A pion has a rest energy of 135 MeV. It decays into two gamma-ray photons, bursts of electromagnetic radiation that travel at the speed of light. A pion moving through the laboratory at v = 0.98c decays into two gamma-ray photons of equal energies, making equal angles θ with the original direction of motion. Find the angle θ and the energies of the two gamma ray photons.

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.