... 34a. L1 Lagrangian pt. #34b. L2 pt. ... The following derivation of the L4 and L5 points follows "When Trojans and Greeks Collide" by I. Vorobyov, "Quantum," p. 16-19, Sept-Oct. ... Suppose we have 3 point-like masses (m 1 , m 2 , m 3 ) orbiting under their mutual attraction. The three form a triangle ABC with sides masses (R 1 , R 2 , R 3 ) where R 1 is the side across from m 1 , R 2 is across from m 2 and R 3 is across from m 3 (Figure 1). ... If we denoted the total mass by M . ...

... A vector , that's what. ... Graphically, each stretch on the ground or velocity can be represented by an arrow in its direction, its length giving the magnitude--for instance, an arrow AB 200 mm (milimeters) long for the airplane's motion and another one BC 40 mm long, in the same direction, for the wind. ... Just as one can combine two vectors into one--their sum--so it is also possible to move in the opposite direction--given a single vector, find two vectors whose sum it is. ...

Proceedings of the Particle Physics and Early Universe Conference (PPEUC). For this paper: postscript PPEUC CMB index 1 Introduction.. ... Combining measurements of the thermal Sunyaev--Zel'dovich effect with X-ray data allows calculation of a direct, physical estimate of Hubble's Constant ( ) without the need for distance-ladder-type arguments. ... 1 Introduction . ... 3 Calculating Hubble's Constant . 4 Errors In Determination of . ... PPEUC Proceedings . Fri Jun 27 15:29:33 BST 1997 ...

... The expansion is measured as a number called the Hubble Constant . ... Our value is about 20% lower than the one got with the Hubble Space Telescope in 1994," said Dr Jim Lovell, leader of the team that made the measurement. The Hubble Constant is named after American astronomer Edwin Hubble, who in the 1920s found that other galaxies were moving away from ours. ... The Hubble Constant links the galaxy's distance with its speed." ... A short run-down on the Hubble Constant: . ...

Next: Initial conditions Up: Old neutron star distribution Previous: Introduction . The problem to be solved is to find stationary space distribution of stars which have had certain initial space and velocity distributions and move in a given potential. ... In principle, the most straightforward way to obtain the solution is to integrate directly the equations of motion for a sufficiently large number of stars with different initial conditions. ... Then space density is given by . ...

The image on the left shows the 7 horns with the X axis along the azimuth arm. ... The beams on the sky are elliptical with the major axis along the azimuth arm. ... If we rotate the feed array by + phi degrees then the projection of each horn center on the X axis is: Px1= S*sin(phi) Px2=S*cos(phi+30) Px3=S*cos(phi-30) . The separation between the projected horn centers are: Distance(Px1-Px0)=S*sin(phi) Distance(Px2-Px1)=S*(cos(30+phi)-sin(phi)=S*(cos(30)cos(phi)-sin(30)sin(phi)-sin(phi)) . ...

... The flux from a fully extended continuum source as transmitted by the science slit, over an arbitrary number of pixels in the spatial direction (Npix s ) and taken over an arbitrary number of pixels in the wavelength direction (Npix ) 1 , is given by: . ... over a Npix ? m by Npix s ? ... d / m converts between diffuse continuum source surface brightness and diffuse emission line surface brightness and is given in the CONT2EML header keyword; it is simply the slit width expressed in Angstroms. ...

... 2.3 Establishing the Extragalactic Distance Scale . ... 2.3.2 The Second Rung: Distances to stellar clusters . ... 2.3.4 Distances to Local Group Galaxies . ... The Luminosity Function of Planetary Nebulae . ... 3.2.2 Clusters of Galaxies . ... 4.2 Evidence for Dark Matter as a Function of Scale Size . ... 4.3 Other Dark Matter Indicators for Galaxies . ... What is the nature of the large-scale distribution of matter in the universe as traced by the three-dimensional galaxy distribution? ...

. XMM-Newton Science Analysis System . eposcorr (eposcorr-3.9.2) [xmmsas_20050815_1803-6.5.0] . Meta Index / Home Page / Description eposcorr calculates angular distances directly using spherical trigonimetry. In particular the following is used to calculate the angular distance, , between two sources (labeled 1 and 2). (9) . where refers to the declination of a source and , the difference of the right ascension of the two sources. XMM-Newton SOC/SSC -- 2005-08-15

Angular Momentum A vector.. Clickers Channel D Wednesday, 30 March 2011 Analogy - between forces and torques. ... Wednesday, 30 March 2011 Angular Momentum · Angular momentum: written L · Definition L = MV r V r Axis M Use perpendicular distance, just like for torque Wednesday, 30 March 2011 Which ball has the most angular momentum? ... Wednesday, 30 March 2011 Why? ... Wednesday, 30 March 2011 And vector angular momentum · · Points in the same direction as the angular velocity. ...

Villains and Heroes of Lights and Lighting Fixtures . If we are to reduce the effects of light pollution, we must learn about the types, both good and bad, of fixtures used in outdoor lighting. ... In fact, this type of fixture is often chosen for this very reason. ... Although these lamps are not very energy efficient, and they are often found in older, inefficient fixtures that enhance light pollution, they still exist in great abundance in most locations and are still sold by the millions. ...