Tamsen and Vera imagine visiting another planet, planet X, whose gravitational acceleration, gX, is different from that of Earth's. They envision a pendulum, whose period on Earth is 2.243 s, that is set in motion on planet X, and the period is measured to be 1.640 s. What is the ratio of gX/gEarth? Neglect any effects caused by air resistance. gX gE = If the average density of planet X is equal to Earth's average density, rhoE, what is the ratio of RX/RE, where RE is the mean radius of Earth? (Assume both planets are spherical. Recall that rho = m/V and Vsphere = 4 3 πr3.) RX RE = For the pendulum to have the same period on planet X as on Earth, would the string length need to be longer or shorter? longer shorter