... By using the tools of sections (20) and (21), the mathematics of approximate solutions developed in (M-5), and assuming all orbits are circles, it is a relatively straightforward job to calculate the distance to the Lagrangian L1 point (or to L2). ... Let the gravitational constant be denoted by G , the mass of the Sun by M , that of Earth by m , the Earth's distance from the Sun by r and its velocity in its orbit by v . ... GMm / r 2 = mv 2 / r . and multiplying both sides by r / m . ...

Educator's Guide to Robotic Spacecraft . ... Spacecraft are complex, technological objects that have to function far from Earth in the harsh environment of space. ... If the students are familiar with spacecraft they can be prompted with body parts and attempt to identify the analogous spacecraft part. This will work well if the students have a high quality picture of a modern spacecraft. ... Identify a mission and a destination for a spacecraft and have teams of students design the spacecraft. ...

... With enough velocity, a spacecraft can break loose from the Earth's gravity and enter an orbit around the Sun, like that of a planet. If it then orbits the Sun with the same period as the Earth--one year--it may keep a fixed position relative to Earth. ... If the distance is just right--about 4 times the distance to the Moon or 1/100 the distance to the Sun--the spacecraft, too, will need just one year to go around the Sun, and will keep its position between the Sun and the Earth. ...

... Turn left on Calvert Street and proceed north approximately 3 1/2 miles to University Parkway. Turn left on University Parkway and proceed approximately 1/3 mile (past JHU stadium and down hill) to San Martin Drive. Turn left at the signal and proceed approximately 1/4 mile to STScI. ... Left onto Coldspring Lane and proceed approximately 1 mile to Roland Avenue (top of hill). ... Turn right at the signal and proceed approximately 1/4 mile to STScI. ...

GRANAT is the Russian x-ray sattelite launched to the high apogee orbit (200,000 km) and operated almost for 10 years (1989 -1999) , carrying out four major instruments: French SIGMA coded-mask hard x-ray telescope (30-1000 keV), Soviet ART-P coded-mask telescope (2??-60?? keV), all-sky monitor WATCH (6-150 keV), and a gamma-burst detector PHEBUS . ... Since September 1994, GRANAT is in the survey mode. ... Explore pages devoted to individual GRANAT instruments (including main scientific results): . ...

... Solar System . ... Comets and Asteroids . ... Vision of Vesta: a dark feature with a diameter of approximately 100 kim near the asteroid's equator can be seen in this image from Dawn (Image credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA) . Between Mars and Jupiter lies the Asteroid Belt. ... The Dawn space probe is expected to go into orbit around Vesta on 16 July, from there it will return some detailed images and other data, staying at the asteroid for about a year before setting off to visit Ceres. ...

. This view showcases Dione's tortured complex of bright cliffs. At lower right is the feature called Cassandra, exhibiting linear rays extending in multiple directions. The image was taken in polarized green light with the Cassini spacecraft narrow-angle camera July 24, 2006, at a distance of approximately 263,000 kilometers (163,000 miles) from Dione. NASA/JPL/Space Science Institute

... The Space Shuttle Docking Ring . ... Glowing across the electromagnetic spectrum, the center of our Milky Way Galaxy is thought to be home to massive stars, rotating gas rings, and a massive black hole. ... Dust and Gas Surrounding Star R Coronae Australis . ... Clementine's star tracker camera image reveals (from right to left) the Moon lit by Earthshine, the Sun's corona rising over the Moon's dark limb, and the planets Saturn, Mars, and Mercury. ... Cassini Spacecraft Approaches Jupiter . ...

... Average resolution at altitude H=668 km . ... Swath width at H=668 km and inclination of beginning of swath 20.48 degrees . ... Resolution at H=668 км . ... Наименование параметра . ... 1 канале . ... Полоса обзора при H=668 км . ... 1-5 спектральной зоне, не более . ... 1 спектральной зоне . 0,48-0,52 мкм . ... 0,915-0,997 мкм . ... 1-4 канал . ... 1-4 каналов . ... Спектральные характеристики каналов (по уровню 0,5): . ... For more information send a mail to: info@sputnik.infospace.ru . ...

... satvelsrc computes as a function of time the component of the spacecraft velocity vector in the direction of given celestial source. ... SAS_ODF . or named via the generic command line parameters -o or -odfdir (see taskmain for details). ... The source coordinates obtained from the ODF can be overridden with the command line paramters withsrccoord=yes srcra=<ra> srcdec=<dec> and withorthosrc=yes defines a fictitious source in the direction perpendicular to the orbital plane. ...

The azimuth encoder rack gear is mounted on the inside of the azimuth ring girder. The azimuth encoder turns on this gear as the azimuth moves 0 to 720 degrees. ... The software assumes that this arc length along the encoder rack gear is correct (at a constant radius of 127/2 feet). The error in the radius of the rack gear becomes an azimuth error. To measure the error in the azimuth encoder rack gear, jon hagen built a proximity sensor. ... To compute the az encoder runout error: . ...

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... This will be done by fitting period-luminosity relations in the form V = a в log P + b to Cepheid variables in these two galaxies. ... 8 Marks 2. ... 3R x3 2 Marks (b) Use this expression for the pressure to show that when 1 is constant, the adiabatic wave equation for the star can be written as x d d 3 R3 2 3 [(x - x4 ) ] + [ x - (31 - 4)] = 0. dx dx 1 GM 2 Marks (c) Show that near x = 0, the solution to this equation is of the form = Ax , where A is a constant and 2 = 3 (31 - 4). ...

LIGHT SCATTERING BY MULTI-LAYERED NON-CONFOCAL ELLIPSOIDS IN THE RAYLEIGH APPROXIMATION V.G. Farafonov St.Petersburg University of Aerocosmic Instrumentation St.Petersburg, 190000 Russia Abstract The Rayleigh approximation is extended to the case of light scattering by multi-layered non-confocal coaxial ellipsoidal particles. ... The particles are assumed to be in a constant electric field, and a system of Laplace equations with corresponding boundary conditions is considered. ...

... Our restless globe and its companion. ... A Look at the Motions of the Earth in Space and How They Are Changing . ... Earth's rotation as viewed from above the north and south geographic poles. ... The Earth revolves around the Sun-also counterclockwise viewed from above the North Pole, clockwise viewed from the South Pole-to give us our years (see Figure 2 ). The plane of the Earth's orbit is called the ecliptic (where eclipses happen). ... Earth's orbit as viewed from the north ecliptic pole. ...

Coordinate Systems used for spacecraft trajectory description: . ... The HGI coordinates are Sun centered and inertially fixed with respect to an X-axis directed along the intersection line of the ecliptic and solar equatorial planes. ... Cometocentric (solar) Ecliptic Coordinate System (CSE) . ... CSE coordinate system for the SC POSITION: axis origin at comet center, X-axis to the SUN, Z-axis to ecliptic north pole, (X,Y)-plane is parallel to the ecliptic plane. ...

THE STUDY OF THE PIONEER ANOMALY THE STUDY OF THE PIONEER ANOMALY The Pioneer Anomaly : Effect, New Data and New Investigation Slava G. Turyshev Jet Propulsion Laboratory, California Institute of Technology Seminar at the Sternberg Astronomical Institute Moscow State University, Moscow, 6 February 2007 1 THE STUDY OF THE PIONEER ANOMALY THE STUDY OF THE PIONEER ... Are they relevant to the Pioneer anomaly? ...

Next: The Quasi--Newton Method. Up: Outline of the Previous: The Newton--Raphson Method. ... At each iteration, one computes . ... Neglecting the second derivatives matrix , we obtain the ``normal equations'' and the Gauss--Newton direction . This so--called Gauss--Newton method is intended for problems where is small. ... The algorithm implemented here is a modification of that Gauss--Newton method, that allows convergence even for rank deficient Jacobians or for large residuals. ...

... Orienting Mir and modules . ... one on top, one on the left side) . ... Solar arrays can help to differ top from bottom - upper side is blue and flat, lower is light and ribbed. ... There are 4 long and 2 short radiators (pointed with yellow arrow on this photo ) on each module. ... So, if you see short radiators between long ones - you see module side. ... Top of each module is marked by 2 small antennas (pointed with green arrow on the photo ) in the middle of its length near ends of long...

... the radiative transfer equation (RTE) for the randomly-irregular magnetized plasma has been derived on the base of general grounds of the multiple scattering theory . ... Solutions of several absolute tasks of the scattering theory have been obtained (on the optical depth of the ionospheric plasma layer, on the value of radio wave anomalous attenuation, on anomalous refraction, on the backscattered signal intensity for the source being placed within a plasma layer). ...