8. Centripetal Forces & Gravitation

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?

Suppose a satellite is in a circular orbit not far above Earth’s surface, and circles the Earth about once every 92 minutes. Find the centripetal acceleration of the satellite in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth’s surface.