... Given the functions (sin?, cos?, sin? and cos ?), we seek formulas that express sin(?+?) and cos(?+ ... As shown in the drawing, to derive the formula we combine two right-angled triangles . ... The triangle ADF is right-angled and has the angle (?+ ... Each of them is one of the two sharp ("acute") angles in its own right-angled triangle. Since the sharp angles in such a triangle add up to 90 degrees, the other two sharp angles must be equal. ... In the right-angled triangle CED DE = DC cos ? ...

Given the functions (sin a , cos a , sin b and cos b ), we seek formulas that express sin( a+b ) and cos( a+b ). ... As shown in the drawing, to derive the formula we combine two right-angled triangles . ABC which has an angle a . ... AB = AC cos a = R cos b cos a The triangle ADF is right-angled and has the angle ( a+b ). ... Each of them is one of the two sharp ("acute") angles in its own right-angled triangle. ... In the right-angled triangle CED DE = DC cos a = R sin b cos a . ...

... ESO is building what will be the World's largest optical telescope array, The Very Large Telescope (VLT). The VLT Project organisation is responsible for the design and construction of the Unit Telescopes, including enclosures, optics, adapter-rotators and coating unit. ... Unit Telescopes Overview - This page is outdated, an update is in process. ... Secondary mirror (M2 Unit) - This page is outdated, an update is in process. ... Coating Unit - This page is outdated, an update is in process. ...

The presence of dust in starburst galaxies complicates the study of their stellar populations as the dust's effects are similar to those associated with changes in the galaxies' stellar ages and metallicities. ... We present the calibration of the flux ratio method for calculating the dust attenuation at a particular wavelength, Att(ЮЛ), based on the measurement of the F(IR)/F(ЮЛ) flux ratio. ... However, at longer wavelengths the relationship is dependent on the assumed stellar properties. ...

... To answer this question, the robot spacecraft Galileo currently in orbit around Jupiter was maneuvered to image the plume site during its recent flyby of Io in August. The Earth and Moon Planetary System . ... How similar in size are the Earth and the Moon? ... Galileo Demonstrates the Telescope . ... Knowing when and where to look, many enthusiastic sky gazers have been able to spot the International Space Station (ISS) as a bright star streaking through the twilight. ...

The following tasks belong to the category CALCULATION: . Calculations with set data'' In parentheses the name of the source file is given. ... Apply a flat field correction to a map by fitting a 2-D polynomial to the background. ( flat.c ) . ... Program to calculate flux in user defined box. ( flux.c ) . ... RESWRI derives the kinematical parameters from the observed velocity field by fitting tilted-rings to the velocity field and fits harmonic terms after convergence of the ROTCUR part of code. ...

... COMBINE/CCD FF asso_tbl . ... Combining FLAT frames: Input=asso_tbl.tbl; output=susi_140_142_143.bdf Statistics of frame no. 0: area [@60,@10:@ 1070 ,@ 1020 ] of frame minimum, maximum : 5.560000e+02 8.654000e+03 mean , standard_deviation: 6.101316e+03 1.913127e+02 Statistics of frame no. 1: area [@60,@10:@ 1070 ,@ 1020 ] of frame minimum, maximum : 8.390000e+02 1.276900e+04 mean , standard_deviation: 8.313817e+03 2.569877e+02 Statistics of ...

... Each day a different image or photograph of our fascinating universe is featured, along with a brief explanation written by a professional astronomer. 2001 October 15 . The Earth and Moon Planetary System . Credit: Northwestern University , JPL , NASA . Explanation: How similar in size are the Earth and the Moon ? ... The Moon can be seen to have a diameter over one quarter that of Earth , relatively large compared to its planetary companion . ... About APOD | ... NASA Technical Rep.: ...

This lesson shows you how to combine uncertainties and calculate with them. Reference Sheet of Uncertainty Propagation Equations . Back Main Uncertainties Page .

... Armagh Observatory, College Hill, Armagh BT61 9DG, +44 (0)28 3752 2928 . ... Aurora . ... Corona . Fireballs . ... Zodiacal Light . ... The first thing to do is get acquainted with what the night sky looks like. ... The National Schools Observatory web site has very good horizon views of the sky for the current night. ... If the object is moving slowly across the sky then it may be one of the larger satellites. ... Cloudbait Observatory - October 2002 . ... October 2003 Aurora at Armagh . ...

... The derivation of the reference multiplet is carried out in one of two basic styles: an `internal' style in which a kind of average multiplet is calculated from the values in the image themselves, without reference to any other information, or a `black body' (bb) style in which the reference multiplet is calculated using the widths of the energy bands (in the case of EPIC images) or the filter bandpasses (in the case of the OM). ...

... The cross entropy for this complex image is given by ( 16 ) and ( 17 ). ... Differentiating ( 31 ) with respect to and , we find the gradient of is given by . and upon differentiating once more we find the Hessian (curvature) matrix of has the form . ... and its Hessian matrix reads . ... From ( 16 ) and ( 17 ), we find the components of the gradient vector of the cross entropy are given by . ... Differentiating once more we find the components of the Hessian of the cross entropy to be given by . ...

This diagram shows how the 'vertical-align' properties on cells combine to determine the height of the row containing the cells. The diagram also illustrates the meaning of some values of 'vertical-align' that apply to table cells: baseline, top, bottom, and middle. The diagram shows a row of five (labeled) table cells of varying heights and alignments. ... The first cell is aligned with the row baseline and extends to just below the row top. ...

... 13, Moscow 119992, Russian Federation, e-mail: busarev@sai.msu.ru; 2 Research Institute Crimean Astrophysical Observatory, p/o Nauchnyi, Crimea 334413, Ukraine, e-mail: prok@crao.crimea.ua Summary: We propose a combined method of astronomical investigations of small or distant planets incorporating registration of a set of integral spectra of an object and their frequency analysis. ... An application of the method is shown on example of asteroid 21 Lutetia. ... 6] Busarev V. V. (2002), Solar Sys. ...

Next: Infrared Data Up: Contents Previous: Optical Photometry . ... For example, one method is to derive the spectral energy distribution (SED) for a target star and compare it to the SED of a dereddened standard star. ... Temperature can be determine via the B - V color (Gilliland 1985): . ... The results produced small extinctions to the background stars of between A and A . ... The most accurate extinction calculation requires both IR and spectral data. Infrared Data . Spectroscopic Data . ...

... Let's assume initial conditions of 1000 Zinder-noodle plants scattered over these 1000 acres. ... We now introduce a new parameter: The blade-muncher. ... One blade-muncher eats 1 zinder-noodle every 10 days. ... Again, go back to the initial conditions but now we introduce the Zardhogs. ... Following Sunshine Moonbeam's edict, describe the evolution of the system if we start with 1000 zindernoodles on 1000 acres, an initial population of 10 blade-munchers and 2 Zardhogs. ...

... The SDSS 2.5-m primary mirror is supported in a manner similar to the Apache Point Observatory 3.5-m telescope primary. ... The axial support is provided by 48 air pistons. The pistons have the same diameter thereby applying equal forces with the same air pressure. ... Each group supports a 120њ sector of the mirror. ... Figure 1: CAD drawing showing the 2.5-m primary mirror and the locations of actuators (green circles) These actuators apply forces (10*cos2 N) to correct astigmatism. ...

... Great oppositions. ... Proxima Centauri. ... Scientists proved that the problem of preserving the Earth's climate and the annual change of seasons can be solved by a small star, negligible mass, but similar to a main-sequence star, moving in a circular orbit around the Sun. ... Sombrero Galaxy. The Sombrero Galaxy, M104, is known as a holder of one of supermassive black holes. ... Roughly estimate the approximate mass of the supermassive black hole in the center of M104 (answer in solar masses m). ...

... Phil Creed's Astronomy Bowl! ... Hidden Hollow's Astronomy Bowl is a fast-paced question-and-answer game designed to both enlighten and challenge stargazers. ... Astronomy Bowl follows the traditional format of alternating toss-up and bonus questions, with a few tweaks. ... The host will read a toss-up question. ... Once a toss-up is correctly answered, that team is given a bonus question. ... If only 14 toss-ups are answered correctly, that means 20 toss-ups and 14 bonus questions will be read. ...

Find Similar Abstracts . ... Determination of the component masses and inclination of a binary system containing a pulsar from relativistic effects . ... BINARY STARS, ORBITAL ELEMENTS, PULSARS, RELATIVISTIC EFFECTS, STELLAR MASS, APSIDES, DOPPLER EFFECT, FREQUENCY SHIFT, INCLINATION . ... Use: Authors Title Abstract Text Text Query with Keywords Return: Query Results Query Form Database: Astronomy Instrumentation Physics and Geophysics ABSTRACT QUERY USER FEEDBACK HELP ...