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# HW_9 - P112 Spring 2008 Homework#9 Reading 8.4-8.6 Not all...

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P112 Spring 2008 Homework #9 Reading: 8.4-8.6 Not all concepts will be covered in class – you are responsible for all material in the reading and in the homework problems. Problems: 1. A single-stage rocket is accelerated from rest from a deep-space platform, where gravity is negligible. If the rocket burns its fuel in a time of 0.5 s, and the relative speed of the exhaust gas is 2100 m/s, what must the mass ration m 0 /m be for a final speed of 8.0 km/s? 2. More than 200 "extrasolar planets" have been discovered orbiting stars other than our own Sun. These discoveries were made using Doppler Shift spectroscopy to measure small motions of these stars due to the gravitational influence of their planets. It's possible that a planet like our own Jupiter could be detected in a distant solar system by this method. Let's calculate how fast our Sun moves relative to the center-of-mass (CM) of our Solar System due to the influence of Jupiter and what the size of the Sun's orbit about the CM is. (a) Jupiter's mass is 1.9 × 10 27 kg, and the radius of its orbit is 7.8 × 10 11 m. Our Sun's mass is 2.0 × 10 30 kg. Since Jupiter contains the majority of the mass of the planets in our Solar System, the location of the Solar System's CM is determined mainly by Jupiter and the Sun. How far from the center of the Sun is the CM of Jupiter + the Sun? Does it lie inside or outside the Sun (Sun's radius = 7.0 × 10 8 m)?

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HW_9 - P112 Spring 2008 Homework#9 Reading 8.4-8.6 Not all...

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