Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50-kg stone thrown upward from the ground at 12.0 m/s returns to the ground in 6.00 s; the circumference of Mongo at the equator is 2.00 × 105 km; and there is no appreciable atmosphere on Mongo. The starship commander. Captain Confusion, asks for the following information: (a) What is the mass of Mongo? (b) If the Aimless Wanderer goes into a circular orbit 30,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?
Solution 58P Introduction We have to calculate the acceleration due to gravity first and then from the acceleration due to gravity we can calculate the mass of the planet. Then, knowing the mass of the planet and the radius of the circular orbit, we can calculate the time taken by the starship. Step 1 Let us first calculate the acceleration due to gravity using the time taken by the stone fall after it was thrown. When we throw some stone upwards, speed will decrease keep decreasing, and at the maximum height the speed will be zero and then it will starts falling. And come back with the same speed it was thrown. Now the time taken during going up or coming down is exactly the half of the total flight time. Now if the total time taken by the stone ist = 6.00 s. Then time taken by going up is t = 3.00 s. As we discussed above, the speed will be zero when the stone reaches at the maximum height. Hence in 3.00 s, the speed of the stone becomes zero starting from 12 m/s. Hence the acceleration due to gravity is g = 12 3 s0 m= 4 m/s2