Aspacecraft positions itself at the point directly between the earth and moon where the net force on it due to the earth and moon together (a) how far is the spacecraft from the earth? (numeric answer.) (b) if the spacecraft were moved slightly away from the point where the net force on it is zero would it undergo simple hamonic motion? explain briefly (c) if the moon were to orbit the earth at the distance you found in part (a), find its period around the earth. express your answer as a number times the actual period of the moon (d) if the earth's radius were to expand to the distance you found in part (a) but the earth's mass were to remain the same, find the acceleration due to gravity on the surface of this earth express your answer as a number times g (the acceleration due to gravity on the surface of the real earth. (e) in part (d), how far from the center of the expanded earth and inside it would the acceleration due to gravity be equal to g (the acceleration due to gravity on the surface of the real earth)? assume uniform density. express your answer as a number times the radius of the real earth is zero. 9.80 m/s 7.35x102 kg 5.98x1024 kg |g (grav. accel, earth's surface) earth-to-moon distance 3.84x10 m 6.67x10nm2/kg 6.02x1023 atoms/mole g (univ. const. of grav.) na (avagadro's number) mass of the moon mass of the earth radius of the earth 6380 km