A planet of mass m = 4.15 x 1024 kg is orbiting in a circular path a star of mass M = 5.05 x 1029 kg. The radius of the orbit is R = 2.95 x 10? km. What is the orbital period (in Earth days) of the planet Ppim? Express your answer to three signicant gures. In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can tr).r to knock it out of its orbit so it will y away and never return. What is the minimum amount of work W applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 993 kg and 231 km. Earth's mass and radius are 5.98 x 1024 kg and 6370 km. In order better to map the surface features of the Moon, a 379 kg imaging satellite is put into circular orbit around the Moon at an altitude of 121 km. Calculate the satellite's kinetic energy K , gravitational potential energ],r U , and total orbital energy E. The radius and mass of the Moon are 1740 km and 7.36 x III]22 kg. A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed um will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical. with an average density p = 4.36 x 105 gm3 and volume V = 1.94 x 1012 m3. Recall that the universal gravitational constant is G = 6.67 x 10-\" N-mszgz. A thin stream of water flows smoothly from a faucet and falls straight down. At one point, the water is flowing at a speed of U1 = 1.71 m/s. At a lower point, the diameter of the stream has decreased by a factor of 0.787. What is the vertical distance h between these two points? h = cmA liquid of density 1330 kg/m flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.05 m/s and the pipe diameter di is 10.9 cm. At Location 2, the pipe diameter d2 is 15.9 cm. At Location 1 Location 1, the pipe is Ay = 8.99 m higher than it is at Location 2. Ignoring viscosity, calculate the difference AP between the fluid pressure at Location 2 and the fluid pressure at Location 1. Ay Location 2 AP = Pa d,A 185 g object is attached to a spring that has a force constant of 78.5 Film. The object is pulled 9.75 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. v..- S .5 Find the locations of the object when its velocity is onethird of the maximum speed. Treat the equilibrium position as zero. Calculate the maximum speed um of the object. positions to the right as positive, and positions to the left as negative. The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leadera physicist, naturallyimmediately makes a determination of the acceleration due to gnawit},r on the Pink Planet's surface by means of a simple pendulum of length 1.33 m. She sets the pendulum swinging, and her collaborators carefully count 104 complete cycles of oscillation during 213 s. What is the result? A uniform thin rod of length 0.73? m is hung from a horizontal nail passing through a small hole in the rod located 0.027 In from tho rod's end. When the rod is set swinging about the nail at small amplitude, what is the period T of oscillation? A 169 kg sculpture hangs from a horizontal rod that serves as a pivot about which the sculpture can oscillate. The sculpture's moment of inertia with respect to the pivot is 15.2 kg-mg. When it is swung at small amplitudes, it is found to oscillate at a frequency of 0.953 Hz. The accleration due to gravity,r is g = 9.81 W52. What is the distance d from the pivot to the sculpture's center of mass