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7.8 Orbits and Harder Circular Motion (3.3, 3.4) F = GMm/r2 1) A satellite near the Earth’s surface makes a circular orbit in 90 minutes. The Earth is 6378 km in radius. A weather satellite completes a circular orbit every 3.5 hours. How far above the Earth’s surface is it? 2) A double star consists of two identical stars, each with a mass of 3.0 x 1030 kg. They are separated by 2.0 x 1011 m between their centres. How long do they take to complete one orbit? (p. 301) 3) A spacecraft has been put in orbit around an asteroid. The asteroid is a spherical rock of radius 15 km and density of 2600 kg/m3. Calculate the speed of the spacecraft if the orbit has a radius of 300 km. 4) Two remote planets consist of identical material, but one has a radius twice as large as the other. It the shortest possible period for a low altitude satellite orbiting the smaller planet is 40 minutes, what is it for the larger planet? (p.301) 5) Roberta Bondar is in a circular orbit above a planet with an altitude equal to the radius of the planet. She fires her rockets to put herself in a new orbit which has a speed 50% greater than before. What is the altitude of the new orbit? 6) The acceleration of gravity on Mars is 3.72 m/s2. Mars has a diameter of 6790 km and a period of 24.72 hours. How far away does a satellite have to be so that it remains stationary to an observer on Mars? 7) Two astronauts have tied their spaceships together with a spring that has an unstretched length of1500 m. It has a force constant of 6.7 N/m. The space ships each have a mass of 2500 kg and are orbiting about their centre of mass with a period of 2.5 minutes. By how much has the cable stretched? 8) A large circus carousel has seats suspended by ropes spinning in a circle. They are 6.2 m from the ground and are moving in a circle of radius 12.8 m once every 7.5 s. The rope breaks on one swing. How far does it land from the centre of the carousel? 9) An Australian bushman hunts kangaroos with a rock tied to the end of a 2-m long vine. He holds the other end 2-m above the ground and swings the rock in a horizontal circle. The vine always breaks when the angle between the vine and vertical reaches 60o. How close must the hunter get?