1. A spacecraft is sent from the Earth to Jupiter by sending it on a eccentric orbit to the Sun and then boosting the engines at its perihelium to get a new orbit whose aphelium is Jupiter as shown in the figure (not to scale). Calculate the minimum distance rp of the Sun (that is the perihelium) that the spacecraft must have if the velocity boost at this point it 10% of the original velocity (v1= 1.1ve, where vj is the velocity at the perihelium of the orbit from the Earth and vj is the velocity at the perihelium of the orbit to Jupiter). Consider that rp + RJ ~ RJ, and use Rj = aj + Ejaj and Re = de +EQE, where R, is the distance from the Sun to Jupiter, aj is the semimajor axis of Jupiter's orbit, ej is the eccentricity of Jupiter's orbit, Re is the distance from the Sun to Earth, ag is the semimajor axis of Earth's orbit, and eg is the eccentricity of Earths's orbit. Here we assume that the initial and final positions are stationary and correspond with the position of the Earth and Jupiter in the moment of departure and arrival of the spacecraft respectively. = Spacecraft trajectories Jupiter Earth 1. A spacecraft is sent from the Earth to Jupiter by sending it on a eccentric orbit to the Sun and then boosting the engines at its perihelium to get a new orbit whose aphelium is Jupiter as shown in the figure (not to scale). Calculate the minimum distance rp of the Sun (that is the perihelium) that the spacecraft must have if the velocity boost at this point it 10% of the original velocity (v1= 1.1ve, where vj is the velocity at the perihelium of the orbit from the Earth and vj is the velocity at the perihelium of the orbit to Jupiter). Consider that rp + RJ ~ RJ, and use Rj = aj + Ejaj and Re = de +EQE, where R, is the distance from the Sun to Jupiter, aj is the semimajor axis of Jupiter's orbit, ej is the eccentricity of Jupiter's orbit, Re is the distance from the Sun to Earth, ag is the semimajor axis of Earth's orbit, and eg is the eccentricity of Earths's orbit. Here we assume that the initial and final positions are stationary and correspond with the position of the Earth and Jupiter in the moment of departure and arrival of the spacecraft respectively. = Spacecraft trajectories Jupiter Earth