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Ameer Said

Numerade educator

A planet with a mass of 6.2 x 1024 kg has a radius of 7.28 x 106 meters. It rotates once every 24.8 hours. There is a satellite with a mass of 2.5 x 104 kg going around the planet at a distance of d = 6.8 x 108 meters from the center of the planet. a) What is the acceleration due to gravity at the surface of this planet? Is this more or less than the Earth’s? How much would a 80 kg person weigh at the surface of this planet? b) How much would the same person weigh inside the planet at a distance of 3.00 x 106 meters? c) What is the escape velocity from this planet if this person wants to fly off to infinity? d) How much work would have to be done for this person to fly off to infinity? e) What is the planet’s period of rotation that would cause this person to fly off the surface? f) What is the height above the surface of this planet where this person can achieve geosynchronous orbit around the planet? g) What is the period of the satellites orbit around the planet in hours? Is it faster or slower than the planet’s rotation? h) If the satellite starts with an initial speed of zero from that height, what will be its speed when it crashes with the planet?

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INSTANT ANSWER

The sun is located at (0, 0) and the earth at (1 AU, 0). 1 AU = 1.5 x 1011 m. Msun = 2 x 1030 kg, Mearth = 5.98 x 1024 kg. Mvenus = 4.87 x 1024 kg. a) Where can a satellite be so that it experiences no gravitational force? b) Where can a satellite be placed on the line adjoining the sun and the earth, so that it experiences the same gravitational force from the earth as from the sun? c) What is the total gravitational force on Venus when it is at (.6, y) AUs from the sun. [solve for the y component by using the equation of a circle x2 + y2 = .722 , since Venus’ orbit is very circular]

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