Question

Planet A with mass Ma = 1.90 times 10^27 kg and radius R.t = 71.5 times10^6 m is located at the origin of a coordinate system. A rocket with mass m_r = 2.02 times 10^6 kg is shot up from the surface of planet A along the y axis with initial velocity v = 30.00 km/s What is the maximum height h the rocket reaches above the surface of planet A? What is the acceleration vector a (vector notation) of the rocket when the rocket is at the maximum height? Planet B with mass M_B = 5.68 times 10^26 kg is brought into position rightarrow r_B = 7.00 times10^8 km j and planet C with mass M_C = 1.02 times 10^26 kg is brought into position rightarrow r_C = 3.75 times 10^8 km i. Draw the approximate configuration of the three masses on the figure. What is the net force vector rightarrow F_A on rightarrow M_A due to M_B and M_C (vector notation)? How much work would an external source need to do to move planet B to infinity?

Answer 1

Use the law of conservation of the energy, the total energy at the surface of the Earth is equal to the total energy at the maximum height г--GMm R, +h 2 (6.67x 10-1 N-m/kg) (1.90x10 kg)1 2 (30.00x 10% m/s)--GM R, +h + 71.5x106 m -GM:-1.3224 x1Ợ J (6.67x10-1H N m'/kg) (1.90x10 kg) 1.3224 x109 J 9.58x10 m h-9.58x10 m-71.5x106 m 24.3x106 m The acceleration at the maximum height is, GM (R4 +h) (6.67x10-11 N-m'/kg2) (1.90x10 kg) 71.5x106 m +24.3x106 m --(1.3x10' m/s')j