close to a massive body run more slowly when compared with processes taking place further away; this effect is known as gravitational time dilation.
Gravitational redshift has been measured in the laboratory and using astronomical observations. Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks, while ongoing validation is provided as a side-effect of the operation of the Global Positioning System (GPS). Tests in stronger gravitational fields are provided by the observation of binary pulsars. All results are in agreement with general relativity. However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.