The most energy-efficient way to send a spacecraft to the moon is to boost its speed while it is in circular orbit about the earth such that its new orbit is an ellipse. the boost point is the perigee of the ellipse, and the point of arrival at the moon is the apogee. calculate the percentage increase in speed required to achieve such an orbit. assume that the spacecraft is initially in a low-flying circular orbit about earth. the distance between earth and the moon is approximately 60 re, where re is the radius of earth

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?