The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 10⁶ m/s . Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s . Our solar system was formed roughly 5 billion years ago. How many orbits has it completed?

Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton’s third law, the forces that push the outer layers away have reaction forces that are inwardly directed on the core of the star. These forces compress the core and can cause the core to undergo a gravitational collapse. The gravitational forces keep pulling all the matter together tighter and tighter, crushing atoms out of existence. Under these extreme conditions, a proton and an electron can be squeezed together to form a neutron. If the collapse is halted when the neutrons all come into contact with each other, the result is an object called a neutron star, an entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a period of ≈ 1 s and, as they do so, send out a pulse of electromagnetic waves once a second. These stars were discovered in the 1960s and are called pulsars. How many revolutions per minute are made by a satellite orbiting 1.0 km above the surface?

FIGURE P13.57 shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter. Find an exact expression for the orbital period T. Hint: Each planet feels two forces.

Three stars, each with the mass of our sun, form an equilateral triangle with sides 1.0 x 10¹² m long. (This triangle would just about fit within the orbit of Jupiter.) The triangle has to rotate, because otherwise the stars would crash together in the center. What is the period of rotation?

Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton's third law, the forces that push the outer layers away have reaction forces that are inwardly directed on the core of the star. These forces compress the core and can cause the core to undergo a gravitational collapse. The gravitational forces keep pulling all the matter together tighter and tighter, crushing atoms out of existence. Under these extreme conditions, a proton and an electron can be squeezed together to form a neutron. If the collapse is halted when the neutrons all come into contact with each other, the result is an object called a neutron star, an entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a period of ≈ 1 s and, as they do so, send out a pulse of electromagnetic waves once a second. These stars were discovered in the 1960s and are called pulsars. What is the radius of a geosynchronous orbit?

The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 10⁸ m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s. The gravitational force on the solar system is the net force due to all the matter inside our orbit. Most of that matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, like a giant star. What is the approximate mass of the galactic center?

The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 10⁸ m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s. Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?