Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) (a) What should the orbital period of that star be? _________yr (b) If its period is 6.0x107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. _________ Solar Masses

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.