If possible, please include your explaination. Tater and Tot II A group of human
ID: 1503539 • Letter: I
Question
If possible, please include your explaination.
Tater and Tot II
A group of human star voyagers has created habitats by tunneling into asteroids. They have used rocket engines of immense power to gradually move the asteroid habitats into interstellar space and start them on their thousand-year journeys to distant suns. One such group of star voyagers have tunneled into a pair of spherical asteroids which they have whimsically named Tater and Tot. The larger asteroid, Tater, has a mass of 2.20×10^21 kg and a radius of 480.0 km . The smaller asteroid, Tot, has a mass of 2.445×10^20 kg and a radius of 231.0 km . Usually, the asteroid-dwellers travel in a low-energy configuration in which Tater and Tot are orbiting about their common center of mass as they speed through interstellar space. On certain occasions, however, they travel in parallel trajectories on either side of their center of mass. To draw this alternate configuration, use an xy coordinate system with positive y as the direction of travel. Locate the center of Tater at the origin, and locate the center of Tot on the positive x axis at a distance of 7700.0 km from the center of Tater. This configuration is energetically expensive because the rockets of Tater and Tot must fire continuously in order to counteract the mutual gravitational attraction of the two asteroids. If the rocket engines were to fail while Tater and Tot were traveling in their parallel-trajectory configuration, the two asteroids would eventually collide due to their mutual gravitational attraction. Every student living within Tater and Tot is, at some time in his or her academic career, asked to calculate the speeds with which the two would collide should this disaster ever occur. You are now asked to do this same calculation. Work in the center-of-mass frame of reference, i.e. even though Tater and Tot are traveling through interstellar space at high speed, work in the frame of reference in which the center of mass of Tater and Tot is at rest.
Accelerations of Tater and Tot
Part A
Suppose that Tater and Tot are 7700.0 km apart when the rocket engines fail on both asteroids. What is the acceleration of Tot when the two asteroids are 7700.0 km apart, and what is the acceleration of Tot just before the asteroids collide? Give magnitudes only. Give your answers as an ordered pair, with the initial acceleration first, followed by a comma, followed by the final acceleration (i.e. just before the collision). Give the magnitude of acceleration only.
Answer: aTot initial, aTot final = ?,? m/s2, m/s2
Part B
What is the acceleration of Tater when the two asteroids are 7700.0 km apart, and what is the acceleration of Tater just before the asteroids collide? Give magnitudes only. Give your answers as an ordered pair, with the initial acceleration first, followed by a comma, followed by the final acceleration (i.e. just before the collision). Give the magnitude of acceleration only. Answer: aTater initial, aTater final = ?,? m/s2, m/s2
Explanation / Answer
Part A) Initial acceleration of Tot = GM/r2
= (6.67 * 10-11 * 2.20×1021)/(7700 * 1000)2
= 2.475 * 10-3 m/sec2
Final acceleration of Tot = (6.67 * 10-11 * 2.20×1021)/(711000)2
= 0.29 m/sec2
Part B) Initial acceleration of Tater = Gm/r2
= (6.67 * 10-11 * 2.445×1020)/(7700 * 1000)2
= 2.75 * 10-4 m/sec2
Final acceleration of Tater = (6.67 * 10-11 * 2.445×1020)/(711000)2
= 0.0322 m/sec2
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