To determine which moon, Phobos or Deimos, should be visited first to maximize fuel efficiency in a hypothetical space mission, we need to consider several factors.
Orbital Mechanics: The key factor in fuel efficiency is taking advantage of the gravitational assists provided by the moons. Phobos is closer to Mars and orbits at a lower altitude compared to Deimos. Therefore, Phobos offers a more significant gravitational assist due to its proximity to Mars.
Hohmann Transfer Orbits: Hohmann transfer orbits are commonly used to transfer between two circular orbits. The most efficient transfer orbit is the one that minimizes the change in velocity (delta-v). The delta-v required to transfer to Phobos from a circular equatorial orbit around Mars is generally lower than that required for Deimos.
Based on these considerations, it is more fuel-efficient to visit Phobos first before moving on to Deimos. The proposed mission plan would involve the following steps:
- Departure from the circular equatorial orbit around Mars with a Hohmann transfer to Phobos.
- Utilize the gravitational assist from Phobos to reduce the spacecraft's velocity and transfer to a low orbit around Phobos.
- Complete the mission objectives on Phobos.
- Depart from Phobos using another Hohmann transfer to transfer back to the circular equatorial orbit around Mars.
- Utilize the gravitational assist from Mars to reduce the spacecraft's velocity and transfer to a higher orbit to intersect with Deimos.
- Complete the mission objectives on Deimos.
By visiting Phobos first and utilizing its proximity and gravitational assist, the spacecraft can save fuel during the transfers and optimize fuel efficiency for the overall mission.