A possible trajectory for sending a spacecraft to Mars is an elliptical orbit with Earth at its perihelion and Mars at its aphelion. The craft would be launched out of low-Earth orbit by a quick burst of rockets into solar orbit, and would then "coast'' until rockets fire again to match its speed to that of Mars and lower it into an orbit about the planet. Neglecting the acceleration and deceleration phases, how long would it take to get from low-Earth orbit to Mars along this "minimal-energy'' trajectory?

Express your answer in years.

To calculate the time it would take to travel from low-Earth orbit to Mars along this "minimal-energy" trajectory, we need to consider the duration of each segment of the journey.

Segment 1: Launch from low-Earth orbit to solar orbit -
This segment involves a quick burst of rockets to propel the spacecraft out of low-Earth orbit and into a solar orbit. The time for this segment can vary depending on the specific propulsion systems used and the desired trajectory. However, typical estimates for this segment range from a few minutes to a few hours.

Segment 2: Coast in solar orbit -
After reaching solar orbit, the spacecraft would "coast" without any significant propulsion until it reaches the vicinity of Mars. The duration of this segment depends on the specific trajectory and the relative positions of Earth and Mars. It can take anywhere from a few months to more than a year.

Segment 3: Match speed with Mars and enter Martian orbit -
Once the spacecraft reaches the vicinity of Mars, rockets would fire again to match its speed to that of Mars and lower it into a Mars orbit. The duration of this segment also depends on the specific trajectory and the desired orbit. It generally takes several minutes to hours to execute this maneuver.

Neglecting the acceleration and deceleration phases, we need to sum up the durations of Segment 1, Segment 2, and Segment 3 to find the total travel time.

Since the question does not provide specific values for these durations, we cannot calculate the exact travel time. However, we can estimate a rough duration based on typical values:

- Segment 1: Let's assume a conservative estimate of 1 hour.
- Segment 2: Assuming a typical duration of 9 months.
- Segment 3: Let's assume a conservative estimate of 1 hour.

Total travel time = Segment 1 + Segment 2 + Segment 3
= 1 hour + 9 months + 1 hour

Converting 9 months to years (assuming 1 year = 12 months):
Total travel time = 1 hour + (9/12) years + 1 hour
= (1 + 9/12 + 1) hours

Hence, the approximate travel time from low-Earth orbit to Mars along this "minimal-energy'' trajectory would be (1 + 9/12 + 1) hours.