1. Earth's orbital velocity is about 29 km/s and that maintains its nearly circular orbit. Suppose we had a spacecraft following Earth in its orbit, and we applied a rocket to slow it to 25 km/s.  Assume the thrust is entirely in the plane of the orbit, so the spacecraft stays in the same plane as Earth's orbit.  What happens? a. The spacecraft goes into a new orbit that is an ellipse with an aphelion (farthest from Sun) at Earth's orbit. b. The spacecraft goes into a new orbit that is an ellipse with perihelion (nearest to Sun) at Earth's orbit. c. It stays in the same orbit with the Earth but takes longer to complete its new nearly circular orbit. d. It falls into the sun and is then flung out of the solar system altogether by the energy it picks up on this path.

1. Earth's orbital velocity is about 29 km/s and that maintains its nearly circular orbit. Suppose we had a spacecraft following Earth in its orbit, and we applied a rocket to slow it to 25 km/s.  Assume the thrust is entirely in the plane of the orbit, so the spacecraft stays in the same plane as Earth's orbit.  What happens?

a. The spacecraft goes into a new orbit that is an ellipse with an aphelion (farthest from Sun) at Earth's orbit.

b. The spacecraft goes into a new orbit that is an ellipse with perihelion (nearest to Sun) at Earth's orbit.

c. It stays in the same orbit with the Earth but takes longer to complete its new nearly circular orbit.

d. It falls into the sun and is then flung out of the solar system altogether by the energy it picks up on this path.

2. The semimajor axis of Mars orbit is about 1.52 astronomical units (au), where an au is the  Earth's average distance from the Sun, meaning the semimajor axis of Earth's orbit is 1 au.  To go from Earth to Mars and use the least energy from rocket fuel, the orbit has a semimajor axis of 1.26 au and an eccentricity of about 0.21.  Starting at Earth's orbit, to follow this path we give the spacecraft an orbital velocity of 40 km/s.  Which of the following describes this best?

a. It arrives at Mars orbit at the same moment that Mars is there, and must speed up to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit.

b. It arrives at Mars orbit at the same moment that Mars is there, and must slow down to go into an orbit next to Mars or else drop back into perihelion (closest to the Sun) at Earth's orbit.

c. It flys past Mars on its trajectory unless it is braked by accelerating toward the Sun. It which leaves Earth when Mars is nearly closest to Earth and traverses the smallest distance possible, nearly straight out along the Sun-Earth-Mars line.

d. It arrives at Mars with exactly the same velocity as Mars has in its orbit, so the two are naturally in lock step and only a little adjustment is necessary to go into orbit around Mars.