1. The problem statement, all variables and given/known data A meteorite is approaching earth at very high speed. In order to avoid an impact on earth, the world space agency has launched two space missions: one mission sends the astronaut Albert to the meteorite approaching earth. The other mission, lead by the space commander Trebla, sets off to another meteorite of similar mass to deviate it from its original course and make it collide with the first one so that they end up in an orbit around earth rather than crashing into it. The first meteorite is elongated with roughly cylindrical shape. Its length is 150 m and its rest mass is ~0.50 Mt (1 * 10^9 kg). Its velocity relative to earth (at the time when the collision is expected) is 0.60c in the direction along its long axis. The second meteorite is roughly spherical with a diameter of 50 m. Its rest mass is 0.41 Mt and due to the alteration of its course it will have a velocity of 0.65 c relative to earth and flying in the exact opposite direction than the first meteorite. Albert’s job is to apply specifically developed foam to the expected collision area. It has a very low density and its mass is negligible compared to the meteorite’s mass, but it will absorb the shock so that we end up with a perfectly inelastic collision. This means: after the collision we have one compound object and no material escapes. c) What is the rest mass and velocity of this compound meteorite? 2. Relevant equations [itex]E = \gamma mc^2 [/itex] [itex]E^2 = p^2 c^2 + m^2 c^4[/itex] Conservation of Energy Conservation of Momentum 3. The attempt at a solution I've tried using conservation of energy from the Earth's frame because that's the relation of the velocities we are given. Thus [itex] E_1 + E_2 = E_f [/itex] , where [itex]E_f[/itex] is the energy of the compound object after the collision. However, because the momentum is nonzero after the collision (by conservation of momentum) we know that the the compound object is still moving after the collision in the Earth's frame. By that logic the final energy must be expressed as [itex]E_f = \gamma Mc^2 [/itex], where there is still a gamma present because the compound object is moving relative to the Earth. My classmates have disagreed and said that you can solve it through [itex] E_1 + E_2 = Mc^2 [/itex] where M is the compound mass. I'm confused because wouldn't that require the compound object to be in the Earth's frame if you are using the velocities of the meteors relative to the Earth's frame? I thought you would have to use the CM frame, at least.