Suppose a particular simple pendulum of length l_0 has a periodof T_0 for small oscillations here on Earth.
(a) Suppose the original pendulum is set up with the same lengthl_0 on the surface of a new planet, Uzaz, and it oscillates with aperiod 5/4 as long as the period of Earth. Given the gravitationalacceleration here on Earth is 9.8 m/s^2, what is the gravitationalacceleration (g)(v) at the surface on Uzaz?
(b) If the radius of Uzaz is known to be 3.5x10^6 m, what mustbe the mass of Uzaz?
(c) Suppose Uzaz rotates once every 18.5 hours. At what altitudeabove the surface of Uzaz must a satellite orbit in order tomaintain synchronicity with a point on the surface of Uzaz?
(d) Suppose your spaceship (8x10^5 N) enters into ellipticalorbit around Uzaz. At perihelion, your ship is (9x10^6 m) fromUzaz, and aphelion it is (1.6x10^7 m) from Uzaz.
Find the following for part (d):
i. the semimajor axis of your ship's orbit.
ii. the eccentricity of your ship's orbit.
iii. the speed of your ship at perihelion and aphelion.
iv. the period of your ship's orbit.
