Question
Please show steps, thank you. I will post the whole questionthis time and break it into multiple questions for more lifesaverpoints. A 10,000kg satellite moves under the influnece of mass M (aplanet). For its first traejectory, its kinetic energy is negative1.5 times its potential energy. It then switches to a trajectorywhere its potential energy is negative 2 times its kineticenergy. Describe each trajectory. Prove your answer. For the first path, g = 4N/kg when the satellite is 1,000,000meters from the planet. Find the satellite's speedwhen the planet is 10,000,000 meters away from the satellite, themass of the planet, and the totalenergy of the path. For the second path, find the total energyand the speed of M when the masses areseparated by 20,000,000m. Find the work in moving from path 1 to path 2, theperiod(s) for the path(s) if theyexist. Please show steps, thank you. I will post the whole questionthis time and break it into multiple questions for more lifesaverpoints. A 10,000kg satellite moves under the influnece of mass M (aplanet). For its first traejectory, its kinetic energy is negative1.5 times its potential energy. It then switches to a trajectorywhere its potential energy is negative 2 times its kineticenergy. Describe each trajectory. Prove your answer. For the first path, g = 4N/kg when the satellite is 1,000,000meters from the planet. Find the satellite's speedwhen the planet is 10,000,000 meters away from the satellite, themass of the planet, and the totalenergy of the path. For the second path, find the total energyand the speed of M when the masses areseparated by 20,000,000m. Find the work in moving from path 1 to path 2, theperiod(s) for the path(s) if theyexist. For the first path, g = 4N/kg when the satellite is 1,000,000meters from the planet. Find the satellite's speedwhen the planet is 10,000,000 meters away from the satellite, themass of the planet, and the totalenergy of the path. For the second path, find the total energyand the speed of M when the masses areseparated by 20,000,000m. Find the work in moving from path 1 to path 2, theperiod(s) for the path(s) if theyexist.
Explanation / Answer
1.the satellite's speed v = (GM/r)^(1/2) G = 6.67 * 10^-11 Nm^2/kg^2,M = mass of planet and r = 10^7m the acceleration due to gravity on planet a = (GM/r^2)^(1/2) or M = (a * r^2/G) -------------(1) the total energy E = K + U ----------------(2) K = -1.5U U = -(GMm/r) m = 10,000 kg 2.the total energy E = K + U --------------(3) U = -2K or K = -(U/2) speed of satellite v = (GM/r)^(1/2) M is obtained from (1) and r = 2 * 10^7 m the work in moving from path 1 to path 2 is obtained bysubtracting equation (2) from (3) the periods for the first and second paths are T = (2 * r^(3/2)/(GM)^(1/2)) s for first path r = 10^7 m for second path r = 2 * 10^7 m