The star Alpha Centauri is 4.37 light-years from earth. The Voyager 2 spacecraft that was launched...

 

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The star Alpha Centauri is 4.37 light-years from earth. The Voyager 2 spacecraft that was launched in 1977 is traveling 3.3 AU/year. (1 AU is the mean distance from the earth to the center of the sun = 1.486 x 108 km). How long will it take, in years, for Voyager 2 to travel the equivalent distance as that to Alpha Centauri? From Special Relativity the mass of an object, m, traveling at the speed, v, can be related to its "rest mass," mo, by the relationship: m = mo -() Where c = speed of light in a vacuum = 2.998 x 108 m/s. The kinetic energy, KE, of the object can be written as: KE = mc - mc Determine the trip time (years) it would take to travel to Alpha Centauri and the kinetic energy per unit rest energy (KE/m,c) for each of the following cases: Voyager 2 spacecraft, and a spacecraft traveling at the speeds; 0.1c [10% of the speed of light], 0.5c, 0.8c, 0.9c, 0.99c. Calculate the kinetic energy needed to achieve each of these velocities for each of the following masses: electron (9.109 x 10-3 kg), proton (1.673 x 10-27 kg), 1 kg, a 68 kg person, and a 500 kg spacecraft. Note, a spreadsheet program will make this problem less painful. The star Alpha Centauri is 4.37 light-years from earth. The Voyager 2 spacecraft that was launched in 1977 is traveling 3.3 AU/year. (1 AU is the mean distance from the earth to the center of the sun = 1.486 x 108 km). How long will it take, in years, for Voyager 2 to travel the equivalent distance as that to Alpha Centauri? From Special Relativity the mass of an object, m, traveling at the speed, v, can be related to its "rest mass," mo, by the relationship: m = mo -() Where c = speed of light in a vacuum = 2.998 x 108 m/s. The kinetic energy, KE, of the object can be written as: KE = mc - mc Determine the trip time (years) it would take to travel to Alpha Centauri and the kinetic energy per unit rest energy (KE/m,c) for each of the following cases: Voyager 2 spacecraft, and a spacecraft traveling at the speeds; 0.1c [10% of the speed of light], 0.5c, 0.8c, 0.9c, 0.99c. Calculate the kinetic energy needed to achieve each of these velocities for each of the following masses: electron (9.109 x 10-3 kg), proton (1.673 x 10-27 kg), 1 kg, a 68 kg person, and a 500 kg spacecraft. Note, a spreadsheet program will make this problem less painful.

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