Chapter 8, Problem 8.46P

Two planets X and Y travel counterclockwise in circular orbits about a star as shown in Figure P11.14. The radii of their orbits are in the ratio 3:1. At one moment, they are aligned as shown in Figure P11.14a, making a straight line with the star. During the next five years, the angular displacement of planet X is 90.0 as shown in Figure P11.14b. What is the angular displacement of planet Y at this moment?

Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed the neutron star can have so that the matter at its surface on the equator is just held in orbit by the gravitational force.

A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?

Neutron stars are extremely dense objects formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force.

Using the solution from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of out Sun. Where does this increase in kinetic energy come from?

A black hole of mass mB = 1.0*1032 kg and a star of mass mS = 2.0*1030 kg rotate about their common center of mass with a period of 23 years. The distance from the center of the black hole to the center of the star is 4.5*1012 m. Gravity is slowly pulling the black hole and the star closer and closer. What will be the period of rotation around their center of mass once the distance between them has been reduced to 6.6*1010 m?

A star in the Andromeda galaxy is found to have a planet orbiting it at an average radius of 3.38x10^10 m and an orbital period of 5.46x10^4 s. a.) what is the star's mass b.) a second planet is found orbiting the same star with an orbital period of 6.19x10^6 s. What is its orbital radius?

In a certain binary-star system, each star has the same mass as our Sun, and they revolve about their center of mass. The distance between them is the same as the distance between Earth and the Sun.What is their period of revolution in years?

Two stars M1 and M2 of equal mass make up a binary star system. They move in a circular orbit that has its center at the midpoint of the line that separates them. If M1 = M2 = 6.95 sm (solar mass), and the orbital period of each star is 2.45 days, find their orbital speed. (The mass of the sun is 1.99 1030 kg.)