KEPLER'S LAW Activity 6. Problem Set Solve the following problems in a separate paper. Show your solutions systematically and clearly. 1. Phobos orbits Mars at an average distance of about 9380 km from the center of the planet and a rotational period of about 7 hr and 39 minutes. Use this information to estimate the mass of Mars. 2. Suppose a small planet is discovered that is 14 times as far from the Sun as the Earth's distance from the sun is 1.5 x 10" km. Use Kepler's law of harmonies to predict the orbital period of this small planet. 3. A simple pendulum is found to vibrate 50 times within 200s. When 1.5m of its length is reduced to a certain length, it vibrates 50 times in 175s. Find the original length of the pendulum. 4. A Christmas ball in a shape of a hollow sphere is hung from the tree by a piece of thread attached to the surface of the ball. The mass and radius of the ball are 0.105 kg and 0.12m, respectively. What will be its period of oscillation when slightly displaced from its equilibrium position? (Hint: / = 5 3 mr ) 5. Calculate the orbital period for Pluto, given that its observed average separation from the Sun is 39.44 astronomical units