Binary stars rotate under mutual gravitational force at separation `2(G/(omega^(2)))^(1/3)`, where `omega` is the angular velocity of each of the star about centre of mass of the system. If difference between the mass of stars is `6` units. Find the ratio of mass of bigger star to smaller star.

Binary stars of comparable masses rotates under the influence of each other's gravity at a distance [(2G)/(omega^(2))]^(1//3) where omega is the angular velocity of each of the system. If difference between the masses of two stars is 6 units. Find the ratio of the masses of smaller to bigger star.

The angular velocity of rotation of star (of mass M and radius R ) at which the matter start to escape from its equator will be

The small dense stars rotate about their common centre of mass as a binary system, each with a period of 1 year. One star has mass double than that of the other, while mass of the lighter star is one-third the mass of the Sun. The distance between the two stars is r and the distance of the earth from the Sun is R , find the relation between r and R .

The two components of Procyon have a separation of 4.55'' and period o 40.6 uears. If the distance of the binary is 11.3 light years, calculate the sum of the masses of the two stars in solar units. If the ratio of their masses is 3:1 , find the mass of each star.

Two stars bound together by gravity orbit othe because of their mutual attraction. Such a pair of stars is referred to as a binary star system. One type of binary system is that of a black hole and a companion star. The black hole is a star that has cullapsed on itself and is so missive that not even light rays can escape its gravitational pull therefore when describing the relative motion of a black hole and companion star, the motion of the black hole can be assumed negligible compared to that of the companion. The orbit of the companion star is either elliptical with the black hole at one of the foci or circular with the black hole at the centre. The gravitational potential energy is given by U=-GmM//r where G is the universal gravitational constant, m is the mass of the companion star, M is the mass of the black hole, and r is the distance between the centre of the companion star and the centre of the black hole. Since the gravitational force is conservative. The companion star and the centre of the black hole, since the gravitational force is conservative the companion star's total mechanical energy is a constant. Because of the periodic nature of of orbit there is a simple relation between the average kinetic energy ltKgt of the companion star Two special points along the orbit are single out by astronomers. Parigee isthe point at which the companion star is closest to the black hole, and apogee is the point at which is the farthest from the black hole. Q. For circular orbits the potential energy of the companion star is constant throughout the orbit. if the radius of the orbit doubles, what is the new value of the velocity of the companion star?

A rigid body of mass m rotates with angular velocity omega about an axis at a distance a from the centre of mass G. The radius of gyration about a parallel axis through G is k. The kinetic energy of rotation of the body is

A double star is a system of two starts moving around the centre of inertia of the system due to gravitation. Find the distance between the components of the double star, if its total mass equals M and the period of revolution T.

A binary star has a time period 3 yeas (time period of earth is one year) while distance between the earth and the sun. Mass of one star is equal to mass of the sun and mass of other is 20n times mass of the sun then calculate n .